https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Biological Sciences sorted by most replies. https://community.wolfram.com/groups/-/m/t/1872608 *Short URL to share this post*: https://wolfr.am/coronavirus ***JOIN*** *our* ***Medical Sciences*** *group for the latest updates & best networking*: https://wolfr.am/MedicalSciences ---------- This post is intended to be the hub for Wolfram resources related to novel coronavirus disease COVID-19 that originated in Wuhan, China. The larger aim is to provide a forum for disseminating ways in which Wolfram technologies and coding can be utilized to shed light on the virus and pandemic. Possibilities include using the Wolfram Language for data-mining, modeling, analysis, visualizations, and so forth. Among other things, we encourage comments and feedback on these resources. Please note that this is intended for technical analysis and discussion supported by computation. Aspects outside this scope and better suited for different forums should be avoided. Thank you for your contribution! ## ________________________________________ ## FEATURED CONTENT - [COVID-19 Livestream Notebook March 24][8] by Stephen Wolfram - [Agent-Based Networks Models for COVID-19][9] by Christopher Wolfram - [Live-Stream: Exploring Pandemic Data][10] by Stephen & Christopher Wolfram + guests - [Live-Stream: Exploring and Explaining Epidemic Modeling][11] by Stephen & Christopher Wolfram + guests ## ________________________________________ ## [CALL for Making COVID-19 Data Computable (*link*)][12] More pandemic-related information and data sets emerging every day. We invite people in the community to contribute to making more data surrounding this topic computable. Here is a call to action with some recommendations for people who want to do more, whether it's just pointing out relevant data sources, or taking the time to make some of that data computable and more instantly ready for other people to explore: https://wolfr.am/COVID-19-DATA . ## ________________________________________ ## [Curated Computable Data (*link*)][13] [FOLLOW THIS LINK][14] to see all available COVID-19 data repositories ready for computation in the Wolfram Language . [Changes in Updates to SARS-CoV-2 Sequences in the Wolfram Data Repository][16] We have published and are continuously updating the Wolfram Data Repository entries. Below are a few key ones. Follow the link above to browse all repositories. We encourage you to make [*your own contributions*][15] of curated data relevant to COVID-19. > **Pandemic Data for Novel Coronavirus COVID-19** > https://www.wolframcloud.com/obj/resourcesystem/published/DataRepository/resources/Epidemic-Data-for-Novel-Coronavirus-COVID-19 > **Genetic Sequences for the SARS-CoV-2 Coronavirus** > https://datarepository.wolframcloud.com/resources/Genetic-Sequences-for-the-SARS-CoV-2-Coronavirus > **Patient Medical Data for Novel Coronavirus COVID-19** > https://datarepository.wolframcloud.com/resources/Patient-Medical-Data-for-Novel-Coronavirus-COVID-19 > **COVID-19 Hospital Resource Use Projections** > https://datarepository.wolframcloud.com/resources/COVID-19-Hospital-Resource-Use-Projections > **OECD Data: Hospital Beds Per Country** > https://datarepository.wolframcloud.com/resources/OECD-Data-Hospital-Beds-Per-Country > **Hospital Beds Per US State** > https://datarepository.wolframcloud.com/resources/Hospital-Beds-Per-US-State ## ________________________________________ ## [Computational Publications (*link*)][17] We encourage you to share your computational explorations relevant to coronavirus on Wolfram Community as stand-alone articles and then comment with their URL links on this discussion thread. We will summarize these articles in the following list: ### ________________________________ ###FEATURED > **COVID-19 Livestream Notebook March 24** by Stephen Wolfram > https://www.wolframcloud.com/obj/s.wolfram/Published/COVID-19-Livestream-March-24.nb > **Agent-Based Networks Models for COVID-19** by Christopher Wolfram > https://community.wolfram.com/groups/-/m/t/1907703 > **Epidemiological Models for Influenza and COVID-19** by Robert Nachbar > https://community.wolfram.com/groups/-/m/t/1896178 > **Epidemic simulation with a polygon container** by Francisco Rodríguez > https://community.wolfram.com/groups/-/m/t/1901002 > **Distance to nearest confirmed US COVID-19 case** by Chip Hurst > https://community.wolfram.com/groups/-/m/t/1911583 ### ________________________________ ### EPIDEMIC MODELING: SIMULATION > **Epidemic simulation with a polygon container** by Francisco Rodríguez > https://community.wolfram.com/groups/-/m/t/1901002 > **Agent based epidemic simulation** by Jon McLoone > https://community.wolfram.com/groups/-/m/t/1900481 > **Modeling the spatial spread of infection diseases in the US** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1889072 > **Geo-spatial-temporal COVID-19 simulations and visualizations over USA** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1900514 > **Life, Liberty, and Lockdowns: cellular automaton approach** by Philip Maymin > https://community.wolfram.com/groups/-/m/t/2181433 ### ________________________________ ### EPIDEMIC MODELING: COMPARTMENTAL > **Teaching notebook on disease models** by Gareth Russell > https://community.wolfram.com/groups/-/m/t/2694698 > **Stochastic Epidemiology Models with Applications to the COVID-19** by Robert Nachbar > https://community.wolfram.com/groups/-/m/t/1980051 > **COVID19: Italian SIRD estimates and prediction** by Christos Papahristodoulou > https://community.wolfram.com/groups/-/m/t/1984320 > **Solver for COVID-19 epidemic model with the Caputo fractional derivatives** by Alexander Trounev > https://community.wolfram.com/groups/-/m/t/1976589 > **EpiPlay: using Mathematica to gamify education in epidemiology** by Rui Alves > https://community.wolfram.com/groups/-/m/t/2535927 > **Epidemiological Model for repetitive rapid testing for COVID-19** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/2075883 > **Phase transition of a SIR agent-based models** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1977230 > **A simple estimate of covid-19 fatalities based on past data** by Kay Herbert > https://community.wolfram.com/groups/-/m/t/1959438 > **SIR Model with Log-normal infected periods** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1946292 > **SEI2HR-Econ model with quarantine and supplies scenarios** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1937880 > **COVID-19 - Policy Simulator - Can you find the perfect policy?** by Jan Brugard > https://community.wolfram.com/groups/-/m/t/1931352 > **Epidemiological Models for Influenza and COVID-19** by Robert Nachbar > https://community.wolfram.com/groups/-/m/t/1896178 > **Exploring Epidemiological Modeling** by Jordan Hasler > https://community.wolfram.com/groups/-/m/t/1920119 > **SEI2HR model with quarantine scenarios** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1926505 > **The SIR Model for Spread of Disease** by Arnoud Buzing > https://community.wolfram.com/groups/-/m/t/1903289 > **COVID-19 - R0 and Herd Immunity - are we getting closer?** by Jan Brugard > https://community.wolfram.com/groups/-/m/t/1911422 > **Basic experiments workflow for simple epidemiological models** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1895675 > **Scaling of epidemiology models with multi-site compartments** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1897377 > **WirVsVirus 2020 hackathon participation** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1907256 > **An SEIR like model that fits the coronavirus infection data** by Enrique Garcia Moreno > https://community.wolfram.com/groups/-/m/t/1888335 > **A SEIRD Model For COVID-19 Using DDEs** by Luis Borgonovo > https://community.wolfram.com/groups/-/m/t/1996374 > **A Neat Package for Compartmental Model Diagrams** by Hamza Alsamraee > https://community.wolfram.com/groups/-/m/t/2078640 > **Redesign of didactics of S(E)IR(D) -> SI(EY)A(CD) models of epidemics** by Thomas Colignatus > https://community.wolfram.com/groups/-/m/t/2004784 > **COVID-19 SIR models: transmission, vaccination, herd immunity dynamics revealed** by Athanasios Paraskevopoulos > https://community.wolfram.com/groups/-/m/t/3008488 ### ________________________________ ### EPIDEMIC MODELING: LOGISTIC > **COVID-19 pandemic data in Italy** by Riccardo Fantoni > https://community.wolfram.com/groups/-/m/t/1909687 > **Predicting Coronavirus Epidemic in United States** by Robert Rimmer >https://community.wolfram.com/groups/-/m/t/1906954 > **Tracking Coronavirus Testing in the United States** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1902302 > **Logistic Model for Quarantine Controlled Epidemics** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1900530 > **Updated: coronavirus logistic growth model: China** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1890271 > **Coronavirus logistic growth model: China** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1887435 > **Coronavirus logistic growth model: Italy and South Korea** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1887823 > **Coronavirus logistic growth model: South Korea** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1894561 > **Logistic growth model for epidemic Covid-19 in Colombia** by Diego Ramos > https://community.wolfram.com/groups/-/m/t/2092786 ### ________________________________ ### GENOMICS > **Analyzing the spread of SARS-CoV-2 variants in California** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/2205357 > **Analyzing the spread of SARS-CoV-2 variants in Florida** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/2206874 > **Analyzing Nextstrain Data with WFR Newick Functions (COVID-19/SARS-CoV-2)** by John Cassel > https://community.wolfram.com/groups/-/m/t/1958952 > **Finding and analyzing a COVID subvariant in Australia** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/2342489 > **Analyzing SARS-CoV-2 Genetic Sequences** by John Cassel & Daniel Lichtblau > https://blog.wolfram.com/2021/08/19/newick-trees-proximity-resources-and-accessions-analyzing-sars-cov-2-genetic-sequences/ > **Estimating the number of times the SARS CoV-2 virus has replicated** by Carlos Munoz > https://community.wolfram.com/groups/-/m/t/1943243 >**From sequenced SARS-CoV-2 genomes to a phylogenetic tree** by Daniel Lichtblau >https://community.wolfram.com/groups/-/m/t/1961461 > **Genome analysis and the SARS-nCoV-2** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/1874816 > **Visualizing Sequence Alignments from the COVID-19** by Jessica Shi > https://community.wolfram.com/groups/-/m/t/1875352 > **A walk-through of the SARS-CoV-2 nucleotide Wolfram resource** by John Cassel > https://community.wolfram.com/groups/-/m/t/1887456 > **Geometrical analysis of genome for COVID-19 vs SARS-like viruses** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1878824 > **Chaos Game For Clustering of Novel Coronavirus COVID-19** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1875994 ### ________________________________ ### DATA ANALYSIS > **Optimal Annual COVID-19 Vaccine Boosting Dates Following Previous Booster Vaccination or Breakthrough Infection** by Jeffrey Townsend > https://community.wolfram.com/groups/-/m/t/3341399 > **Probability of early infection extinction depends linearly on the virus clearance rate** by Nóra Juhász > https://community.wolfram.com/groups/-/m/t/3307502 > **Detecting Global Community Structure in a COVID-19 Activity Correlation Network** by Hiroki Sayama > https://community.wolfram.com/groups/-/m/t/3056172 > **Analyzing trends of COVID-19 through public news feeds** by Silvia Hao > https://community.wolfram.com/groups/-/m/t/2569395 > **Deep neural network detection & clinical staging of COVID-19 chest X-rays** by Peter Riley > https://community.wolfram.com/groups/-/m/t/2389110 > **COVID-19 - The Swedish Experiment - Is it working?** by Jan Brugard > https://community.wolfram.com/groups/-/m/t/1974412 > **A simple COVID-19 spread model** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/1945196 > **COVID19: The performance of the Swedish strategy** by Christos Papahristodoulou > https://community.wolfram.com/groups/-/m/t/1990972 > **Exploring social trends on Covid-19 pandemic using WikipediaData** by Jofre Espigule-Pons > https://community.wolfram.com/groups/-/m/t/1931508 > **Google Mobility Data** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1946686 > **Understanding Aggregate COVID Curves** by Christopher Wolfram > https://community.wolfram.com/groups/-/m/t/2068457 > **Apple mobility trends data visualization** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1942813 > **Computing COVID-19 Spread Rates in US Cities** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/1930261 > **COVID-19 data and the Newcomb Benford Distribution** by Gustavo Delfino > https://community.wolfram.com/groups/-/m/t/1913908 > **Short-time trends for COVID-19**, by Fabian Wenger > https://community.wolfram.com/groups/-/m/t/1912710 > **What countries are hit hard by COVID19 outbreak?** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1904507 > **COVID19 in Iran: under-diagnosis issue** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1891140 > **Coronavirus analysis: descriptive statistics with SQL functions** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2206078 > **Covid-19 vaccine campaigns efficacy analysis** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2383314 > **Argentina: COVID-19 Data Analysis** by Tobias Canavesi > https://community.wolfram.com/groups/-/m/t/1932910 > **Analysis of the Change in Phillips Curve After COVID-19 with Regression** by Seojin Yoon > https://community.wolfram.com/groups/-/m/t/2055704 > **COVID wave alert: statistical analysis and visualization** by Antonio Neves > https://community.wolfram.com/groups/-/m/t/2115658 > **Predicting COVID-19 using cough sounds classification** by Siria Sadeddin > https://community.wolfram.com/groups/-/m/t/2166833 > **Covid-19 vaccination data analysis using SQL functions** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2324474 > **Analyzing COVID-19 vaccine sentiment over time** by Arshaan Sayed > https://community.wolfram.com/groups/-/m/t/2317293 > **VAERS data analysis using SQL functions** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2351726 > **Correlating COVID-19 government measures to biweekly/daily outbreaks** by Arshaan Sayed > https://community.wolfram.com/groups/-/m/t/2362327 > **Plotting Covid19 sentiment in different regions of Chennai** by Aditya Sairam Prakash > https://community.wolfram.com/groups/-/m/t/2388236 ### ________________________________ ### DATA VISUALIZATIONS > **CDC COVID19 vaccination data across US counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2282418 > **Top 20 COVID countries HeatMap by absolute death and death in ppm** by Rodrigo Murta > https://community.wolfram.com/groups/-/m/t/2004800 > **COVIDWORLD app: current data and visualizations for SARS-CoV2 pandemic** by Rui Alves > https://community.wolfram.com/groups/-/m/t/2473065 > **US Counties COVID-19 confirmed cases by population density timelines** by Bob Sandheinrich > https://community.wolfram.com/groups/-/m/t/1992898 > **3D Modeling of the SARS-CoV-2 Virus in the Wolfram Language** by Jeff Bryant > https://community.wolfram.com/groups/-/m/t/1989540 > **California COVID19 Data** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2132204 > **COVID-19 progress in Peru macro regions: coast vs mountain vs jungle** by Francisco Rodríguez > https://community.wolfram.com/groups/-/m/t/1965079 > **COVID-19 reopening criterion: a simple visualization** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1962615 > **100 Days of COVID19 Over US Counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1956368 > **Population Density Map** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1955760 > **Google Mobility Data** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1946686 > **COVID19 Case-Fatality Ratio, Income, and Age: Simple Visualization** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1939045 > **Data Analysis of Coronavirus in Mexico** by Ivan Martinez > https://community.wolfram.com/groups/-/m/t/1927657 > **Confirmed COVID-19 Cases in Catalonia** by Bernat Espigulé Pons > https://community.wolfram.com/groups/-/m/t/1919468 > **Distance to nearest confirmed US COVID-19 case** by Chip Hurst > https://community.wolfram.com/groups/-/m/t/1911583 > **COVID19 Confirmed Cases: US Counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1950980 > **COVID19 data visualization across US counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2119049 > **Maps for Visualizing Covid-19's Effect** by Eric Mockensturm > https://community.wolfram.com/groups/-/m/t/1934457 > **US Counties COVID-19 deaths plot** by Bob Sandheinrich > https://community.wolfram.com/groups/-/m/t/1918332 > **Comparing the spread of COVID-19 between countries**, Jan Brugard > https://community.wolfram.com/groups/-/m/t/1905992 > **NY Times COVID-19 data visualization** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1911668 > **COVID-19 cases for each administrative division in Spain** by Bernat Espigulé Pons > https://community.wolfram.com/groups/-/m/t/1910116 > **Propagation risk of COVID-19 by local contact in Spain (10 - 14 March)** by Bernat Espigulé Pons > https://community.wolfram.com/groups/-/m/t/1898126 > **Visualizing the Pandemic Data COVID-19** by Martijn Froeling > https://community.wolfram.com/groups/-/m/t/1899870 > **COVID-19 visualization of turning point** by Isao Maruyama > https://community.wolfram.com/groups/-/m/t/1899911 > **Mapping "Live" COVID Data on a Globe** by Gabriel Lemieux > https://community.wolfram.com/groups/-/m/t/1902102 > **Novel Coronavirus COVID-19 in Brazil** by Estevao Teixeira > https://community.wolfram.com/groups/-/m/t/1905950 > **Mapping Novel Coronavirus COVID-19 Outbreak** by Jofre Espigule-Pons > https://community.wolfram.com/groups/-/m/t/1868945 > **Ways to visualize COVID-19 simulation results?** by Kyle Keane > https://community.wolfram.com/groups/-/m/t/1962739 > **General and COVID-19 deaths in Sweden** by Oscar Rodriguez > https://community.wolfram.com/groups/-/m/t/2006377 > **COVID19 Tokyo per days of the week** Isao Maruyama > https://community.wolfram.com/groups/-/m/t/2133807 ### ________________________________ ### DATA PROCESSING > **Cov-Tell: Daily COVID-19 Updates with Alexa (made with Wolfram APIFunction)** by Jessica Shi > https://community.wolfram.com/groups/-/m/t/1958307 > **Build a COVID-19 Chest X-Ray Image Uploader with Cloud & Data Drop** by Jofre Espigule-Pons > https://community.wolfram.com/groups/-/m/t/1919770 > **Scraping OpenTable's "State of the Industry" page** by Aaron Enright > https://community.wolfram.com/groups/-/m/t/1911043 > **City-level Search Tool for Coronavirus (COVID-19) Confirmed Cases** by David Lomiashvili > https://community.wolfram.com/groups/-/m/t/1913247 > **Web Scraper: New York Times Coronavirus Data** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1894426 > **TraCOV: Personalized COVID-19 Risk Analysis Tool** by Jessica Shi > https://community.wolfram.com/groups/-/m/t/1977700 > **Mobility changes data: transforming to Wolfram Language dataset** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2160386 ### ________________________________ ### MASKS > **Effect of mandatory mask usage in COVID cases** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1919060 > **Face mask detection: classifying image data** by Siria Sadeddin > https://community.wolfram.com/groups/-/m/t/2139499 ## ________________________________________ ## [Livestream Archives (*link*)][18] - Stephen & Christopher Wolfram + guests [Exploring Pandemic Data][19] - Stephen & Christopher Wolfram + guests [Exploring and Explaining Epidemic Modeling][20] - Robert Nachbar - [Epidemiological Models for Influenza and COVID-19][21] - Brian Wood - [COVID-19 Dashboard Visualizations][22] - John Cassel - [Behind the Genetic Sequences for Novel Coronavirus SARS-CoV-2][23] - Keiko Hirayama - [Patient Data Exploration for the Novel Coronavirus COVID-19][24] - Keiko Hirayama - [Pandemic Data Exploration for the Novel Coronavirus COVID-19][25] - Diego Zviovich - [Geo-spatial-temporal COVID-19 Simulations and Visualizations Over USA][26] - Anton Antonov - [COVID19 Epidemic Modeling: Compartmental Models][27] - Anton Antonov - [Scaling of Epidemiology Models with Multi-site Compartments][28] - Anton Antonov - [Simple Economic Extension of Compartmental Epidemiological Models][29] - Juan Klopper - [Coronavirus medical data analysis][30] - Juan Klopper - [Coronavrirus epidemiological data analysis][31] - Rory Foulger - [Coronavirus Data Exploration - Wolfram Livecoding with Students][32] ## ________________________________________ ## Other useful resources - Arnoud Buzing [GitHub][33] repository and [Notebook Gallery][34] for coronavirus - [Modeling a Pandemic like Ebola with the Wolfram Language](https://blog.wolfram.com/2014/11/04/modeling-a-pandemic-like-ebola-with-the-wolfram-language) - [Epidemics at Wolfram Demonstrations](https://demonstrations.wolfram.com/search.html?query=epidemic) - [IGSIRProcess - IGraph Epidemic models][35] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1China_c.png&userId=1624544 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1.5US_c.png&userId=1624544 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2World_c.png&userId=1624544 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3Genetic_c.png&userId=1624544 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4Patient_c.png&userId=1624544 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5Resources_c.png&userId=1624544 [7]: https://www.wolframcloud.com/obj/examples/COVID19Preview.png [8]: https://www.wolframcloud.com/obj/s.wolfram/Published/COVID-19-Livestream-March-24.nb [9]: https://community.wolfram.com/groups/-/m/t/1907703 [10]: https://youtu.be/Vs5APySGYnk [11]: https://youtu.be/kC6LHAv_lx0 [12]: https://community.wolfram.com/groups/-/m/t/1908923 [13]: https://datarepository.wolframcloud.com/search/?i=COVID-19 [14]: https://datarepository.wolframcloud.com/search/?i=COVID-19 [15]: https://reference.wolfram.com/language/workflow/SubmitToTheWolframDataRepository.html [16]: https://community.wolfram.com/groups/-/m/t/2238214 [17]: http://wolfr.am/StaffPicks [18]: https://www.youtube.com/playlist?list=PLxn-kpJHbPx3_hUbroRYC_7NxcOwZ1SWa [19]: https://youtu.be/Vs5APySGYnk [20]: https://youtu.be/kC6LHAv_lx0 [21]: https://youtu.be/pcFB6_yrxGE [22]: https://youtu.be/vUq8qx7kTYA [23]: https://youtu.be/HCJgv3N_kDo [24]: https://youtu.be/MlI_8o4A3BA [25]: https://youtu.be/P86ZY-znE64 [26]: https://youtu.be/Kjk-sYlg-U0 [27]: https://youtu.be/LRs9rYCXIzs [28]: https://youtu.be/b8oCNjRI0gY [29]: https://youtu.be/C-sjXQiPE7s [30]: https://youtu.be/gA0TPQZgNY0 [31]: https://youtu.be/I-n3zN4aU6c [32]: https://youtu.be/4xCfPIiredM [33]: https://github.com/arnoudbuzing/wolfram-coronavirus [34]: https://wolfr.am/JZNRriEE [35]: http://szhorvat.net/mathematica/IGDocumentation/#epidemic-models Vitaliy Kaurov 2020-02-04T15:18:14Z https://community.wolfram.com/groups/-/m/t/2251812 A new study group for Building and Applying Epidemic Models with the Wolfram Language begins Monday, May 10, 2021! Making progress in an online course can be daunting when you have to study all alone. Join a cohort of fellow Wolfram Language users for a two-week study group in which you will start in week one with the basics of implementing compartment-based epidemiological models in the Wolfram Language. In the second week, you will cover multi-group models–taking into account vital demographics (i.e. birth, death) and age groups–in addition to introducing control measures and ending with stochastic models. **Sign up here**: https://wolfr.am/UZfPoLAq Jeremy Stratton-Smith 2021-04-23T20:17:17Z https://community.wolfram.com/groups/-/m/t/1888335 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- September 27: This site will now be updated about twice a month, middle and end. We will try to update the models. For the most part, the epidemics have run their modeling course and have taken a new turn in many places. We will maintain this site only as a source of information for a while longer, or until we compute new models for the renewed outbreaks. August 29: This site will only be updated on weekends or Mondays, from now on. We will try to compute new models based on fresh data if time allows. The Finland section will be changed somewhat. July 29: We now have a model for the world in the main section June 15, 22: (Notebook not yet ready today June 22, hopefully soon) -- As of June 22 I will be on holiday, or doing something else, until August 17. Some sections will not be updated on a daily basis. In the table of contents ("WHAT IS INCLUDED IN THIS POST" just below), I will indicate how often each section will be updated. I will also make a note to this effect in each of the corresponding sections. There are some forecasts which will be checked on the date that is given for the forecast. At times I will be in wilderness areas without electricity, so some updates at that time might not arrive promptly. Before June 22 (or a bit later, apologies) I will post a notebook which calculates parameters for some of the models automatically. There will be enough in it to get you started with your own data. The table of contents is updated now accordingly (and corrected) June 3-5: In a reply to the Europe section, a picture with forecasts for fatalities per capita for USA, UK, Sweden, and Italy, updated daily. Minor corrections in the text were made on June 5. May 29: contents have been reorganized slightly, the table of contents is now up to date again. See detailed update notices after the main text, and in each section (this post contains several sections where results are shown, see table of contents ("INCLUDED IN THIS POST") just a bit below. May 20: I have updated the table of contents ("INCLUDED IN THIS POST" below) NEW, May 10: Daily new cases forecast trends obtained from optimally fitted "TRUE" models (to learn about this, read the next paragraph and go to the response posted today at the bottom of the post ... it will be up in a few minutes). A notebook will be provided with some guidance as to how to obtain optimal fits almost automatically when I have time to finish putting it together. WARNING: There is a lot of details involved in what I am doing which gives rise to mistakes, especially when something new comes around. I just corrected some blatant ones. Hopefully they dwindle out to zero with time. On April 21, 26, and a importantly on May 3 and 4, I have tried to improve and restructure this presentation and make a note of various conceptual issues. I have also added "TRUE" (or truer) models of the outbreak (where the number of cases is matched to the R curve - read ahead). I realize that as it was before today (and maybe still), it was poorly and hastily written. I will continue to make improvements as I have time. If nothing else, please read this paragraph. Hopefully it is easier to read now and clearer. I specify where to find material in various sections, now close to the beginning and not in too many places. NOTE and DISCLAIMER: we are using a formalism to model data ... this is not exactly the same as having a model of the outbreak itself ... only an approximation that allows us to have some understanding the dynamics of the outbreak and make some forecasts with reasonable accuracy. Modulo the explanations of compartmental models ahead and in the linked post, for the purposes of modeling the outbreak, the only data we have is the number of detected cases. This corresponds to the R curve in the outbreak: each detected infection is an individual that de facto gets quarantined and removed from the infective process. We have no other data available. We don't have data that tells us when an individual becomes exposed or infectious. However, we are using a compartmental model differently: we are considering the R curve to be those individuals that have recovered from the infection or died. And the I curve as the number of detected cases minus those that have recovered and died. The point is, these definitions of our compartments are sound in the sense that they are disjoint (that is, true compartments); and the dynamics of how individuals move from one of our so defined compartment to another can be described with the equations of the SEIR and SIR models. And so, we have a model of the data which we are able to collect. To make this clear, we present in this section, along with other content outlined below, two models for the outbreak in Italy (for which the data is very good), a "TRUE" model of the outbreak, in which the data is matched to the R curve (removed individuals), and OUR VERSION of the model of the data as we have endeavored to look at it for the most part in this post. Without further ado: SEIR MODELS: For an explanation of SEIR (and SIR) models see Robert Nachbar's post: https://community.wolfram.com/groups/-/m/t/1896178 The equations of the slightly modified SEIR model are given ahead. It is possible to model the data by assuming a low enough susceptibility. I explain in the discussion with Robert Nachbar below why the main effect of containment measures is to lower the effective number of susceptible individuals when it is imposed (relatively speaking, at the beginning). Using this idea, it is also possible to model what could happen if you lift restrictions too early by letting the susceptibility increase (see picture) and you then reintroduced them (this is not a forecast, just a possible scenario). As a CAVEAT, these models are models using the DETECTED number of cases, not the TRUE number of cases, AT THE MOMENT THEY ARE DETECTED, not at the moment they are exposed or become infectious. Also, our compartments do not correspond to the compartments of a "true" model of the outbreak. We are taking the I compartment to be the number of detected cases minus the number of recovered and fatal cases, the sum of which is the R compartment. Our ASSUMPTION is that we can model the I compartment moving to the R compartment as individuals moving from being infected to being recovered or dead ... so intuitively we are tacitly assuming that our model gives us a picture of the outbreak with a delay, reflected in the data as it becomes available. Regardless of these considerations, our model allows us to understand how the disease evolves in time as it pertains to the data we have at hand. At least, we were able, in the Chinese model, to predict an end of outbreak time well in advance (the evidence is in Rimmer's response to this post where a similar prediction is made based on our model). INCLUDED IN THIS POST: 1) SEIR models for data from China. A SIR model for Italy. A "TRUE" SIR model for Italy and for the US. And a daily new cases forecast obtained from the "TRUE" model for the US. (The Finland model now lives in its own section (3) only, see ahead. The Spanish model has been replaced and lives in its own section (2). On the last weekend of May a new notebook will be available in the notebook section (5)). As of June 22 and until August 17, this section will continue to be maintained on an as frequent as possible basis, daily if possible. If not, in the updates below, I will indicate if there is to be a pause 2) In a response below, various models for Spain, UK, France, Germany, and Austria, see section for details. This section will be maintained once a week, on Mondays, starting June 22 and until August 17. 3) in a separate response below, two models for Finland (SIR and "TRUE"), a model as Norway, and "TRUE" models for Denmark and Sweden. In a reply to that section, there is detailed information for Sweden (case forecasts and fatality forecasts). From June 22 to August 17, both these section will be maintained on a daily basis if possible. Otherwise, you will be notified as to when updates will occur. 4) in a separate response, a brief discussion of SIR models (with models for China, Italy, and two more models for Finland) in a separate response. Also there, a document of cases/tests ratios for various countries in the SIR models section. This section includes a picture of positivity rates for several countries updated once a week. The positivity rates picture will be updated last on June 22, and again on August 17, weekly. 5) in a separate response, a notebook, towards the end of the post. This section includes a pdf document with dialy new cases for many countries updated once a week. By June 22, this section will contain a notebook which shows how to fit parameters automatically. From June 22 to August 17, the pdf document will not be updated. The notebook and pdf document are also posted in a reply to Kaurov, above the Scandinavian countries section. 6) Daily new cases forecast trends obtained from optimally fitted "TRUE" models in the latest response (May 10). Read more in the new section. Notebook will be provided to make automatic fits. From June 22 to August 17, this section will not be updated. 7) Fatalities per million for USA, UK, Sweden, and Italy. Details in the section, a reply to the Europe section. This section will be updated as frequently as possible between June 22 and August 17. SIR MODELS (see SIR section for equations) At the end of the post in a new response I discuss a simpler SIR-like model for the Chinese, Italian, and Finnish data which is practically as good - the equations are there. It has two advantages over the SEIR model: a) the classic SIR model has analytic solutions, so straightforward (somewhat) computational optimization can be carried out to estimate the parameters - although our equations are not the classical ones as they have a delay; b) it yields for the data we are trying to model values of R0 that are congruent to the observed ones, 5.43 for China - compared to 5.7 obtained in the just published study led by Steven Sanche and Lin Yeng-Ting, Los Alamos N. L. (arXiv:2002.03268) in Emerging Infectious Diseases, V26, Num 7 - (a note about this for the SEIR model below) without further ado (more on this ahead); and c) (UPDATE 3) if we look at the susceptibility curves (S in the diagrams), we see that they do not necessarily reach 0. If they are asymptotic to a positive value, that means there is a herd immunity effect - the value of the asymptote being the number of people who remain susceptible under containment that will not get infected; moreover, we can see that the susceptibility curve is very close to its asymptote near the peak of the infections curve (I in the diagrams), so that targeted testing is warranted as an effective measure of containment at that stage. That section contains a model of China (final) and a model for Italy (that is not updated), and a two models for Finland, one using the JHU data instead of the Finnish authorities data, and another one using another recovery schedule using an estimate based on the scant recovery data for Finland. A SIR model for Finland and the SEIR model alternate every so often here; the SIR model uses THL (Finnish health authorities) data. Both models are available in the Finland section, and the model for Germany in its section is, alternatingly, either a SEIR or a SIR model. We have removed, in the Finland, an SIR model that shows what it looks like to reach a plateau or steady state, rather than a peak; the equations for this are necessarily different than the simple SIR equations given in the SIR section, In the SIR section there are also other models for Finland, one using JHU and the other using a different recovery schedule. The newer models are adjusted quite frequently, especially with respect to the number of susceptible individuals, as they continue to grow. They tend to stabilize about three weeks after control measures have been in place. After the I curve peaks, it is possible to begin to get an idea of how long the outbreak will last. EQUATIONS and PARAMETERS OF MODIFIED SEIR MODEL Now the equations (for the SIR model, see the SIR section at the end of the post and after most of the discussions). s'(t) = -Beta * s(t) * i(t) / p, e'(t) = Beta * s(t) * i(t) / p - Sigma * e(t), i'(t) = Sigma * e(t - m) - Gamma * i(t - n), r'(t) = Gamma * i(t - n) The function s(t) is the number of susceptible people (the people that can get exposed to the pathogen) at time t. e(t) is the number of people that have been exposed to the pathogen and can become infected; i(t) is the number of people who are infected; r(t) is the number of people who have become resistant to the pathogen: they have recovered and developed immunity or died. Now the parameters. beta is usually considered to be the rate of infection or "force of infection"; sigma is the usually the rate at which an exposed individual becomes infective; gamma is usually the removal rate. We introduced m and n, shift or delay parameters to line up the model curves with the data. Here, we are operating with a delay. In our model, an individual is in the I compartment when it gets detected (a case of infection) and we continue to consider it infective until it gets "removed" when it has recovered or passed (not when it gets caught). In reality (in a true model of the outbreak, as in the second example for Italy in the pictures), individuals become infective before they get caught, and they get removed when they get detected. If we assume some kind of uniform delay in the process, we can try to fit the model to the data as we have compartmentalized it (cases and recovered+deceased). Thus we get a description of the dynamics of the outbreak as described by the data we can collect. IN ANY CASE, OUR MODELS ARE MODELS OF THE DATA ... the SEIR (SIR) formalism works well, and they have predictive value. The parameter values are in the titles of the pictures for each country. In general we assume e(0)=i(0)=1 unless stated otherwise in the model label. Also, s(0)=p, and r(0)=0. R0 in our SEIR-like and SIR-like MODELS: In the SEIR models, the basic reproduction number (R0) is constant and it depends on the parameters of the equations below. If we do the usual calculation (roughly beta/gamma in the equations below), R0 in our models is about an order of magnitude larger than the estimated-observed R0. There is an intuitive explanation for that. If we were to model the DETECTED number of cases using the BELIEVED or TRUE number of susceptible individuals, thought to be an order of magnitude higher than the detected ones, then we would need to scale down beta by an order of magnitude to get our results, among other things. That would give us the R0 that is being measured (my understanding is that R0 was estimated on DETECTED number of cases - but if this is wrong, then my explanation for the disparity is not correct). The main effect of lockdown is to lower the number of people that can be exposed to the pathogen when it is imposed, roughly at the beginning of the outbreak (see reply to Rober Nachbar's response for a thought experiment that explains this). Recall, the basic reproduction number (R0) is constant. The R0 numbers obtained in the SIR models discussed in a separate section are congruent with the values that are proposed in the research litereature (more about that in the SIR section). A NOTE ABOUT SOME DATA Some countries do not provide any or most data pertaining to recoveries. We have estimated this data, sometimes extrapolating from available data, sometimes using an estimating function based on average rates from countries that do provide the data, etc. It would take too long to discuss what we have done in each case where recovery data seems to be missing or partial. We explain the Finnish case. The THL (Finnish health authorities) data for the Finnish model comes from the Finnish Department of Health and Welfare (THL acronym in Finnish). There is a delay in the release of the data of 1-2 days. however, the recovery data comes from Johns Hopkins University and occasional reports from the Finnish authorities. According to the medical chief of staff of the infections diseases clinic at the Helsinki and Uusimaa hospital district, it was "important to define what people mean when they talk about recovery", and that "eventually it would be important to compile statistics to better understand the disease" and "was taking the numbers with a grain of salt" noting that "the criteria undrelying the data are not always clear and they are not always the same in each country". He also said that "tracking recovered patients was not a top priority". (quotes source is Yle news, the state run news agency). We have serialized the occasional recovery data according to how cases might have arisen in time to obtain a recovery rate function. We verify the accuracy of this function every time a new datum becomes available. We use this function also to estimate Norway recoveries. The US model now uses an alternative recovery schedule based on an average of the recovery schedules of countries which are providing these data, as the US recovery data seems lower than it ought to be. See my comment in the day's update (April 15). We also use an estimate for UK data which is not available. Some countries have changed the way they count in the middle of the process, and we have adjusted for this (or not) as we see fit - again, it would take too long to discuss this. For the most part, we use the data that is available and take it from there. SOME EXTRAS: In the notebook section, where there is space, I include a pdf document with a smoothened version (14 day moving average) of the daily tallies for several countries in Europe, as well as USA and South Korea. In the SIR section, where there is space, there is a picture of the current positivity rates (number of cases/number of tetsts conducted so far). It is a useful diagnostic of where a country stands in the process. August 29 - September 5,12,20,27: updated. We will update the US daily tally only once every two weeks now, during weekends. There is now sufficient data for a new model. We will try to compute it if we have time. Next update, in two weekends. August 22-28: updating ... We will stop updating the Italian model ... it has run its course, and Italy is on its way to new growth. We shall continue updating the US daily pictures and the weekly US and world models. There is now sufficient data to compute a new model for the US. Hopefully we have time to do this soon. August 2-21: Updated. Weekly readjusted today, 16th. The weekly models for the world and US are updated. It appears the situation in the US is now stable (no more growth) but there is a long tail ahead. You can see this from the daily case numbers as well. July 28-August 1: Updated. We are replacing the TRUE model for US with a TRUE weekly model based on the second rise in the outbreak, which is now starting to stabilize. We project 11 million detected cases in a stretch of about 60 weeks starting our count on June 7 (but the final number might be less if a vaccines becomes available before that). We will try to derive a forecast from this model later and combine it with the daily cases counting graph. We have removed one of the pictures for Italy and put up a new model for the whole world. More data is needed to get a good estimate on the projected number of cases - our guess, at least twice what this model suggests. June 19-July 27: Updated. Our model for the US will have to be recalculated once things stabilize. Right now there is very substantial growth in the number of cases. Results for Italy will be posted with a delay of one day. This section will continue to be updated daily after June 22, unless a note to the contrary is made, for example, during travel in the wilderness without access to electricity. June 13-19: Updating. It seems there is an uptick of cases in the US. We note there is a fatalities per Million model in a reply to the European section for several countries (Italy, USA; Brazil, Sweden, and the UK). This modeling, matching the R curve of a SIR model to fatalities per million cumulative provides a forecast of fatalities for those countries. Our forecast is compared to those of IHME and other institutions. Details are in that section May 29-June 12: Updating. I have removed the Finland model in this section, it can still be found in the section for Finland and the Nordics. And I move up to this section the daily new cases forecast that comes out of the "TRUE" model for the US. It might illustrative to show what you can get out of this model. At the very bottom of this post in their own section similar forecasts for Italy and the Nordics can be found. We also have a new fit for the "TRUE" model for Italy. May 28: There is a new model fit for Finland. There is also a new model fit for USA. At the bottom of the post, in the last section, there are new forecasts for the daily number of cases ... you can compare the old and the new model fits. May 23-28: Updating. We will wait until the end of May to fit a new "TRUE" model for the US. A semiautomatic, almost optimal fit for the Finland model has been obtained. We will try to fit models automatically from now one, slowly but surely. An automatically fitted, almost optimal SIR model for Italy is now posted. May 19-22: updating. On May 20 the table of contents above ("INCLUDED IN THIS POST" section) was updated. May 18: there is no data for Finland May 17 yet. May16-17: The Italy "TRUE" models has been fitted again this weekend; next weekend we do the U.S. May 10-15. Updating. The US and Italy "TRUE" models are now optimally fitted. The Italy model is fitted to 4 May when restrictions were lifted. A notebook to do this will be provided later. From these models one can derive the daily new cases forecast trends in the new section at the end of the post (for more info, read there, it will be up shortly). It takes about 2-4 hours of compute time to make some of these fits. These models will not be fitted again as restrictions are slowly lifting ... which changes the forecast, hopefully in a noticeable way (or hopefully not, from the state of things point of view). The Italy SEIR model has been replaced by a SIR model. Earlier on May 10 I had posted the wrong file for the US model ... it is now correct. And apologies, had the wrong label on the Italy "TRUE" model, now corrected (hopefully) ... May 8-9: I will leave the "TRUE" model for the US now. It is perhaps the most reliable picture of what lies ahead. One of my usual SEIR models forecasts a higher (4.4 million) susceptible population, but that number does not square with the "TRUE" model, although soon I will do an automatic and optimal fit of it, which might push this number up. Over the weekend, a new model for Italy will be forthcoming and "TRUE" models will start to be produced in a fully automated way (I will later post a notebook with the code that does the optimization; it is written withing the simplicity of built in Mathematica functionality, which means it is somewhat slow and NMinimize needs help. May 6-7: Updating. Soon we will have to update our standard model for Italy. The "TRUE" model looks very reliable now, enough to make long term forecasts and provide a picture as to what to expect in the longer run. May 5: The US SEIR models will now alternate with a "TRUE" SIR model (see first paragraph of text above and subsequently for explanation). Also, there is an SEIR model for Italy and now a "TRUE" SIR model as well. April 30 - May 4: updating, US model alternating every so often April 29: updating. Today I put back the US model with the actual recovery data that is provided. The two models will alternate. One of our alternative Finnish models squares with the latest THL recovery estimates, so we are showing that model instead of the model we had yesterday. This picture will be updated again at 2 PM EEST. April 28: Tomorrow I will start alternating the US model with the model obtained from the recovery data that is provided. I found a source of daily increments for the Spanish data. The Italian model has been stable now for weeks, since before the peak of the I curve. Their official data is quite good comparably speaking. April 27: updating. I will not update Spain after today until I get hold of the data from local authorities if I can. The JHU data is inconsistent both in number of cases and in recoveries. It seems the historical series is being updated retrospectively, but according to the Spanish authorities, it is not yet ready. The temporary lump sums provided temporarily make for very poor data. When it becomes ready, I will continue to update this model. If I can obtain reliable information from press reports, I will update my data thus by hand. April 25-26: updating. Today, April 26, the recovery data from Spain is highly anomalous, for the second time (in the past, counting method changed). Unless this datum is corrected, from now on I will use an estimate based on a recovery rate function that can be computed from the data up to yesterday, or constant adjustment as of today based on today's estimate. Using this function, we obtain today's picture. April 24: updating. It seems the model for Spain might require a steeper rise up again. April 23: updating. I have posted yet a new model for Finland which is probably more accurate. It is hard to say, as the entire time series changes each day due to delays in testing reports. The date in the Spanish model is now correct. I seem to have made, unfortunately, a correct forecast of the consequences of going back to work too soon! April 22: updating. Spain went back to work ten days ago. We see new growth and forecast it will continue so ... may we be wrong. April 21: updating. I changed the text above to improve it and hopefully make it more readable, and highlight important issues. I changed the standard SEIR Finland model for an SIR model that to me, seems more realistic, given the daily tally trends. The problem with Finnish data is that the entire time series gets corrected every day, not just the last day. While this makes for accuracy, it makes modeling difficult. I will alternate with the usual SEIR model. April 19+20: updating. There is yet another model for Finland using another estimate for the recovery schedule. At the end of the SIR section there is a picture of the current positivity rates (number of cases/total number of tests). This should be a useful diagnostic. I will start keeping a history of these data from now on (I only have a history for Finland). April 18: updating. There is an additional model for Finland in the SIR section using JHU data instead of THL data April 17: updating. This section now has the SIR model for Finland, we believe it is a more accurate model for the time being, and based on a just published estimate of recoveries. Our extrapolating function seems to be working quite well and we have adjusted it to reflect this last change. April 16: updating. The German model in its section is now an SIR model. In the Finland section there is a SIR model in which a plateau, rather than a peak, is reached April 15: updating. Today I will show an alternative model for the USA that uses an average recovery rate obtained from other countries rather than the reported data, which seem low (understandably so, it is not a priority to test people who have tested positive and are recovering at home). The daily tally in the US has slowed down somewhat, which would lend credibility to the model, which shows the infection curve getting close to a peak. Also, in the previous model, the number of susceptible individuals was probably too high. I will compute an estimated peak date tomorrow based on this model. I will continue to track the old model, but it doesn't fit here. I am thinking of adding another response to the post with a number of models which don't fit here, but I haven't made up my mind about it yet. April 13-14: Today is the last day the China model will be updated (April 13). April 14: I am adding a SIR model of Italy in the response with the SIR model for China. There is also a SIR model for Finland in the Finland section. It is possible to compute an effective R that is time dependent (but that won't be in the post, although I will make a notebook available in that section at a later time with this). I will add SIR models for other countries as well. I am working on an optimization program for the SIR model to further automate the determination of parameters - if I ever complete this it will also be in the SIR notebook eventually. On another note, I plan to add a section with models for other Scandinavian countries as soon as I have time. April 12: updating. Today I am adding a response with a section which discusses the simpler SIR-like model (which I managed to make work almost just as well as the SEIR model, although it is somewhat more difficult to get it to work). The SIR-like model has the advantage that analytical solutions are known for SIR models which might be modified for our specific instance of the model, and in the case of our investigations, it yields an adequate value for R0 without the need for any further explanations. April 11: updating. The daily tally pdf document in the Finland section is now per million inhabitants. Again note the disparity between European countries wishing to pursue an exit strategy at the moment, and South Korea, the role model country. I have added a picture which explores a scenario in which Spain lifts restrictions (as it has announced) today. We are able to model (with some mathematical ingenuity) the effect of this on the S curve, and subsequent effect on the number of infections. We hope this does not happen, but it might. April 10; updating. I added some explanations in the text and a picture that illustrates what could happen when restrictions are lifted too early and then reintroduced - this is not a forecast, just a plausible scenario. I moved the notebook to a new response at the end of the post. April 9: updating. In the Finland section there is a pdf document with the smooth version of the daily tallies for several Euro countries, USA, and South Korea. The Italy model seems very stable now. April 8. Updating. Today I added, in the main part of the text above, an "intuitive" note about the basic reproduction number (R0) in these models and why they are about an order of magnitude larger than the measured rates. April 6-7. Updating throughout the day. France and UK models temporarily suspended due to missing or inconsistent data, until more data is available April 5: Updating throughout the day. There is a new model for Austria in the Europe section. It's I curve has p Enrique Garcia Moreno E. 2020-02-26T16:43:12Z https://community.wolfram.com/groups/-/m/t/1974412 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- ![enter image description here][1] &[Wolfram Notebook][2] [Old]: https://www.wolframcloud.com/obj/c29137dd-dcdf-4dd1-827e-3495b64a8436 [Original]: https://www.wolframcloud.com/obj/a9d60a60-4adf-41ec-ad5a-a666b1591cf0 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image.jpeg&userId=20103 [2]: https://www.wolframcloud.com/obj/956d65fd-abfb-45d9-802d-9a79013e7b14 Jan Brugard 2020-05-14T15:04:02Z https://community.wolfram.com/groups/-/m/t/3242718 I am a relatively new user to Mathematica. Could someone tell me the best and most efficient way to code in Mathematica these three differential equations, shown in the image, for a three gene negative feedback loop? I have included an image below of how I was doing this previously with brute force in Excel using small time increments of 0.000025 min. Obviously, Mathematica is a much better way to do this calculation. You can see that each differential equation includes the gene product calculated by one of the other two differential equations so all 3 equations are interlinked. I would like to be able to simulate various three-gene negative feedback systems by changing the parameters on the left-hand side of the image below. Thank you in advance for any help that you can provide me on coding in these three differential equations into Mathematica and informing me on the best way to do simulations in Mathematica. ![Three gene negative feedback loop][1] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image001.png&userId=3242173 Scott Klakamp 2024-08-06T17:09:21Z https://community.wolfram.com/groups/-/m/t/1896178 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- **Recent updates:** - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_1.nb][1] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_2.nb][2] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_3.nb][3] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_4.nb][4] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_5.nb][5] &[Wolfram Notebook][6] [1]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_1.nb [2]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_2.nb [3]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_3.nb [4]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_4.nb [5]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_5.nb [6]: https://www.wolframcloud.com/obj/fcfa338d-3fd1-4918-8890-dad8b455ae16 Robert Nachbar 2020-03-11T17:39:06Z https://community.wolfram.com/groups/-/m/t/1906954 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- &[TrackingUS][1] [1]: https://www.wolframcloud.com/obj/331be1ee-421c-473f-bd75-fd858f28ff48 Robert Rimmer 2020-03-24T20:58:57Z https://community.wolfram.com/groups/-/m/t/1903289 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ea3730f2-681f-488a-8c9b-76857f000e80 Arnoud Buzing 2020-03-21T23:18:15Z https://community.wolfram.com/groups/-/m/t/122095 The latest way I have found to use my expensive math software for frivolous entertainment is this. Here's is a way to describe it. [list] [*]1000 dancers assume random positions on the dance-floor. [*]Each randomly chooses one "friend" and one "enemy". [*]At each step every dancer [list] [*]moves 0.5% closer to the centre of the floor [*]then takes a large step towards their friend [*]and a small step away from their enemy. [/list] [*]At random intervals one dancer re-chooses their friend and enemy [/list] Randomness is deliberately injected. Here is the dance... [mcode]n = 1000; r := RandomInteger[{1, n}]; f := (#/(.01 + Sqrt[#.#])) & /@ (x[[#]] - x) &; s := With[{r1 = r}, p[[r1]] = r; q[[r1]] = r]; x = RandomReal[{-1, 1}, {n, 2}]; {p, q} = RandomInteger[{1, n}, {2, n}]; Graphics[{PointSize[0.007], Dynamic[If[r < 100, s]; Point[x = 0.995 x + 0.02 f[p] - 0.01 f[q]]]}, PlotRange -> 2][/mcode] [img]/c/portal/getImageAttachment?filename=OPTfnlfrnds.gif&userId=11733[/img] Thanks to Vitaliy for posting this on my behalf, complete with animations :-) Background: I had read somewhere that macro-scale behaviour of animal swarms (think of flocks of starlings or shoals of herring) is explained by each individual following very simple rules local to their vicinity, essentially 1) try to keep up and 2) try not to collide. I started trying to play with this idea in Mathematica, but it was rather slow to identify the nearest neighbours of each particle. So I wondered what would happen if each particle acted according to the locations of two other particles, regardless of their proximity. The rule was simply to move away from one and towards the other. The contraction (x = 0.995 x) was added to prevent the particle cloud from dispersing towards infinity or drifting away from the origin. I tweaked the "towards" and "away" step sizes to strike a balance between the tendency to clump together and to spread apart (if you make the step sizes equal you get something more like a swarm of flies). With each particle's attractor and repeller fixed, the system finds a sort of dynamic equilibrium, so to keep things changing I added a rule to periodically change the attractor and repeller for one of the particles. The final adjustment was to make the "force" drop towards zero for particles at very close range. This helps to stop the formation of very tight clumps, and also prevents a division-by-zero error when a particle chooses itself as its attractor or repeller. The description of the system as a dance was an attempt to explain the swirling pattern on the screen without using mathematical language. I'd love to see what other "dances" can be created with other simple rules. Simon Woods 2013-09-11T18:31:12Z https://community.wolfram.com/groups/-/m/t/1868945 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4686Wuhan_Coronavirus_Outbreak_Jan29.gif&userId=95400 [2]: https://www.wolframcloud.com/obj/c2eafc69-4016-4e05-a8ad-b1d22a37379f Jofre Espigule-Pons 2020-01-29T02:18:52Z https://community.wolfram.com/groups/-/m/t/2080664 ![Patient Travel History ][1] Hey everyone! For anyone interested in COVID-19 data analysis, I will be running a study group on that very topic, starting Monday, September 28! It will accompany my [course][2] on Wolfram U, which I highly encourage you to watch. Sign up [here][3] for the study group. Do you have anything specific you would like to see covered? Let me know. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=250linesclear.png&userId=2069037 [2]: https://www.wolfram.com/wolfram-u/covid-data-analysis-and-visualization/ [3]: https://register.gotowebinar.com/register/1427575520699286286?source=community Hamza Alsamraee 2020-09-21T15:40:19Z https://community.wolfram.com/groups/-/m/t/2546972 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/9f15876a-0afc-428f-809c-2859aec6189e Samikshaa Natarajan 2022-06-08T21:48:48Z https://community.wolfram.com/groups/-/m/t/1976589 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- First version of this code been published on https://mathematica.stackexchange.com/questions/221609/solver-for-covid-19-epidemic-model-with-the-caputo-fractional-derivatives As it is known in biological system with memory it would be suitable to use fractional derivatives to describe evolution of the system. In a current version of Mathematica 12.1 there is no special solver for integrodifferential equations. Here we show solver with using Haar wavelets for dynamic system (3) presented in a paper M.A. Khan, A. Atangana, [Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative](https://doi.org/10.1016/j.aej.2020.02.033), Alexandria Eng. J. (2020) [![Figure 1][1]][1] with differential operator replaced with the Caputo definition for fractional derivative as follows $$\frac {d f}{dt}\rightarrow \frac {1}{\Gamma (1-q)}\int_0^t{\frac{f'(x)dx}{(t-x)^{q}}}$$ The code below allows us to reproduce Figure 7 from the paper linked above. Let define functions h[x_, k_, m_] := WaveletPsi[HaarWavelet[], m x - k]; h1[x_] := WaveletPhi[HaarWavelet[], x]; Then we can calculate integrals Integrate[h[t, k, m], {t, 0, x}, Assumptions -> {k >= 0, m > 0, x > 0}] Integrate[h1[t], {t, 0, x}, Assumptions -> {x > 0}] Integrate[h[x, k, m]/(t - x)^q, {x, 0, t}, Assumptions -> {t > 0, k >= 0, m > 0, q < 1}] Integrate[h1[x]/(t - x)^q, {x, 0, t}, Assumptions -> {t > 0, q < 1}] With these integrals let define functions p[x_, k_, m_] := Piecewise[{{(1 + k - m*x)/m, k >= 0 && 1/m + (2*k)/m - 2*x < 0 && 1/m + k/m - x >= 0 && m > 0}, {(-k + m*x)/m, k >= 0 && 1/m + (2*k)/m - 2*x >= 0 && k/m - x < 0 && 1/m + k/m - x >= 0 && m > 0}}, 0] p1[x_] := Piecewise[{{1, x > 1}}, x] pc[t_, k_, m_, q_] := Piecewise[{{-(t^(1 - q)/(-1 + q)), k == 0 && 1/m - 2*t >= 0 && m > 0 && t > 0 && 1/m - t >= 0}, {-((m^(-1 + q)*(1/(-k + m*t))^(-1 + q))/(-1 + q)), k > 0 && 1/m + (2*k)/m - 2*t > 0 && k/m - t < 0 && m > 0 && 1/m + k/m - t > 0}, {(-t^q + 2*m*t^(1 + q) - m*t*(-(1/(2*m)) + t)^q)/ (t^q*(-(1/(2*m)) + t)^q*(m*(-1 + q))), k == 0 && m > 0 && 1/m - 2*t < 0 && 1/m - t >= 0}, {(1/(-1 + q))*((2^(-1 + q)*m^(-1 + 2*q)*(-(-(k/m) + t)^q - 2*k*(-(k/m) + t)^q + 2*m*t*(-(k/m) + t)^q + 2*k*(-((1/2 + k)/m) + t)^q - 2*m*t*(-((1/2 + k)/m) + t)^ q))/((1 + 2*k - 2*m*t)*(k - m*t))^q), k > 0 && 1/m + (2*k)/m - 2*t == 0 && m > 0 && 1/m + k/m - t > 0}, {-((1/(-1 + q))*((2^(-1 + q)*m^(-1 + 2*q)* (-2*(-((1/2 + k)/m) + t)^ q*((1 + 2*k - 2*m*t)*(k - m*t))^ q - 2*k*(-((1/2 + k)/m) + t)^q* ((1 + 2*k - 2*m*t)*(k - m*t))^q + 2*m*t*(-((1/2 + k)/m) + t)^q*((1 + 2*k - 2*m*t)* (k - m*t))^q + (-((1 + k)/m) + t)^q* ((1 + 2*k - 2*m*t)*(k - m*t))^q + 2*k*(-((1 + k)/m) + t)^q*((1 + 2*k - 2*m*t)*(k - m*t))^ q - 2*m*t*(-((1 + k)/m) + t)^q* ((1 + 2*k - 2*m*t)*(k - m*t))^ q + (-(k/m) + t)^q* ((1 + 2*k - 2*m*t)*(1 + k - m*t))^q + 2*k*(-(k/m) + t)^q*((1 + 2*k - 2*m*t)*(1 + k - m*t))^q - 2*m*t*(-(k/m) + t)^q*((1 + 2*k - 2*m*t)*(1 + k - m*t))^ q - 2*k*(-((1/2 + k)/m) + t)^q* ((1 + 2*k - 2*m*t)*(1 + k - m*t))^q + 2*m*t*(-((1/2 + k)/m) + t)^q*((1 + 2*k - 2*m*t)* (1 + k - m*t))^ q))/(((1 + 2*k - 2*m*t)*(k - m*t))^q* ((1 + 2*k - 2*m*t)*(1 + k - m*t))^q))), k > 0 && m > 0 && 1/m + (2*k)/m - 2*t <= 0 && 1/m + k/m - t <= 0}, {-((1/(2*m*(-1 + q)))*((2^q*m^(2*q)*t^q*(-(1/m) + t)^q* (-(1/(2*m)) + t)^q - 2^(1 + q)*m^(1 + 2*q)*t^(1 + q)* (-(1/m) + t)^q*(-(1/(2*m)) + t)^q - 2^(1 + q)*m^(2*q)* t^q*(-(1/(2*m)) + t)^(2*q) + 2^(1 + q)*m^(1 + 2*q)* t^(1 + q)*(-(1/(2*m)) + t)^(2*q) + t^q*((-1 + m*t)*(-1 + 2*m*t))^q - 2*m*t^(1 + q)* ((-1 + m*t)*(-1 + 2*m*t))^q + 2*m*t*(-(1/(2*m)) + t)^q* ((-1 + m*t)*(-1 + 2*m*t))^q)/(t^ q*(-(1/(2*m)) + t)^q* ((-1 + m*t)*(-1 + 2*m*t))^q))), k == 0 && 1/m - 2*t < 0 && 1/m - t < 0 && m > 0}, {(1/(-1 + q))*((2^(-1 + q)*m^(-1 + q)*((-m^q)*(-(k/m) + t)^q - 2*k*m^q*(-(k/m) + t)^q + 2*m^(1 + q)*t*(-(k/m) + t)^q + 2*k*m^q*(-((1/2 + k)/m) + t)^q - 2*m^(1 + q)*t* (-((1/2 + k)/m) + t)^ q - ((1 + 2*k - 2*m*t)*(k - m*t))^q* (1/(-1 - 2*k + 2*m*t))^q - 2*k*((1 + 2*k - 2*m*t)*(k - m*t))^q* (1/(-1 - 2*k + 2*m*t))^q + 2*m*t*((1 + 2*k - 2*m*t)*(k - m*t))^q* (1/(-1 - 2*k + 2*m*t))^q))/((1 + 2*k - 2*m*t)*(k - m*t))^ q), 1/m + (2*k)/m - 2*t < 0 && k > 0 && m > 0 && 1/m + k/m - t > 0}}, 0] pc1[t_, q_] := Piecewise[{{-(t^(1 - q)/(-1 + q)), t <= 1}}, -(((-1 + t)^q*t + t^q - t^(1 + q))/((-1 + t)^q*t^q*(-1 + q)))] Now we have all functions to solve a problem with the given parametres Np0 = 8266000; μp (*Natural mortality rate*)= 1/(76.79 365); Πp (*Birth rate*)= μp Np0 ; ηp \ (*Contact rate*)= 0.05; ψ (*Transmissibility multiple*) = 0.02; ηw (*Disease transmission coefficient*)= 0.000001231; θp (*The proportion of asymptomatic \ infection*)= 0.1243; ωp (*Incubation period*)= 0.00047876; ρp (*Incubation period*)= 0.005; τp (*Removal or recovery rate of Ip*)= 0.09871; τap (*Removal or recovery rate of Ap *)= 0.854302; ϱp (*Contribution of the virus to M by Ip*)= 0.000398; ϖp (*Contribution of the virus to M by Ap*) = 0.001; πp(*Removing rate of virus from M*) = 0.01; Let define variables var1 = {Sp1, Ep1, Ip1, Ap1, Rp1, Mp1}; var = {Sp, Ep, Ip, Ap, Rp, Mp}; aco = {aS, aE, aI, aA, aR, aM}; aco1 = {aS1, aE1, aI1, aA1, aR1, aM1}; aco0 = {aS0, aE0, aI0, aA0, aR0, aM0}; The problem can be solved on the unit interval, hence we calculate the collocation points as follows J = 4; M = 2^J; dx = 1/(2*M); A = 0; xl = Table[A + l dx, {l, 0, 2 M}]; xcol = Table[(xl[[l - 1]] + xl[[l]])/2, {l, 2, 2 M + 1}]; We can represent our solution with functions defined above as Sp1[x_, q_] := Sum[aS[i, j] pc[x, i, 2^j, q], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aS1 pc1[x, q]; Sp[x_] := Sum[aS[i, j] p[x, i, 2^j], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aS1 p1[x] + aS0; Ep1[x_, q_] := Sum[aE[i, j] pc[x, i, 2^j, q], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aE1 pc1[x, q]; Ep[x_] := Sum[aE[i, j] p[x, i, 2^j], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aE1 p1[x] + aE0; Ip1[x_, q_] := Sum[aI[i, j] pc[x, i, 2^j, q], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aI1 pc1[x, q]; Ip[x_] := Sum[aI[i, j] p[x, i, 2^j], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aI1 p1[x] + aI0; Ap1[x_, q_] := Sum[aA[i, j] pc[x, i, 2^j, q], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aA1 pc1[x, q]; Ap[x_] := Sum[aA[i, j] p[x, i, 2^j], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aA1 p1[x] + aA0; Rp1[x_, q_] := Sum[aR[i, j] pc[x, i, 2^j, q], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aR1 pc1[x, q]; Rp[x_] := Sum[aR[i, j] p[x, i, 2^j], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aR1 p1[x] + aR0; Mp1[x_, q_] := Sum[aM[i, j] pc[x, i, 2^j, q], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aM1 pc1[x, q]; Mp[x_] := Sum[aM[i, j] p[x, i, 2^j], {j, 0, J, 1}, {i, 0, 2^j - 1, 1}] + aM1 p1[x] + aM0; All unknown variables should be joined together in one list varM = Join[aco0, aco1, Flatten[Table[{aS[i, j], aE[i, j], aI[i, j], aA[i, j], aR[i, j], aM[i, j]}, {j, 0, J, 1}, {i, 0, 2^j - 1, 1}]]]; Now we are ready to solve the problem. Since we solve system of equations on the unit interval we define scaling function (120 is the length of interval time in days) tn[q_]:= (1/120)^q; eq1[t_, q_] := -tn[q]/Gamma[1 - q] Sp1[t, q] + Πp/ Np0 - μp Sp[t] - ηp Sp[ t] (Ip[t] + ψ Ap[t])/(Sp[t] + Ep[t] + Ip[t] + Ap[t] + Rp[t]) - Np0 ηw Sp[t] Mp[t]; eq2[t_, q_] := -tn[q]/Gamma[1 - q] Ep1[t, q] + ηp Sp[ t] (Ip[t] + ψ Ap[t])/(Sp[t] + Ep[t] + Ip[t] + Ap[t] + Rp[t]) + Np0 ηw Sp[t] Mp[t] - (1 - θp) ωp Ep[ t] - θp ρp Ep[t] - μp Ep[t]; eq3[t_, q_] := -tn[q]/Gamma[1 - q] Ip1[ t, q] + (1 - θp) ωp Ep[t] - (τp + μp) Ip[t]; eq4[t_, q_] := -tn[q]/Gamma[1 - q] Ap1[t, q] + θp ρp Ep[ t] - (τap + μp) Ap[t]; eq5[t_, q_] := -tn[q]/Gamma[1 - q] Rp1[t, q] + τp Ip[ t] + τap Ap[t] - μp Rp[t]; eq6[t_, q_] := -tn[q]/Gamma[1 - q] Mp1[t, q] + ϱp Ip[ t] + ϖp Ap[t] - πp Mp[t]; With these equations we can calculate Figure 6 from the paper above with the next piece of code eq[q_] := Flatten[ParallelTable[{eq1[t, q] == 0, eq2[t, q] == 0, eq3[t, q] == 0, eq4[t, q] == 0, eq5[t, q] == 0, eq6[t, q] == 0}, {t, xcol}]]; Do[icv[i] = {Sp[0] == 8065518/Np0, Ep[0] == 200000/Np0, Ip[0] == 282/Np0, Ap[0] == 200/Np0, Rp[0] == 0, Mp[0] == 50000/Np0}; eqM[i] = Join[eq[i], icv[i]]; solv[i] = FindRoot[eqM[i], Table[{varM[[j]], .1}, {j, Length[varM]}], MaxIterations -> 1000]; lstSv[i] = Table[{x 120 , Np0 Evaluate[Sp[x] /. solv[i]]}, {x, 0, 1, .01}]; lstEv[i] = Table[{x 120, Np0 Evaluate[Ep[x] /. solv[i]]}, {x, 0, 1, .01}]; lstIv[i] = Table[{x 120, Np0 Evaluate[Ip[x] /. solv[i]]}, {x, 0, 1, .01}]; lstAv[i] = Table[{x 120, Np0 Evaluate[Ap[x] /. solv[i]]}, {x, 0, 1, .01}]; lstRv[i] = Table[{x 120, Np0 Evaluate[Rp[x] /. solv[i]]}, {x, 0, 1, .01}]; lstMv[i] = Table[{x 120, Np0 Evaluate[Mp[x] /. solv[i]]}, {x, 0, 1, .01}];, {i, {99/100, 9/10, 8/10, 7/10, 6/10}}];] Visualization of solution: {ListLinePlot[Table[lstSv[i], {i, {99/100, 9/10, 8/10, 7/10, 6/10}}], Frame -> True, FrameLabel -> {"t, days", "\!\(\*SubscriptBox[\(S\), \(p\)]\)"}, PlotRange -> All], ListLinePlot[ Table[lstEv[i], {i, {99/100, 9/10, 8/10, 7/10, 6/10}}], Frame -> True, FrameLabel -> {"t, days", "\!\(\*SubscriptBox[\(E\), \(p\)]\)"}, PlotRange -> All], ListLinePlot[ Table[lstIv[i], {i, {99/100, 9/10, 8/10, 7/10, 6/10}}], Frame -> True, FrameLabel -> {"t, days", "\!\(\*SubscriptBox[\(I\), \(p\)]\)"}, PlotRange -> All], ListLinePlot[ Table[lstAv[i], {i, {99/100, 9/10, 8/10, 7/10, 6/10}}], Frame -> True, FrameLabel -> {"t, days", "\!\(\*SubscriptBox[\(A\), \(p\)]\)"}, PlotRange -> All], ListLinePlot[ Table[lstRv[i], {i, {99/100, 9/10, 8/10, 7/10, 6/10}}], Frame -> True, FrameLabel -> {"t, days", "\!\(\*SubscriptBox[\(R\), \(p\)]\)"}, PlotRange -> All], ListLinePlot[ Table[lstMv[i], {i, {99/100, 9/10, 8/10, 7/10, 6/10}}], Frame -> True, FrameLabel -> {"t, days", "M"}, PlotRange -> All, PlotLegends -> Automatic]} [![Figure 2][3]][3] [1]: https://i.stack.imgur.com/mwuYC.png [2]: https://i.stack.imgur.com/j05bg.png [3]: https://i.stack.imgur.com/3NjrP.png Alexander Trounev 2020-05-16T17:30:58Z https://community.wolfram.com/groups/-/m/t/518062 I am trying to model the growth of cancer stem cells using loops, but don't have any experience modeling loops and [this page][1] wasn't very helpful. The equations I have constructed thus far are as follows: For[i = 1; c[0] = 1; c[1] = 1, i < 10, i++, c[i_] := c[i - 1]*(1 + p1*v - (1 - p1) v - dr); Print[c[i]]] For[i = 1; p[0] = 0, i < 10, i++, p[i_] := c[i - 1] (1 - p1) v + p[i - 1] (1 + p2*v - (1 - p2) v - d); Print[p[i]]] For[i = 1; d[0] = 0, i < 10, i++, d[i_] := p[i - 1] (1 - p2) v + t[i - 1] (1 - dr]); Print[d[i]]] I want to create a loop such that for i between 2 and n, I can determine the number of each type of cells (c=cancer stem cells, p=progenitor cells, d=terminally differentiated cell) there are symbolically. Once this is determined, I would also like to include a loop such that when the value of receptor occupancy, as defined as receptor occupancy= ((c[i]*f1 + p[i]*f2 + d[i]*f3) r)/k is less than than some value x1, then v is changed to v*y1 and when it is less than some other value x2, the value of p1 is changed to p1*y2. Any help would be great! [1]: https://reference.wolfram.com/language/tutorial/LoopsAndControlStructures.html c bro 2015-06-24T19:54:27Z https://community.wolfram.com/groups/-/m/t/1257547 # Intro One of the most popular Reddit's channels **Data Is Beautiful** (with multi-million membership of subscribers) has just started **Battle Competitions** for data visualizations that will run monthly. This is a call to Wolfram Community members to collaborate on **JAN 2018 Battle**. ***Direct reference to the JAN 2018 Battle***: https://redd.it/7nm6ed ## Solutions - **Heatmap of inter- and intra- species comparison** *by Vitaliy Kaurov*: - http://community.wolfram.com/groups/-/m/t/1257577 - **Bubble chart for 4D data** *by Sander Huisman*: - http://community.wolfram.com/groups/-/m/t/1257885 - **Population - pyramid like visualization**: *by George Varnavides* - http://community.wolfram.com/groups/-/m/t/1258056 - **Growth Rate in "Intensity Space"** *by Henrik Schachner* - http://community.wolfram.com/groups/-/m/t/1258281 - **Intraspecies comparison using RadarChart** *by Diego Zviovich* - http://community.wolfram.com/groups/-/m/t/1260507 - **Interspecies comparison using HeatmapPlot** by *Anton Antonov* - http://community.wolfram.com/groups/-/m/t/1261444 - **Scatter plot slices of temperature dynamics** *by Vitaliy Kaurov* - http://community.wolfram.com/groups/-/m/t/1261948 - **RadarChart for each pecies** by *Anton Antonov* - http://community.wolfram.com/groups/-/m/t/1261438 ## Rules of this thread Reddi requires direct links to the images. Hence a separate post is necessary. Here are the steps: - Make a separate post solving the challenge with detailed title describing your specific method of visualization and starting with tag [Reddit-DiBB0118] (Data is Beautiful Battle 01/2018) - Make a comment in this thread simply stating the title and copying your post URL. See my example in the comments. I will collect the solutions in the "solutions" section above. This method enables you to post your own posts on Reddit if you want to keeping your authorship. ## Goal I simply suggest that Wolfram Community members brainstorm in the comments below about how the best to visualize the dataset. Feel free to submit **your own** solutions to Reddit if you want to as they require the original authors. The main goal though is simply to have fun here on Community. **Don't forget to vote up the posts you like**. ## Important Battles have simple rules explained clearly in the Reddit battle thread linked above. To not get disqualified it is advised to read rules carefully. You can ask Reddit admins any additional questions directly in the thread comments. I recommend reading other people comments as they clarify the nature of the dataset. ## Getting the data w/ Wolfram Language (WL) The dataset is located at a web page: http://aquatext.com/tables/algaegrwth.htm The nature of the data is clear from the website description. It is easy to get the raw data with the following WL command: raw = Import["http://aquatext.com/tables/algaegrwth.htm", "Data"] /."0..06" -> .06; You need `/."0..06" -> .06` because the data has a clerical error resulting in the import of a string instead of a number. One way of obtaining a simple rectangular array / table of data is: data=Cases[raw,{_String,__?NumberQ},Infinity]/. x_List/;First[x]=="Temperature":>{"Temperature",5,5,10,10,25,25,30,30}; which can be viewed as TableForm[data] ![enter image description here][3] [1]: https://www.reddit.com/r/dataisbeautiful/ [2]: http://community.wolfram.com/groups/-/m/t/1257577 [3]: http://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot2018-01-02at6.20.30PM.png&userId=11733 Vitaliy Kaurov 2018-01-03T00:33:35Z https://community.wolfram.com/groups/-/m/t/326240 Triggered by the recent outbreak of Ebola India Bruckner, a pupil from Aberdeen's [St Margaret's School for Girls][1], and myself worked on a little model this summer to understand the basics of the spreading of diseases in populations and the relationship to transportation networks. The model is very basic, but shows some interesting features and is very straight forward to implement in Mathematica. When I was typing these lines I saw that Arnoud Buzing had posted something, reason enough to interrupt my typing and to check out what he had posted: [Visualizing the Ebola Outbreak][2]. I hope that my post is going to complement Arnoud's to some extent. So, my question is how the global air transport network might lead to a spreading of a disease. I will use a very standard SIR (susceptible-infected-recovered) model, which is certainly far from being ideal for Ebola; [but similar types of models are to too bad either][3]. It rather simulates an outbreak of some generic disease from which you recover. If we assumed that everyone died in an outbreak the SIR model might also be appropriate. I will introduce the equations below. I also need a list of all airports and all flight connections. On the website [Openflights.org][4] you will find all data we need. I saved the file "airports.dat" and the file "routes.dat". So that's the data. I first import the data: airports = Import["~/Desktop/airports.dat", "CSV"]; routes = Import["~/Desktop/routes.dat", "CSV"]; This is a plot of all airports in that database. GeoRegionValuePlot[Table[GeoPosition[airports[[i, {7, 8}]]] -> 1., {i, 1, Length[airports]}], PlotStyle -> PointSize[0.003], PlotRange -> 1, ImageSize -> Full] which gives ![enter image description here][5] Alright, now the routes. First, we create a list of rules for all airport IDs and their coordinates: codecoords = Table[airports[[i, 5]] -> GeoPosition[airports[[i, {7, 8}]]], {i, 1,Length[airports]}]; We then calculate the links: links = Monitor[Table[routes[[j, {3, 5}]] /. codecoords, {j, 1, Length[routes]}], ProgressIndicator[j, {1, Length[routes]}]]; and clean out missing data: linksclean = Select[links, Head[#[[1]]] == GeoPosition && Head[#[[2]]] == GeoPosition &]; Now comes a nice figure: With[{locations = RandomChoice[linksclean, 14000]}, GeoGraphics[{{Green, Opacity[0.3],AbsoluteThickness[0.0001], GeoPath[locations, "Geodesic"]}}, GeoRange -> "World", GeoProjection -> Automatic, GeoBackground -> GeoStyling["ReliefMap"], ImageSize -> {1200, 600}]] which gives ![enter image description here][6] Ok. Interestingly I can only plot 16000 max at a time. Somewhere between 16-17k the Kernel quits. That might be Integer related. Could be a limit in the programming of Geographics. Not sure. I have more than enough memory and can plot the remaining 2-3k airports in a second figure and use Show to display all. (It would be great if someone from WRI could comment.) Anyway, let's go to some modelling. The basic idea of an [SIR model][7] is that a population is modelled in three compartments Susceptibles (S), Infected (I) and Recovered (R). I will use a time-discrete model; there are continuous models around, too, and if anyone is interested I can provide the ODE model as well. Here are the three equations: sus[i_] := sus[i] = sus[i - 1] - [Rho] sus[i - 1] inf[i - 1]; inf[i_] := nf[i] = inf[i - 1] + [Rho] sus[i - 1] inf[i - 1] - [Lambda] inf[i - 1]; rec[i_] := rec[i] = rec[i - 1] + [Lambda] inf[i - 1]; The meaning of sus, inf and rec should be clear by now; they are given as percentages of the total population, their sum is 100%. The variable i represents time. $ ho$ is an infection rate and $lambda$ is a recovery rate. The infections increase with the product of susceptibles and infected. By adding the right hand sides it becomes clear that the population does not change over time. We come up with some values for the parameters and iterate: sus[1] = 0.95; inf[1] = 0.05; rec[1] = 0; [Rho] = 0.2; [Lambda] = 0.1; tcourse = Table[{sus[i], inf[i], rec[i]}, {i, 1, 100}]; The time course looks like this: ListPlot[Transpose[tcourse]] ![enter image description here][8] The monotonously decreasing function show susceptibles, the increasing function recovered, and the remaining curve the infected. We now need to do some cleaning up of the original airport data, before we proceed to a multi-airport/city model. (*Extract the names and GPS coordinates*) rawdata = Sort[Select[airports[[All, {5, 7, 8}]], #[[1]] != "" &]][[81 ;;]]; (*These are just the coordinates*) airportcoords = rawdata[[All, {2, 3}]]; (*These are just the names. *) names = rawdata[[All, 1]]; (*Here are the names to indices*) rules = MapThread[#1 -> #2 &, {names, Range[Length[names]]}]; (*The "population" is initially set to 1 for all airports, this allows us to take different airport sizes into consideration later.*) pop = Table[1., {j, 1, Length[names]}]; routesraw = Import["~/Desktop/routes.dat", "CSV"]; (*There are many links so this takes a while*) links = Select[routesraw[[All, {3, 5}]] /. rules, NumberQ[#[[1]]] && NumberQ[#[[2]]] &]; From that we now construct (a first guess at) the coupling or adjacency matrix: couplingdummy = Table[0, {i, 1, Length[names]}, {j, 1, Length[names]}]; For[k = 1, k <= Length[links], k++, couplingdummy[[links[[k, 1]], links[[k, 2]]]] = 1; couplingdummy[[links[[k, 2]], links[[k, 1]]]] = 1]; I do know about ConstantArray, but for some reason that does not work. The first line constructs a matrix full of zeros and the second adds ones where there are links. The problem is that apparently in that dataset some airports are not linked at all. We can sort them out by: indices = Select[Table[If[Total[couplingdummy[[i]]] > 0, i], {i, 1, Length[couplingdummy]}], NumberQ]; We now delete the columns and rows of the couplingdummy matrix intermed = couplingdummy[[#]] & /@ indices; transintermed = Transpose[intermed]; coupling = transintermed[[#]] & /@ indices; Again I had a much more elegant way of doing this, with the advantage that it did not work. To speed up the following calculations I use that the coupling matrix is sparse, but I like the original too much to throw it away just yet. coulinginterm = coupling; coupling = SparseArray[coulinginterm]; We adapt our "population/airport size" vector: pop = Table[1., {j, 1, Length[indices]}]; and set the following parameters: [Rho] = 0.2; [Lambda] = 0.1; Mairports = Length[indices]; [Mu] = 0.05; $\rho$ and $lambda$ are as before. Mairports is the number of airports that we model and $\mu$ is a "migration rate". It comes from the original model which we built for different cities were it describes the migration between different cities. Here is models the "propensity to fly". We now define an effective coupling matrix. It is the adjacency matrix times the population vector (i.e. people in the catchment area of the airport). In our case the vector has all ones, so it is just the adjacency matrix. It allows us later to model more general situations. meanNN = coupling.pop; When we want to model the outbreak as populations at the positions of all airports, each of which is described by an SIR model, we need to couple lots of populations, because there are lots of airports. The following uses the sparsity of the adjacency matrix to speed up the calculation. sumind = Table[Take[Flatten[ArrayRules[coupling[[k, All]]][[All, 1]]], Length[ArrayRules[coupling[[k, All]]]] - 1], {k, 1, Mairports}]; It generates a list of all airports that are coupled/linked to a given airport. Now we are ready to write down the central equations: sus[i_, j_] := sus[i, j] = (1 - [Mu]) (sus[i - 1, j] - [Rho] sus[i - 1, j] inf[i - 1, j]) + [Mu] Total[Table[sus[i - 1, sumind[[j, u]]]*pop[[sumind[[j, u]]]], {u, 1, Length[sumind[[j]]]} ] ]/meanNN[[j]]; inf[i_, j_] := inf[i, j] = (1 - [Mu]) (inf[i - 1, j] + [Rho] sus[i - 1, j] inf[i - 1, j] - [Lambda] inf[i - 1, j]) + [Mu] Total[Table[inf[i - 1, sumind[[j, u]]]*pop[[sumind[[j, u]]]], {u, 1, Length[sumind[[j]]]} ] ]/meanNN[[j]]; rec[i_, j_] := rec[i, j] = (1 - [Mu]) (rec[i - 1, j] + [Lambda] inf[i - 1, j]) + [Mu] Total[Table[rec[i - 1, sumind[[j, u]]]*pop[[sumind[[j, u]]]], {u, 1,Length[sumind[[j]]]} ] ]/meanNN[[j]]; The terms with the Total are "migration terms" that describe the travelling behaviour of the people in the catchment area of the airports. i is the time index and j labels the airports. Next come the initial conditions: For[i = 1, i <= Mairports, i++, sus[1, i] = 1.; inf[1, i] = 0.0; rec[1, i] = 0.;] sus[1, 1] = 0.95; inf[1, 1] = 0.05; rec[1, 1] = 0.0; In the catchment areas of all airports there are only susceptibles, apart from airport number 1, which will have 5% infected people. Now we can finally iterate the whole thing: tcourse = Monitor[Table[{sus[i, j], inf[i, j], rec[i, j]}, {i, 1, 500}, {j, 1,Mairports}], ProgressIndicator[i, {0, 500}]]; Great. Let's save that just in case your notebook tends to crash at this point, just l like mine did when I was playing with this. Export["~/Desktop/SIR-tcourse.csv", tcourse]; If you wish you can now plot the time course of some of the airport catchment areas: ListPlot[Flatten[Table[{tcourse[[All, j, 1]], tcourse[[All, j, 2]], tcourse[[All, j, 3]]}, {j, 1, 200}], 1], ImageSize -> Large] ![enter image description here][9] Now that is not very helpful yet. To generate nicer plots, i.e. to normalise, we first calculate the maximal number of sick people at any of the airports: maxsick = Max[Flatten[tcourse[[All, All, 2]]]]; We then generate movie frames, and go and get some coffee.... frames = Monitor[Table[GeoRegionValuePlot[Table[GeoPosition[airportcoords[[indices[[i]]]]] -> inf[k, i]/maxsick, {i, 1, Length[indices]}], PlotStyle -> PointSize[0.003], PlotRange -> 1, ImageSize -> Full,ColorFunction -> "Rainbow"], {k, 1, 300}], ProgressIndicator[k, {0, 300}]]; Actually, you might want to get another coffee when you want to export the frames: Export["~/Desktop/SIR-frames-World.gif", frames]; Alright. That gif is a bit large to embed it into this post, but you can download it from [here][10]. All I can do is show you some frames to get an idea of how this looks: ![enter image description here][11] Of course we can look at the network structure and try to understand the pattern of infections. This command is useful: CommunityGraphPlot[AdjacencyGraph[Normal[coupling]]] ![enter image description here][12] You clearly see the communities in North America, Europe and Asia. This one is also pretty: Show[TreePlot[Subgraph[grph, ConnectedComponents[grph][[1]]], Center, PlotStyle -> Directive[Gray, Opacity[0.02]]], TreePlot[Subgraph[grph, ConnectedComponents[grph][[1]]], Center, EdgeRenderingFunction -> None]] ![enter image description here][13] We have several enhancements of this. First we can easily look at different countries individually. What if an ebola patient arrives at some airport in the US? [See simulation here][14]. (Careful 50 MBs!) There is also something we can do if we want to go the the level of cities. The main problem is that the Wolfram database does not yet have data for all streets between cities. In one of the online conferences it was said that that will be introduced in some later version, which I cannot wait to play with. Until then we have to cheat. (or use some online database; I prefer cheating.) We developed a model of the spreading of a disease in Nigeria. So we could go about this like this: Clear["Global`*"] CountryData["Nigeria", "Population"] Graphics[CountryData["Nigeria", "Polygon"]] Then get city names, coords and population: names = CityData[{All, "Nigeria"}]; citypop = Table[CityData[names[[i]], "Population"], {i, 1, Length[names]}]; citycoords = Table[CityData[names[[i]], "Coordinates"], {i, 1, Length[names]}]; Here comes the cheat. Because we don't have the streets we use Delaunay triangulation: Needs["ComputationalGeometry`"] dtri = DelaunayTriangulation[citycoords]; list = {}; Table[ Do[AppendTo[list, {i, dtri[[All, 2]][[i, j]]}], {j, 1, Length[dtri[[All, 2]][[i, All]]]}], {i, 1, Length[dtri]}]; coupling = Table[0, {i, 1, Length[names]}, {j, 1, Length[names]}]; For[i = 1, i < Length[list] + 1, i++, coupling[[list[[i]][[1]], list[[i]][[2]]]] = 1;] coulinginterm = coupling; coupling = SparseArray[coulinginterm]; which gives the following network Graphics[Join[ Table[Circle[citycoords[[i]], 0.02], {i, 1, Length[names]}], DeleteCases[ Flatten[Table[ If[coupling[[i, j]] == 1, Line[{citycoords[[i]], citycoords[[j]]}]] , {i, 1, Length[names]}, {j, 1, i}], 1], Null]]] ![enter image description here][15] The point in the middle corresponds to the airport where it all starts; then come its neighbours and then their neighbours etc. You could now animate this and change the colours to see how the disease spreads through the different layers. It would be nice if someone could implement that. There are obviously some problems, i.e. "streets" leaving the country etc, but the general idea should work. The rest is quite the same as before: (*Paramters*) [Rho] = 0.2; [Lambda] = 0.1; Mcities = Length[names]; [Mu] = 0.05; (*Initiation*) For[i = 1, i <= Mcities, i++, sus[1, i] = 1.; inf[1, i] = 0.0; rec[1, i] = 0.;] (*Starting Outbrake at the following city*) sus[1, 1] = 0.95; inf[1, 1] = 0.05; rec[1, 1] = 0.0; meanNN = coupling.citypop; sumind = Table[ Take[Flatten[ArrayRules[coupling[[k, All]]][[All, 1]]], Length[ArrayRules[coupling[[k, All]]]] - 1], {k, 1, Mcities}]; sus[i_, j_] := sus[i, j] = (1 - [Mu]) (sus[i - 1, j] - [Rho] sus[i - 1, j] inf[i - 1, j]) + [Mu] Total[ Table[sus[i - 1, sumind[[j, u]]]*citypop[[sumind[[j, u]]]], {u, 1, Length[sumind[[j]]]} ] ]/meanNN[[j]]; inf[i_, j_] := inf[i, j] = (1 - [Mu]) (inf[i - 1, j] + [Rho] sus[i - 1, j] inf[i - 1, j] - [Lambda] inf[i - 1, j]) + [Mu] Total[ Table[inf[i - 1, sumind[[j, u]]]*citypop[[sumind[[j, u]]]], {u, 1, Length[sumind[[j]]]} ] ]/meanNN[[j]]; rec[i_, j_] := rec[i, j] = (1 - [Mu]) (rec[i - 1, j] + [Lambda] inf[i - 1, j]) + [Mu] Total[ Table[rec[i - 1, sumind[[j, u]]]*citypop[[sumind[[j, u]]]], {u, 1, Length[sumind[[j]]]} ] ]/meanNN[[j]]; This time we try to work in parallel: LaunchKernels[]; tcourse = ParallelTable[{sus[i, j], inf[i, j], rec[i, j]}, {i, 1, 500}, {j, 1, Mcities}]; // AbsoluteTiming (There is something strange here. This ran in MMA9 in 6.3 seconds- I still have data from the course I taught last year. MMA10 takes ages. After the installation of MMA10 also MMA9 seems to take longer 43 seconds. Is this a bug report?). Note that this time the population sizes of the cities are taken into account and are relevant. If you run Manipulate[ Graphics[{Line[Flatten[CountryData["Nigeria", "Coordinates"], 1]], Join[Table[{ RGBColor[tcourse[[t, i, 2]], tcourse[[t, i, 1]], tcourse[[t, i, 3]]], Disk[citycoords[[i]], 0.1]}, {i, 1, Length[names]}]]}], {t, 1, 500, 1}] or poly = Graphics[Polygon[Flatten[CountryData["Nigeria", "Coordinates"], 1]], ImagePadding -> None]; Animate[ImageSubtract[ Graphics[ListDensityPlot[ Join[{{4, 3.25, 0}, {4, 14, 0}, {14, 3.25, 0}, {14, 14, 0}}, Table[{citycoords[[k]][[1]], citycoords[[k]][[2]], 1. - tcourse[[t, k, 1]]}, {k, 1, Mcities}]], InterpolationOrder -> 3, ColorFunction -> "Rainbow", PlotRange -> All, Frame -> False, PlotRangePadding -> None]], poly], {t, 1, 500, 1}, DefaultDuration -> 20.] or better infmax = Max[tcourse[[All, All, 2]]]; frames = Table[ ImageSubtract[ Graphics[ ListDensityPlot[ Join[{{4, 3.25, 0}, {4, 14, 0}, {14, 3.25, 0}, {14, 14, 0}}, Table[{citycoords[[k]][[1]], citycoords[[k]][[2]], tcourse[[t, k, 2]]/infmax}, {k, 1, Mcities}]], InterpolationOrder -> 3, ColorFunction -> "Rainbow", PlotRange -> All, Frame -> False, PlotRangePadding -> None, ColorFunctionScaling -> False]], poly], {t, 1, 500, 6}]; you get nice animations like this one: ![enter image description here][16] I have noticed that Nigeria needs to be rotated, but I hope that the idea becomes clear. I am also aware that there are many flaws in this. SIR is certainly not the best way forward to model Ebola. Any population dynamicist and/or health expert can certainly come up with an endless list of problems. The network is not perfect. For more serious applications we actually use models for the cities, i.e. street connections among close cities and airport connections among countries etc. The problem is that if we simulate between 200-20000 cities per country plus the airports, a standard laptop runs into trouble. On the bright side, we have a cluster on which this kind of larger simulations work just fine. Hope that you like this anyway, Marco [1]: http://www.st-margaret.aberdeen.sch.uk [2]: http://community.wolfram.com/groups/-/m/t/325956 [3]: http://mtbi.asu.edu/files/Mathematical_Models_to_Study_the_Outbreaks_of_Ebola.pdf [4]: http://openflights.org/data.html [5]: /c/portal/getImageAttachment?filename=Airportsall.jpg&userId=48754 [6]: /c/portal/getImageAttachment?filename=Airports-world.jpg&userId=48754 [7]: http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology [8]: /c/portal/getImageAttachment?filename=SingleSIR.jpg&userId=48754 [9]: /c/portal/getImageAttachment?filename=SIR-airportstcourse.jpg&userId=48754 [10]: https://www.dropbox.com/s/9y6d16z82qjw261/SIR-frames.gif?dl=0 [11]: /c/portal/getImageAttachment?filename=SIR-airports-frames.jpg&userId=48754 [12]: /c/portal/getImageAttachment?filename=Airports-CommNetwork.jpg&userId=48754 [13]: /c/portal/getImageAttachment?filename=SIR-networkrings.jpg&userId=48754 [14]: https://www.dropbox.com/s/0qwgmi7ks8dpsjh/SIR-USA-frames.gif?dl=0 [15]: /c/portal/getImageAttachment?filename=SIR-Nigerianetwork.jpg&userId=48754 [16]: /c/portal/getImageAttachment?filename=SIR-movie.gif&userId=48754 Marco Thiel 2014-08-22T20:18:58Z https://community.wolfram.com/groups/-/m/t/127970 I am trying to find the equations and the solution to an equation that seems to have several names: Hodgkin-Huxley Cable Equation, Propogation Equation, Wave Equation.  I am looking for the equation and solution to the action potential as it goes down an axon in Mathematica code. I am stuck with being in a wheel chair and tied to oxygen thus I cannot get to a library.  I no longer work as a professor so I have no one to ask.  So I am stuck.  I would appreciate any help Thank you Jake Jake Trexel 2013-09-22T22:06:08Z https://community.wolfram.com/groups/-/m/t/1646303 # UNET [](https://zenodo.org/badge/latestdoi/137186334) [](https://github.com/dwyl/esta/issues) ---------- ![Automated 3D muscle segmentation using UNET / RESNET using DIXON MRI data][17] A package to generate and train a UNET deep convolutional network for 2D and 3D image segmentation. Some code was based on [work][1] by [@Ali Hashmi][at0], which was also dicussed in [this post][2] The full version of the toolbox can be found on my [github page][3]. * [Information](#information) * [Install toolbox](#install-toolbox) * [Using the toolbox](#using-the-toolbox) * [Functionality](#functionality) * [Visualization](#visualization) * [Example](#example) ## Information UNET is developed for [Mathematica](https://www.wolfram.com/mathematica/). It contains the following toolboxes: - UnetCore - UnetSupport Documentation of all functions and their options is fully integrated in the Mathematica documentation. The toolbox always works within the latest version of Mathematica and does not support any backward compatibility. All code and documentation is maintained and uploaded to github using [Workbench](https://www.wolfram.com/workbench/). ## Install toolbox Install the toolbox in the Mathematica UserBaseDirectory > Applications. FileNameJoin[{$UserBaseDirectory, "Applications"}] ## Using the toolbox The toolbox can be loaded by using <<UNET` The notbook ``UNET.nb`` shows examples of how to use the toolbox on artificially generated 2D data. There are also examples how to visualize the layer of your trained network and how to visualize the training itself. ## Functionality The network supports multi channel inputs and multi class segmentation. * UNET generates a UNET convolutional network. * 2D UNET ![UNET 2D][4] * 3D UNET ![UNET 3D][5] * Loss Layers: Training the data is done using three loss layers: a SoftDiceLossLayer, BrierLossLayer and a CrossEntropyLossLayer. ![SoftDiceLossLayer, BrierLossLayer and a CrossEntropyLossLayer][6] * Convolution Blocks: The toobox contains five different convolution blocks that build up the network: [UNET][7], UResNet, [RestNet][8], UDenseNet, [DensNet][9]. ![Convolution blocks][10] * SplitTrainData splits the data and labels into training, validation and test data. ![split train Data][11] * TrainUNET trains the network. ![Train UNET][12] ## Visualization * Visualize the network and results. * Visualize the features of the layers. ![Visualize layer features][13] * Visualize the results. ![Visualize the results][14] * Animate the training process. ![UNET 2D animation][15] ![UNET 3D animation][16] ## Example * Example: 3D segmentation of lower legg muscles using MRI data. ![Automated 3D muscle segmentation using UNET / RESNET using DIXON MRI data][17] [1]: https://github.com/alihashmiii/UNet-Segmentation-Wolfram [2]: https://community.wolfram.com/groups/-/m/t/1341081?p_p_auth=w8PIeeiA [3]: https://github.com/mfroeling [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=UNET2D.PNG&userId=1332602 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=UNET3D.PNG&userId=1332602 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Loss.PNG&userId=1332602 [7]: https://arxiv.org/abs/1505.04597 [8]: https://arxiv.org/abs/1512.03385 [9]: https://arxiv.org/abs/1608.06993 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=convblocks.PNG&userId=1332602 [11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Split.PNG&userId=1332602 [12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Train.PNG&userId=1332602 [13]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Visualize1.PNG&userId=1332602 [14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Visualize2.PNG&userId=1332602 [15]: https://community.wolfram.com//c/portal/getImageAttachment?filename=amin0-v2.gif&userId=1332602 [16]: https://community.wolfram.com//c/portal/getImageAttachment?filename=amin4-v2.gif&userId=1332602 [17]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Muscle_Segmentation.jpg&userId=1332602 [at0]: https://community.wolfram.com/web/alihashmi87 Martijn Froeling 2019-04-03T20:01:26Z https://community.wolfram.com/groups/-/m/t/2029621 ![enter image description here][2] &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/a47a8852-7ac2-41d2-86f6-0dcfefb86b7a [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=mainpic.jpg&userId=2025530 Yury POLYACHENKO 2020-07-14T16:48:25Z https://community.wolfram.com/groups/-/m/t/2927764 ![Introducing the Wolfram ProteinVisualization paclet!][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main2.bmp&userId=20103 [2]: https://www.wolframcloud.com/obj/353c8f22-23af-4a49-b43c-b0b0f1645249 Soutick Saha 2023-05-31T14:38:54Z