Group Abstract Group Abstract

Message Boards Message Boards

Solver for COVID-19 epidemic model with the Caputo fractional derivatives

Attachments:
COVID19model.nb
POSTED BY: Alexander Trounev
19 Replies
Sort By:
Vedat Erturk
Vedat Erturk
Posted 4 years ago

Thank you for your reply. I will use your code for solving my fractional system and cite one of these references.Thank you.
POSTED BY: Vedat Erturk

Actually this code is original and it is not explained in cited papers. If you gonna use this code, then, please refer to our papers as well

  1. Mohammad, M., Trounev, A., Cattani, C.: An efficient method based on framelets for solving fractional Volterra integral equations, Entropy 2020, 22(8), 824. https://doi.org/10.3390/e22080824.

  2. Mohammad, M., Trounev, A.: On the dynamical modeling of Covid-19 involving Atangana-Baleanu fractional derivative and based on Daubechies framelet simulations, Chaos, Solitons & Fractals, 140, 2020. https://doi.org/10.1016/j.chaos.2020.110171.

  3. Mohammad, M., Trounev, A.: Fractional nonlinear Volterra–Fredholm integral equations involving Atangana–Baleanu fractional derivative: framelet applications, Advances in Difference Equations, 618, (2020). https://doi.org/10.1186/s13662-020-03042-9.

  4. Mohammad, M., Trounev, A., Cattani, C.: The dynamics of COVID-19 in the UAE based on fractional derivative modeling using Riesz wavelets simulation, Adv Differ Equ 2021, 115 (2021). https://doi.org/10.1186/s13662-021-03262-7.
POSTED BY: Alexander Trounev
Vedat Erturk
Vedat Erturk
Posted 4 years ago

Hello again, Alexander, Please see the attached code for my system. I am having an error. I would be appreciate if you help me correct my mistakes.Thanks.

Attachments:
Haar_wavelet.nb
POSTED BY: Vedat Erturk

It looks like it can not be solved with Haar wavelets. May be we need more sophisticated method since your system of equations is not trivial.

POSTED BY: Alexander Trounev
vserturk
vserturk
Posted 4 years ago

Hello Alexander,
I tried to solve another system via your code.
Please see the attached file for the solution.
I compare the solution with other two methods.
I see It's really so much different.
blue curve:wavelet method
black curve:adams method
red curve:Nuri's method
order:0.7
I need your comment.

Attachments:
275150805.nb
sample.pdf
POSTED BY: vserturk
POSTED BY: Alexander Trounev
vserturk
vserturk
Posted 4 years ago

Dear Alexander Trounev, I corrected my code with your help.Thank you. Another thing is that, If it is possible, can you please send me a paper where you have used the given haar wavelets method in the sense of caputo derivative? Because I can see that you used this method in the sense of atangana-baleanu derivative. Thank you in advance.

Kind regards

-Vedat
POSTED BY: vserturk

The usage of Haar wavelets and Caputo fractional derivative is explained in this post, while combination of Euler wavelets and Caputo fractional derivative is described, for instance, in our paper "A novel numerical method for solving fractional diffusion-wave and nonlinear Fredholm and Volterra integral equations with zero absolute error" published in Axioms.

POSTED BY: Alexander Trounev
vserturk
vserturk
Posted 4 years ago

Dear Alexander Trounev, I hope you are doing well. Regarding your code,please see the attachment for my question.

I can not get the plots of S (t) versus I (t), I (t) versus R (t), and S (t) versus R (t).Could you please help me with that?.Thank you.

Attachments:
f3fc2398-21c0-4c...nb
POSTED BY: vserturk
vserturk
vserturk
Posted 4 years ago

I tried it in a separate code since I can not do that inside the code. .Please see the attachment for my code. What can I do to get more smooth curves?

Attachments:
phase_plots.nb
phase_plots.pdf
POSTED BY: vserturk

What problem do you try to solve? It looks like you use my code on interval (t,0,30000} with number of collocation points $2^8=256$, while main dynamics takes about $t=300$ for q=99/100. I can recommend to reduce time interval to {t,0,300} and plot picture like this one enter image description here
POSTED BY: Alexander Trounev
vserturk
vserturk
Posted 4 years ago

I considered [0,30000] instead of [0,300]. Because I can observe the stability points of the system much better. Please see the attached file for my fractional order system. enter image description here

Attachment

Attachments:
S_I_R_plots.nb
image.jpg
POSTED BY: vserturk

It is nice code, but for a large interval we need to increase number of collocation points. Therefore, for 30000 we need about $2^{10}=1024$ colocation points. Then it could be problem to get solution with FindRoot.

POSTED BY: Alexander Trounev
vserturk
vserturk
Posted 4 years ago

Hello again, Alexander, Please see the attached code for my system. I am having an error. I would be appreciate if you help me correct my mistakes.Thanks.

Attachments:
2_i.nb
2_i.pdf
POSTED BY: vserturk

This post has been listed in the main resource-hub COVID-19 thread: https://wolfr.am/coronavirus in the section Computational Publications. Please feel free to add your own comment on that discussion pointing to this post ( https://community.wolfram.com/groups/-/m/t/1976589 ) so many more interested readers will become aware of your excellent work. Thank you for your contribution!
POSTED BY: EDITORIAL BOARD

enter image description here -- you have earned Featured Contributor Badge enter image description here

Your exceptional post has been selected for our editorial column Staff Picks http://wolfr.am/StaffPicks and Your Profile is now distinguished by a Featured Contributor Badge and is displayed on the Featured Contributor Board. Thank you!
POSTED BY: EDITORIAL BOARD

Thank you for your selection. Now I should make a last step to force this code run 10-100 times faster. And then we can incorporate real data to evaluate parameters for every region.
POSTED BY: Alexander Trounev
Vedat Erturk
Vedat Erturk
Posted 4 years ago

Hello Alexander,I hope you are doing fine at Corona virus times. I guess you wrote this code: https://mathematica.stackexchange.com/questions/221609/solver-for-covid-19-epidemic-model-with-the-caputo-fractional-derivatives Could you please suggest me a reference for the Haar wavelet method? Vedat
POSTED BY: Vedat Erturk

There are many papers about Haar wavelets applications. For example, method for solving ODEs with Haar wavelets described by Ü. Lepik (2009) Haar wavelet method for solving stiff differential equations, Mathematical Modelling and Analysis, 14:4, 467-481. To link to this article: http://dx.doi.org/10.3846/1392-6292.2009.14.467-481

Method for solving integral equations proposed by Ülo Lepik and Enn Tamme, Solution of nonlinear Fredholm integral equations via the Haar wavelet method, Proc. Estonian Acad. Sci. Phys. Math., 2007, 56, 1, 17–27.

POSTED BY: Alexander Trounev
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard