I just register up for this course!
Where can I download the course series notebook file?

Hi Mr. Jeremy, Thanks for your feedback. Really I did via Dr. Robert's package, but it seems something went wrong or I missed some critical point if you could guide me? This is the screenshot. Maybe because I used the vital demographic as well? Regards.

Attachments:

Screenshot 2021-...jpg

Hi Manal, sorry for the delay in getting back to you. While you could go about modifying the code I provided for formatting the graphs in the first few lectures, I think I would recommend making use of the functions in Bob's package and use CompartmentModelGraph instead if you want to be able to automatically include things like death rates to your graph. It would be reinventing the wheel to certain extent to modify my code when Bob has already handled it!

The endemic equilibria can be found with Solve, the way you have been trying. I may just take a long time to get a fully symbolic solution. Unless you want to prove that an endemic equilibrium is unstable when R0 < 1, you generally don't need to determine it symbolically.

For data fitting, it's easier to do things numerically, and an endemic equilibrium can be included in the fitting data.

Regarding the asymptomatic compartment A, if counts of asymptomatic people are not available yo just don't include that compartment in the fitting data. Assuming 0 and would be a mistake.

When using standard incidence for the force of infection, the death compartment(s) are excluded from the denominator, just as you suggest. You can do as N[t]-D[t] or as S[t]+E[t]+A[t]+I[t]+R[t]+V[t].

I'll have to poke around for a data source for UAE cases and deaths.

Thanks a lot for your clarifications, recommendations, and prompt response. Regards

Is there any way to compute the endemic equilibrium points other than this code? My Wolfram Mathematica keeps running forever without any output? I wonder if there is any other solution to do so and so I will continue my analysis. Thanks in advance

Attachments:

SVEAIRS TREATMEN...nb

Really many thanks for your valuable comments. I did all the spaces as required. I wonder regarding the point of DFE where we solve all differential equations to get RHS zero. Are there any commands to find the point of DFE in wolfram?? or it is better to solve them manually (sometimes it will be very complicated to find them in a symbolic computation) any advice to evaluate them? I did the transition from S to E to have two forced due to reduction in infection based on the state of the infected individual (Asym. or Inf.) and added as well the force of infection for Vto E as well. I attached my file for your reference. Thanks again for your help and advice.

Attachments:

SVEAIRS TREATMEN...nb

Is there a way I can default any .nb attachments to "not preview" to avoid cluttering the Forum? Or should they either be shorter, not sent and sent elsewhere?

Sorry, I thought that is how I had attached my two .nb that are cluttering the forum

Thank you, I'll make the correction.

Hi!

It appears that you are using \[RightArrow], or <esc> -><esc>, instead of \[Rule], or ->, for the options to the functions, and that that's why the functions are not evaluating. There a great many instances of this problem in the notebook, and they have to be fixed one-by-one because using Edit > Find with ReplaceAll will also change the transitions that do use the right arrow character.

The format for the values of some of the options for DynamicTransmissionModel are a bit complex, and I'm addressing that by writing much better documentation in symbol reference pages, but they are not ready yet. The option

ForceOfInfection -> {\[Lambda], Subscript[\[ScriptCapitalI], a], 
  Subscript[\[ScriptCapitalI], s] {"Standard", Automatic}}

is missing a pair of curly braces and a comma, and should be coded this way

ForceOfInfection -> {\[Lambda], {Subscript[\[ScriptCapitalI], a], 
   Subscript[\[ScriptCapitalI], s]}, {"Standard", Automatic}}

I pushed a new version of both packages to the Cloud over the weekend, and one of the changes renamed the CompartmentalModelGraph option VertexColor to CompartmentColors to avoid confusion with the Polygon option VertexColors.

There are two errors in the input:

vitalModelData = 
 DynamicTransmissionModel[model, t, 
  ForceOfInfection -> {\[Lambda], \[ScriptCapitalA], \
\[ScriptCapitalI], {"Standard", Automatic}}, 
  BirthCompartments \[RightArrow] \[ScriptCapitalS]]

The first is that the infectious compartments need to be in a list by themselves, and the second is that there was one more \[RightArrow] in the last option. This code works:

vitalModelData = 
 DynamicTransmissionModel[model, t, 
  ForceOfInfection -> {\[Lambda], {\[ScriptCapitalA], \
\[ScriptCapitalI]}, {"Standard", Automatic}}, 
  BirthCompartments -> \[ScriptCapitalS]]

By the way, are you working in a notebook on the desktop or in the Wolfram Cloud? I'm wondering if there is something I should do to make it just as easy to work in either environment.

Unfortunately, same error, I did to group the infectious compartments together! is there any other error?

Attachments:

Screenshot 2021-...jpg

Dear Dr. Nachbar, Greetings. Thanks for your continuous help and support, for my model SVEAIRS including vital demographic and vaccination, I wonder regarding the treatment model data give an output percentage as shown? moreover, the ngm command gives me an error as well? any comments or suggestions? Thanks again and regards

Attachments:

SVEAIRS copy3.nb

Hello All!

Sorry for putting this up here so late, but I noticed an error I've been getting with the first notebook of this series. I don't see a population key for AdmistrativeRegion so perhaps that is why i'm getting the error so these lines of code don't render?

It would be excellent if you (Robert N) could comment on this some time (it relates to he previous post)

Many thanks for your responses.

It did, indeed, make sure I did not use up all my susceptible. For our discussions I removed another detail: in many countries we vaccinate irrespective of antibodies/ past infections, so needing a factor of approx. (1-R[t]).

While I was a Control Engineer decades ago, for this I am a “hobby epidemiologist. I have done loads of SIR modelling and am well familiar with the herd immunity that one can achieve via recovered cases and vaccination. E.g. effective reproduction number

Re[t] = k Ro S[t] = k Ro (1 – R[t] – V[t])) = 1 for herd immunity, where k is for NPIs or season. They seem like disease free equilibria to me.

But I am unclear if these are valid equilibria for NextGenerationMatrix and, if so, what parameters to use to extract them. When I flip from “your” vaccine model with S[t]*phi[t] to mine, with vt[t]. none are found. I note yours is inextricably linked to VitalDemographics while mine is not.

Which is why I sent my “too long” post /Notebook

Is there a way to only display a short summary so Notebooks do not swamp the Forum?

Computing the number of lives saved, money saved, quality adjusted life years (QALYs) gained, etc. are one of the leading reasons pharmaceutical companies build these epidemiology models. In a nutshell, the model is run without vaccination as the base case, and then for several vaccination strategies (varying age of vaccination, number of doses, assumptions about efficacy, etc.). The health and economics outcomes are computed for each strategy (including no-vaccine) and compared to each other. The results are used to choose the best strategy to propose to regulators (FDA).

The strategies are typically simulated over a 10, 25, 50, or 100 year time horizon because the results are often time-dependent. Sometimes it takes several years for the vaccination program to reach its full effect in a population.

Has the Stochastic Models video been released ?

Regarding the force of infection in age-stratified vs unstratified models, the really isn't an omission of the contract rate from the unstratified case. When one writes the transition

Transition[S, \[Beta] \[Lambda][t], I]

the interpretation of the parameter \[Beta] is up to the user, and as was mentioned in the sessions it is often a composition of several effects including probability of transmission and contact rate. If the code inserted a contact rate parameter in the force of infection for the unstratified case

\[Lambda][t] -> m I[t]

then the infection term in the equations would be

\[Beta] m S[t] I[t]

The two parameters would always appear together and a single composite parameter would suffice.

In the age stratified case, a contact matrix is used and the force of infection is

Subscript[\[Lambda], i][t] -> Sum[Subscript[M, i, j] Subscript[I, j][t], {j, nAges}]

and the infection term in the equations would be

\[Beta] Subscript[S, i][t] Sum[Subscript[M, i, j] Subscript[I, j][t], {i, nAges}]

The parameter \[Beta] would appear with different elements of the contact matrix, and a single parameter does not suffice.

It's really a matter of detail about how one wants to model a combination of effects, and of convenience.

The series materials are provided daily in the invitation link you get to join the session. You will get them there, but for now, if you have registered here is the link where you can get notebooks. Files for the series

Hopefully, I am not doing something wrong by sharing this.

Where are the study notebooks, please? I have joined very late....

Hi Ravi,

It is easier to pick the solutions you want to plot from the full list. They are in S, E, I, R order, I and R are the third and fourth.

With[{seirSolutions = 
   seirCompartments /. 
    ParametricNDSolve[seirEquations /. seirInitialConditions, seirCompartments, {t, 0, 100000},
    {\[Beta], \[Gamma], \[Sigma]}]}, 
 Manipulate[
  Show[{Plot[
     Evaluate@
      Through[seirSolutions[\[Beta], \[Gamma], \[Sigma]]][[3 ;; 4]], {t, 0, tmax}, 
     PlotRange -> {{0, tmax}, {0, ymax}}]}],
     (*paramters in model*)
     {{\[Beta], 1/2}, 0, 1}, {{\[Gamma], 1/10}, 0, 1}, {{\[Sigma], 3/4}, 0, 1}, 
  Delimiter,
    (*plot range limits*)
   {{tmax, 100, "\!\(\*SubscriptBox[\(t\), \(max\)]\)"}, 0, 200}, 
   {{ymax, 1000000, "\!\(\*SubscriptBox[\(y\), \(max\)]\)"}, 0, 1000000}, 
  SaveDefinitions -> True]]

NDSolve and ParametricNDSolve both return lists of Rules. I find it more convenient to work with those lists of Rules than just a list of their Values (right hand sides) as is done in your code. This way I work directly with the variables I need rather than some part of a list. (In general I try to avoid using Part.)

I also find it easier to solve for the variables vi rather than vi[t].

I made a couple changes to your code. In the first cell I used

seirCompartments = {\[ScriptCapitalS], \[ScriptCapitalE], \
\[ScriptCapitalI], \[ScriptCapitalR]};

and in the second cell I used

Plot[{\[ScriptCapitalS][\[Beta], \[Gamma], \[Sigma]][
     t], \[ScriptCapitalR][\[Beta], \[Gamma], \[Sigma]][t]} /. 
   seirSolutions // Evaluate, {t, 0, tmax}, 
 PlotRange -> {{0, tmax}, {0, ymax}}]

Attachments:

Kiran--SEIR example.nb

Related to the question asked, I would like to know the following: From c19Data = ResourceFunction["JHUCOVID19VaccineData"][] how do I determine what the keys are, and how do I extract a set of values, for example the time series corresponding to TotalVaccineDosesAllocated?

Thank you. It worked well. If I may trouble you again: I did following your instructions for the ResourceFunction["COVID19EpidemicData"] found in WSG14_Session1.nb but got an unexpected result (as shown in the attachment). What did do wrong?

Attachments:

COVID19EpidemicData.png

Thank you.

Hi

The c19Data = ResourceFunction["JHUCOVID19VaccineData"][]

will not load on my machine running Mathematica Desktop. It runs forever then gives a kernal dead error .

When I run it in the cloud , it runs but gives a number of warnings