Can anyone help me in fitting a SVEAIHR epidemic model to the observe data please?

I want to fit SVEAIHR epidemic model to a COVID-19 data which has second waves. I want to fit the infection(I) of the model to the daily new cases in the data(column highlighted with yellow colour). Data attached here please.

[Steven Lord]

Reopening because I think there is some relevant information in the SimBiology documentation that could help this user.

Answer 1

[Florian Augustin]

Hi Sonam,

Following up on Steven's comment, here are a few general links that may be helpful for how to fit models to data in SimBiology.

A prerequisite for using SimBiology would be to build a SimBiology model of your SVEAIHR model. The documention for model building in Simbiology may be a good starting point, if your model is not already in SimBiology. Here is a simple example for how to construct a simple model. You can also use the SimBiology Model Builder app to build your model without having to write any code.

To fit the model to your data, you can use SimBiology parameter estimation functions, or use the SimBiology Model Analyzer app to fit the model to data. Here is a collection of examples for different estimation functionalities in SimBiology.

Admittedly, those are a lot of links and information. Feel free to follow up on this thread here if you have specific questions about SimBiology.

I am not sure if this is relevant to your question, but I just wanted to mention that Matlab also has other functions that may be of interest. If you would like to fit a general curve (without using a SimBiology model) to your data, you could take a look at the Curve Fitting toolbox.

Hope this helps,

-Florian

[Florian Augustin]

Hi,

I just saw that there are two examples for SimBiology SEIR models for COVID-19 on File Exchange and wanted to share the link here. The link also lists the corresponding publications.

By means of one of those examples, here is how you would fit a model to data using SimBiology. You can open the model in the Model Analyzer app by typing

simBiologyModelAnalyzer Covid19_SEIR_Lin.sbproj

on the Matlab command line (you can inspect the model by clicking on the Model Builder button in the toolstrip of the Model Analyzer app). Within the Model Analyzer app you can add a new Program -> Fit Data to perform parameter estimation for the model. The program will ask you to import data first, and you can import the Excel table by selecting "Load Data From File". After importing the data, the "Fit Data" program opens and you can configure it following along with this example for how to use the SimBiology Model Analyzer app to fit the model to data.

-Florian

[Sagar Karmakar]

Hi,

I am trying to build a Lotka-Volterra predator-prey model using simBiology app in MATLAB, for example

X'=r*X - beta*X*Y

Y'=c*beta*X*Y - mu*Y

But I can't understand how I introduce parameters (beta) and (c*beta) in the reaction (as there are only one reaction from X to Y).

Please help me!

[Florian Augustin]

Hi Sagar,

you could take a look at the Lotka-Volterra example that is shipping with SimBiology:

% Load the SimBiology model in the MATLAB Command Window
modelObj = sbmlimport("lotka");

% Open the model in the SimBiology Model Builder
% (assuming the app is not already open; otherwise
%  import the model from within the app: click on 
%  Model button and select "Import Model from MATLAB")
simbiology(modelObj);

This model is slightly different than the equations you posted, but it will give you an idea how to create your model. If you are new to SimBiology, check out the documention for model building in Simbiology to get started.

I hope this helps,

Florian

[Sagar Karmakar]

d(y1)/dt = 1/unnamed*(Reaction1 - Reaction2)

d(y2)/dt = 1/unnamed*(Reaction2 - Reaction3)

d(z)/dt = 1/unnamed*(Reaction3)

This is the model equation for Lotka-Volterra example in SimBiology app where outflow from first equation and inflow in second equation both are reaction2 (c2*Y1*Y2) but in my case they are defferent. I also read the documention for model building in Simbiology but no hint there for the type of model I want to build. Can I build these type of models where reaction fluxes are not same (inflow and outflow fluxes)?

Please help me

[Florian Augustin]

Hi,

SimBiology has two ways of defining differential equations: reactions and rate rules. Below is an example how you could set up your model (using MATLAB R2022b, but you can use earlier versions as well).

% Create model.
model = sbiomodel("prey-predator");

% Create prey and predator species.
environment = addcompartment(model, "environment", 1);
addspecies(environment, "Prey"    , 10);
addspecies(environment, "Predator", 10);

% Create parameters: r, beta, c, mu.
addparameter(model, "r"   , 10);
addparameter(model, "beta", 1);
addparameter(model, "c"   , 0.1);
addparameter(model, "mu"  , 2);

Here is how you can add the dynamics using reactions with mass action kinetic laws and custom reaction rates:

% Add reactions for proliferation and death of prey
prolifPrey = addreaction(model, "Prey -> 2 Prey");
prolifPreyKL = addkineticlaw(prolifPrey, "MassAction");
prolifPreyKL.ParameterVariableNames = "r";
deathPrey = addreaction(model, "Prey -> null");
deathPrey.ReactionRate = "beta*Prey*Predator";

% Add reactions for proliferation and death of predators
prolifPredator = addreaction(model, "null -> Predator");
prolifPredator.ReactionRate = "c*beta*Prey*Predator";
deathPredator = addreaction(model, "Predator -> null");
deathPredatorKL = addkineticlaw(deathPredator, "MassAction");
deathPredatorKL.ParameterVariableNames = "mu";

Alternatively, you can define dynamics using rate rules:

% Alternative: using rate rules.
% addrule(model, "Prey = r*Prey - beta*Prey*Predator", "rate");
% addrule(model, "Predator = c*beta*Prey*Predator - mu*Predator", "rate");

You can simulate and plot the results using sbiosimulate (or a SimFunction) and sbioplot:

simData = sbiosimulate(model);
sbioplot(simData);

Hope this helps,

Florian