SIR model - Solver to fit pre-existing data possible? If so, how would one do that?

Question

Zach 2022-12-9

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1874492-sir-model-solver-to-fit-pre-existing-data-possible-if-so-how-would-one-do-that

回答： Neelanshu 2023-10-5

Hello. For a school project, I am tasked with fitting a SIR model to some pre-existing data of cases. The suggested process to accomplish this, as described by my instructor, is to tweak the transmission rate, recovery rate, and starting percentage manually until the curve fits the values.

I am asking if it is instead possible to create a solver that fits this pre-existing data. Importantly, the data provided does not have a model that would fit it perfectly.

Here is the code provided by my instructor:

%% SIR base model, calibrate -- United States data

% This script models the spread and recovery of a disease using the SIR

% model. It also plots real data to help calibrate the parameters.

%

% Model inspired by this video: https://www.youtube.com/watch?v=k6nLfCbAzgo

% Data from: https://ourworldindata.org/coronavirus-data

%

% Real-world data is passed in to figure 2. User can then tweak transm and

% recov to try to match the real data

%% Parameters

% tweak these three to calibrate

transm = 13.00; % transmission rate

recov = 12.825; % recovery rate

start_scale = 15; % fudge factor to account for many early cases not being reported

% Real-world data

r_days = 1:7:36;

r_cases = [34,287,2988,13963,27103,30613]; % Pre-existing data

r_Pop = 33.05E7; % Actual population

% adjusted for model

Pop = 1; % read numbers as a fraction. Total Population = 100%

I_start = r_cases(1)/r_Pop*start_scale; % the starting percentage of infected people

n_days = 180; % # of days to simulate

%% Pre-allocate variables

% in each category, there is one index for each day

I = zeros(n_days,1);

S = I;

R = I;

% fill in starting value

I(1) = I_start;

S(1) = Pop - I_start;

R(1) = 0;

%% Run simulation, day-by-day

for day = 2:n_days

% compute changes

del_S = -transm * S(day-1) * I(day-1);

del_R = recov * I(day-1);

del_I = -del_S - del_R;

% update values

S(day) = S(day-1) + del_S;

I(day) = I(day-1) + del_I;

R(day) = R(day-1) + del_R;

end

%% Plot results

x = 1:n_days;

% time series of just I and the real-world data -- zoomed in

figure(3)

hold on

plot(x,I,'b-','LineWidth',3)

plot(r_days,r_scaled,'ro','MarkerSize',15)

xlim([0,max(r_days)]) % zoom in to known data domain

xlabel('Day','FontSize',16)

ylabel('New cases','FontSize',16)

title(words,'FontSize',18)

Thank you!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Neelanshu 2023-10-5

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1874492-sir-model-solver-to-fit-pre-existing-data-possible-if-so-how-would-one-do-that#answer_1326649

Hi Zach,

I understand that you are facing an issue in creating a solver to fit preexisting data, given that no optimal SIR model fits the data.

You can try “fminsearch” function which is a nonlinear programming solver that find the minimum of a problem. Please refer to the below documentation to know more about “fminsearch” function:

https://www.mathworks.com/help/matlab/ref/fminsearch.html?searchHighlight=fminsearch%28&s_tid=srchtitle_support_results_1_fminsearch%2528

I have implemented the following and obtained transm, recov and start_scale as 13.6021, 12.6324 and 15.0049 respectively. I have assumed that real world cases will be normalized by population.

var = [ I S R];

initialParams = [transm recov start_scale];

data = r_cases/r_Pop;

objectiveFunction = @(params) myObjectiveFunction(params, data, var);

% Set the options for the solver

options = optimset('Display', 'iter', 'MaxIter', 1000, 'TolFun', 1e-6);

% Run the solver to fit the data

fittedParams = fminsearch(objectiveFunction, initialParams, options);

% Display the fitted parameters

disp('Fitted Parameters:');

disp(fittedParams);

% Define the objective function

function error = myObjectiveFunction(params, data, var)

% Extract the parameters

param1 = params(1);

param2 = params(2);

param3 = params(3);

% Generate the model predictions using the parameters

% Modify this part according to your model

modelPredictions = myModelFunction(param1, param2, param3,var);

% Calculate the error between the model predictions and the observed data

error = sum((modelPredictions([1 8 15 22 29 36],1) - data').^2);

end

% Define your model function

function modelPredictions = myModelFunction(transm, recov, start_scale, var)

% Modify this function according to your model

% Use the provided parameters to generate the model predictions

% For example:

I = var(1);

S = var(2);

R = var(3);

for day = 2:180

% compute changes

del_S = -transm * S(day-1) * I(day-1);

del_R = recov * I(day-1);

del_I = -del_S - del_R;

% update values

S(day) = S(day-1) + del_S;

I(day) = I(day-1) + del_I;

R(day) = R(day-1) + del_R;

end

modelPredictions = [I' S' R'];

end

Hope it helps,

Regards,

Neelanshu

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

SIR model - Solver to fit pre-existing data possible? If so, how would one do that?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

SIR model - Solver to fit pre-existing data possible? If so, how would one do that?

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

WeChat

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

0 个评论
显示 -2更早的评论隐藏 -2更早的评论