How to solve SIR model with using DTM (Differential Transform Method)

I am trying to use dtm for solving SIR model, Although my code is run but I think the DTM part is wrong. I need help for DTM part

here is my code

function sir_model_dtm()

% Parameters
alpha = 0.3;    % Infection rate
beta = 0.1;     % Recovery rate
N = 1000;       % Total population
I0 = 1;         % Initial number of infected individuals
R0 = 0;         % Initial number of recovered individuals
S0 = N - I0 - R0; % Initial number of susceptible individuals

% Time parameters
T = 100;        % Total simulation time
dt = 1;         % Time step

% Initialize arrays to store results
S = zeros(1, T);
I = zeros(1, T);
R = zeros(1, T);

% Initial conditions
S(1) = S0;
I(1) = I0;
R(1) = R0;

% Simulate the SIR model using DTM
for t = 2:T
    % Compute new values
    S(t) = S(t-1) - alpha*S(t-1)*I(t-1)/N * dt;
    I(t) = I(t-1) + (alpha*S(t-1)*I(t-1)/N - beta*I(t-1)) * dt;
    R(t) = R(t-1) + beta*I(t-1) * dt;
end

% Plot the results
t = 0:dt:T-dt;
plot(t, S, 'b', t, I, 'r', t, R, 'g', 'LineWidth', 2);
legend('Susceptible', 'Infectious', 'Recovered');
xlabel('Time');
ylabel('Number of individuals');
title('SIR Model');

end

[Sam Chak]

Hi @mohammad amin akhlaghi,

Providing the mathematical formulas for Differential Transform Method would be helpful, as it saves users from having to search for it online.

[William Rose]

@Sam Chak, thank you.

Answer 1

[Athanasios Paraskevopoulos]

function sir_model_dtm()
    % Parameters
    alpha = 0.3;    % Infection rate
    beta = 0.1;     % Recovery rate
    N = 1000;       % Total population
    I0 = 1;         % Initial number of infected individuals
    R0 = 0;         % Initial number of recovered individuals
    S0 = N - I0 - R0; % Initial number of susceptible individuals
    
    % Time parameters
    T = 100;        % Total simulation time
    dt = 1;         % Time step
    
    % Initialize arrays to store results
    S = zeros(1, T);
    I = zeros(1, T);
    R = zeros(1, T);
    
    % Initial conditions
    S(1) = S0;
    I(1) = I0;
    R(1) = R0;
    
    % Simulate the SIR model using DTM
    for t = 2:T
        % Current values
        S_curr = S(t-1);
        I_curr = I(t-1);
        R_curr = R(t-1);
        
        % Compute intermediate values using DTM (predictor step)
        S_inter = S_curr - alpha * S_curr * I_curr / N * dt;
        I_inter = I_curr + (alpha * S_curr * I_curr / N - beta * I_curr) * dt;
        R_inter = R_curr + beta * I_curr * dt;
        
        % Compute new values (corrector step)
        S(t) = S_curr - 0.5 * dt * (alpha * S_curr * I_curr / N + alpha * S_inter * I_inter / N);
        I(t) = I_curr + 0.5 * dt * ((alpha * S_curr * I_curr / N - beta * I_curr) + (alpha * S_inter * I_inter / N - beta * I_inter));
        R(t) = R_curr + 0.5 * dt * (beta * I_curr + beta * I_inter);
    end
    
    % Plot the results
    t = 0:dt:T-dt;
    plot(t, S, 'b', t, I, 'r', t, R, 'g', 'LineWidth', 2);
    legend('Susceptible', 'Infectious', 'Recovered');
    xlabel('Time');
    ylabel('Number of individuals');
    title('SIR Model');
end