% Define the time vector and observed data
time = [0, 1, 2, 3, 4, 5]; % Example time points
observed_I = [10, 15, 20, 25, 30, 35]; % Example observed infectious data
% Initial guess for parameters
beta_guess = 0.3;
gamma_guess = 0.1;
params0 = [beta_guess, gamma_guess];
% Initial conditions
S0 = 1000; % Initial number of susceptible individuals
I0 = observed_I(1); % Initial number of infectious individuals
R0 = 0; % Initial number of recovered individuals
y0 = [S0; I0; R0];
% Define the objective function for fitting
obj_fun = @(params,time) model_error(params, time, y0);
% Perform the curve fitting
options = optimoptions('lsqcurvefit', 'Display', 'off');
[params_fit, ~] = lsqcurvefit(obj_fun, params0, time, observed_I, [], [], options);
% Display the fitted parameters
beta_fit = params_fit(1);
gamma_fit = params_fit(2);
disp(['Fitted beta: ', num2str(beta_fit)]);
disp(['Fitted gamma: ', num2str(gamma_fit)]);
hold on
plot(time,observed_I,'o')
plot(time,model_error(params_fit,time,y0))
hold off
grid on
function error = model_error(params, time, y0)
beta = params(1);
gamma = params(2);
% Solve the differential equations
[~, y] = ode45(@(t, y) sir_model(t, y, beta, gamma), time, y0);
% Extract the infectious data from the solution
model_I = y(:, 2);
% Compute the error as the difference between model and observed data
error = model_I.';
end
function dydt = sir_model(t, y, beta, gamma)
S = y(1);
I = y(2);
R = y(3);
N = S + I + R; % Total population
dSdt = -beta * S * I / N;
dIdt = beta * S * I / N - gamma * I;
dRdt = gamma * I;
dydt = [dSdt; dIdt; dRdt];
end
