Error in Model Fitting

Hello! i have been to run this model fitting code but keeps on getting these error messages as:

1. FUN must have two input arguments.
2. userFcn_ME = initEvalErrorHandler(userFcn_ME,funfcn_x_xdata{3}, ...
3. [params_fit, ~] = lsqcurvefit(obj_fun, params0, time, observed_I, [], [], options);

Find attached, the code,, Please help

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


function error = model_error(params, time, observed_I, 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 - observed_I';
end

% 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) model_error(params, time, observed_I, 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)]);

Answer 1

[Torsten]

% 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)]);

Fitted beta: 1.6778

disp(['Fitted gamma: ', num2str(gamma_fit)]);

Fitted gamma: 1.2954

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

[Abdullahi]

can we plot the curve?

[Torsten]

Included (see above).

[Abdullahi]

Thank you so much..

Let me modify the code to fit my model..

[Torsten]

Your original code could be used with "lsqnonlin".

"lsqcurvefit" is slightly different. Here, you don't return the error, but the values obtained from the simulated model.

[Abdullahi]

I don't actually know the difference between the two..

what do you recommend?

[Torsten]

Both solvers are equivalent - only the user interfaces are different.