Parse error at observed data (2024)

Error in solution>objectiveFunction (line 50)
[t, y] = ode45(@(t, y) SITRModel(t, y, beta, gamma, delta, alpha, lambda, mu, N), tspan, y0);

Error in fminsearch (line 209)
fv(:,1) = funfcn(x,varargin{:});

% Define the SITR model as a system of ODEs

function dydt = SITRModel(t, y, beta, gamma, delta, alpha, lambda, mu, N)

S = y(1); % Susceptible

I = y(2); % Infectious

Q = y(3); % Isolated

T = y(4); % Treated

R = y(5); % Recovered

dSdt = -beta * S * I / N;

dIdt = beta * S * I / N - gamma * I - delta * I - alpha * I;

dQdt = delta * I - lambda * Q;

dTdt = alpha * I - mu * T;

dRdt = gamma * I + lambda * Q + mu * T;

dydt = [dSdt; dIdt; dQdt; dTdt; dRdt];

end

% Observed data (replace with actual data)

% Format: [time, infected, isolated, treated, recovered]

observed_data = [0, 1, 0, 0, 0;

10, 50, 10, 5, 15;

20, 100, 25, 15, 50;

30, 150, 35, 30, 100;

40, 200, 50, 50, 200];

% Initial conditions

N = 1000000; % Total population

S0 = N - 1;

I0 = 1;

Q0 = 0;

T0 = 0;

R0 = 0;

y0 = [S0, I0, Q0, T0, R0];

% Time points for the solution (based on observed data)

tspan = observed_data(:, 1);

% Define the objective function for optimization

function error = objectiveFunction(params,tspan,SITRModel,y0,N,observed_data)

beta = params(1);

gamma = params(2);

delta = params(3);

alpha = params(4);

lambda = params(5);

mu = params(6);

% Solve the ODE with the current parameters

[t, y] = ode45(@(t, y) SITRModel(t, y, beta, gamma, delta, alpha, lambda, mu, N), tspan, y0);

% Interpolate the model's output to match the time points of observed data

model_values = interp1(t, y(:, 2:5), tspan);

% Calculate the sum of squared errors

error = sum((model_values - observed_data(:, 2:5)).^2, 'all');

end

% % Initial guess for parameters [beta, gamma, delta, alpha, lambda, mu]

initial_params = [0.3, 0.1, 0.05, 0.02, 0.1, 0.1];

initial_params = initial_params + rand(1,6)/100

% % Perform optimization using fminsearch

options = optimset('MaxFunEvals', 1000, 'MaxIter', 1000);

optimized_params = fminsearch(@(params)objectiveFunction(params,tspan,@SITRModel,y0,N,observed_data), initial_params, options);

% Display optimized parameters

disp('Optimized parameters:');

disp(optimized_params);

% optimized_params = initial_params;

% Solve the system with optimized parameters

[t, y] = ode45(@(t, y) SITRModel(t, y, optimized_params(1), optimized_params(2), optimized_params(3), optimized_params(4), optimized_params(5), optimized_params(6), N), linspace(0, 160, 100), y0);

% Plot the solution with optimized parameters

figure;

plot(t, y(:, 1), 'b-', t, y(:, 2), 'r-', t, y(:, 3), 'g-', t, y(:, 4), 'm-', t, y(:, 5), 'k-');

legend('Susceptible', 'Infectious', 'Isolated', 'Treated', 'Recovered');

title('Fitted SITR Model for COVID-19');

xlabel('Days');

ylabel('Population');

grid on;

% Observed data (replace with actual data)

% Format: [time, infected, isolated, treated, recovered]

observed_data = [

0, 1, 0, 0, 0;

10, 50, 10, 5, 15;

20, 100, 25, 15, 50;

30, 150, 35, 30, 100;

40, 200, 50, 50, 200

];

% Initial conditions

N = 1000000; % Total population

S0 = N - 1;

I0 = 1;

Q0 = 0;

T0 = 0;

R0 = 0;

y0 = [S0, I0, Q0, T0, R0];

% Time points for the solution (based on observed data)

tspan = observed_data(:, 1);

% Initial guess for parameters [beta, gamma, delta, alpha, lambda, mu]

initial_params = [0.3, 0.1, 0.05, 0.02, 0.1, 0.1];

objectiveFunction(initial_params,y0,N,observed_data)

% Perform optimization using fminsearch

options = optimset('MaxFunEvals', 10000, 'MaxIter', 10000);

%optimized_params = fminsearch(@(params)objectiveFunction(params,y0,N,observed_data), initial_params, options);

optimized_params = fmincon(@(params)objectiveFunction(params,y0,N,observed_data), initial_params, [],[],[],[],zeros(6,1),[],[],options);

% Display optimized parameters

disp('Optimized parameters:');

disp(optimized_params);

objectiveFunction(optimized_params,y0,N,observed_data)

% Solve the system with optimized parameters

[t, y] = ode15s(@(t, y) SITRModel(t, y, optimized_params,N), linspace(0,160,100), y0,odeset('RelTol',1e-9,'AbsTol',1e-9));

% Plot the solution with optimized parameters

figure;

plot(t, y(:, 1), 'b-', t, y(:, 2), 'r-', t, y(:, 3), 'g-', t, y(:, 4), 'm-', t, y(:, 5), 'k-');

legend('Susceptible', 'Infectious', 'Isolated', 'Treated', 'Recovered');

title('Fitted SITR Model for COVID-19');

xlabel('Days');

ylabel('Population');

grid on;

% Define the objective function for optimization

function error = objectiveFunction(params,y0,N,observed_data)

% Solve the ODE with the current parameters

[t, y] = ode15s(@(t, y) SITRModel(t, y, params,N), observed_data(:,1), y0,odeset('RelTol',1e-9,'AbsTol',1e-9));

% Calculate the sum of squared errors

error = sum((y(:,2:5) - observed_data(:,2:5)).^2, 'all');

end

% Define the SITR model as a system of ODEs

function dydt = SITRModel(t, y, params,N)

beta = params(1);

gamma = params(2);

delta = params(3);

alpha = params(4);

lambda = params(5);

mu = params(6);

S = y(1); % Susceptible

I = y(2); % Infectious

Q = y(3); % Isolated

T = y(4); % Treated

R = y(5); % Recovered

dSdt = -beta * S * I / N;

dIdt = beta * S * I / N - gamma * I - delta * I - alpha * I;

dQdt = delta * I - lambda * Q;

dTdt = alpha * I - mu * T;

dRdt = gamma * I + lambda * Q + mu * T;

dydt = [dSdt; dIdt; dQdt; dTdt; dRdt];

end