This code is incorrect, so I need to correct it to plot a bifurcation
Define the DDE function
function ddefunc
% Define parameters
kappa = 0.1; % kappa
eta = 0.2; % eta
theta = 0.1; % theta
epsilon = 0.01; % epsilon
sigma = 0.05; % sigma
phi = 0.02; % phi
xi = 1; % delay value
% Define the DDEs
ddefun = @(t, y, Z) [kappa - eta*Z(3,1)*y(1)*exp(-kappa*xi) - (kappa + phi)*y(1); % dS/dt
eta*Z(3,1)*y(1)*exp(-kappa*xi) - (theta + kappa)*y(2); % dE/dt
theta*y(2) - (epsilon + sigma + kappa)*y(3); % dI/dt
sigma*y(3) + phi*y(1) - kappa*y(4)]; % dR/dt
% Solve the DDE
sol = dde23(ddefun, xi, [0.99, 0.01, 0, 0], [0, 50]);
% Solve DDE for different xi values and plot bifurcation
xi_values = linspace(0, 0.5, 50); % Range of delay values
max_I = zeros(size(xi_values)); % To store max I values
for i = 1:length(xi_values)
xi = xi_values(i);
sol = dde23(ddefun, xi, [0.99, 0.01, 0, 0], [0, 50]);
max_I(i) = max(sol.y(3, :)); % Max value of I(t)
end
% Plot bifurcation diagram
figure;
plot(xi_values, max_I, 'b', 'LineWidth', 2);
xlabel('Delay \xi');
ylabel('Max Infectious Population I_{max}');
title('Bifurcation Diagram of SEIR Model with Delay');
grid on;
end
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