I need code of matlab that plot the bifurcation of SEIR with one delay tau, I need to plot the bifurcation in 2d and 3d.
The code uses the built-in `ode45` solver to simulate the model equations, and the `plot` function to visualize the results in both 2D and 3D.
```matlab
% SEIR model with one delay tau
% Parameters
beta = 0.5; % Transmission rate
gamma = 0.1; % Recovery rate
alpha = 0.05; % Incubation rate
delta = 0.1; % Delayed transmission rate
tau = 1; % Delay
% Time span
tspan = 0:0.1:100;
% Initial conditions
S0 = 0.9;
E0 = 0.05;
I0 = 0.04;
R0 = 0.01;
y0 = [S0, E0, I0, R0];
% Function handle for the SEIR model
seir_model = @(t, y) [
-beta * y(1) * y(3) - delta * y(1) * y(3 - tau);
beta * y(1) * y(3) + delta * y(1) * y(3 - tau) - alpha * y(2);
alpha * y(2) - gamma * y(3);
gamma * y(3)
];
% Solve the ODEs
[t, y] = ode45(seir_model, tspan, y0);
% Extract variables
S = y(:, 1);
E = y(:, 2);
I = y(:, 3);
R = y(:, 4);
% Plot bifurcation diagram in 2D
figure;
plot(t, I);
xlabel('Time');
ylabel('Infected (I)');
title('Bifurcation Diagram - Infected (I) vs. Time');
% Plot bifurcation diagram in 3D
figure;
plot3(S, I, R);
xlabel('Susceptible (S)');
ylabel('Infected (I)');
zlabel('Recovered (R)');
title('Bifurcation Diagram - SIR Model');
```
Adjust the parameter values, period, and initial conditions according to your specific requirements. The code will generate two separate figures: one for the bifurcation diagram in 2D (Infected vs. Time) and another for the bifurcation diagram in 3D (Susceptible, Infected, and Recovered).
Hope it helps: credit AI
Mohamed H Hassan, Based on your requirements, I wrote this code for your SIER with user-set parameters. It displays results in visual diagrams, providing a quick tool to understand the dynamics. In case you have quesitons, ask me on WhatsApp further about your requirements; https://wa.me/+923440907874
this code
function seir_bifurcation()
% Set up parameter ranges
beta_range = linspace(0.1, 1.5, 100);
tau_range = linspace(1, 10, 100);
% Initialize matrices to store results
X = zeros(length(beta_range), length(tau_range));
Y = zeros(length(beta_range), length(tau_range));
Z = zeros(length(beta_range), length(tau_range));
% Loop through parameter values
for i = 1:length(beta_range)
for j = 1:length(tau_range)
% Set parameters
beta = beta_range(i);
tau = tau_range(j);
% Solve SEIR equations numerically
[t, sol] = ode45(@(t, y) seir_equations(t, y, beta, tau), [0, 100], [0.9, 0.1, 0.0, 0.0]);
% Store results
X(i, j) = beta;
Y(i, j) = tau;
Z(i, j) = sol(end, 1); % Store the final value of S
end
end
% 2D Bifurcation Plot
figure;
contourf(Y, X, Z, 20, 'LineColor', 'none');
colorbar;
title('SEIR Bifurcation (2D)');
xlabel('Time Delay (\tau)');
ylabel('\beta');
xlim([min(tau_range), max(tau_range)]);
ylim([min(beta_range), max(beta_range)]);
% 3D Bifurcation Plot
figure;
surf(Y, X, Z, 'EdgeColor', 'none');
colorbar;
title('SEIR Bifurcation (3D)');
xlabel('Time Delay (\tau)');
ylabel('\beta');
zlabel('Susceptible (S)');
xlim([min(tau_range), max(tau_range)]);
ylim([min(beta_range), max(beta_range)]);
end
function dydt = seir_equations(t, y, beta, tau)
% SEIR equations with time delay
S = y(1);
E = y(2);
I = y(3);
R = y(4);
% Time-delayed infection term
I_delayed = interp1(t - tau, max(0, y(3)), t, 'linear', 0);
% SEIR differential equations
dSdt = -beta * S * I_delayed;
dEdt = beta * S * I_delayed - E;
dIdt = E - I;
dRdt = I;
dydt = [dSdt; dEdt; dIdt; dRdt];
end
Credit OPENAI
To understand the bifurcation diagram for continuous systems you can look at this video, there is also a code in the description https://www.youtube.com/watch?v=OXTS-d9HdB4