Drawing a heatmap of the max value of a state variable against two parameters in the system

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Bas123
Bas123 2023-4-12
评论： Bas123 2023-4-15
I am working with an epidemic ODE model and I wish to draw a heatmap of y(4) Max against the two parameters p and eta. Any help would be greatly appreciated. Thank you!!!
function dy=EpiModel(t,y)
dy = zeros(5,1);
%Model paramters
c = 0.001;
theta = 0.1134;
beta = 0.4;
p = 0.05;
eta = 0.05;
epsilon = 0.084;
gamma = 0.2;
delta = 0.011;
mu = 0.000011;
%Equations
dy(1) = theta - (p+c*beta*y(4)+mu)*y(1);
dy(2) = p*y(1) - (eta*c*beta*y(4)+mu)*y(2);
dy(3) = c*beta*y(4)*y(1) + eta*c*beta*y(4)*y(2) - (epsilon+mu)*y(3);
dy(4) = epsilon*y(3) - (gamma+delta+mu)*y(4);
dy(5) = gamma*y(4) - mu*y(5);
end
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Torsten
Torsten 2023-4-15
移动：Torsten 2023-4-15
tspan = 0:0.01:100;
y0 = [100000;0;0;1;0];
p = 0.001:0.001:0.01;
eta = 0.001:0.001:0.02;
for i = 1:numel(p)
for j = 1:numel(eta)
[~,Y] = ode45(@(t,y)EpiModel(t,y,p(i),eta(j)),tspan,y0);
maxy4(i,j) = max(Y(:,4));
end
end
contourf(eta,p,maxy4)
colorbar
function dy=EpiModel(t,y,p,eta)
...
end

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