pid for dynamic malaria

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af af
af af 2021-1-21
回答： Sam Chak 2022-8-20
Can the pid controller be set to malaria dynamics?
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af af
af af 2021-1-24
i put [T,Y]=ode45(@malariaSEIRS,tspan,y0);
but it still gives an error
Walter Roberson
Walter Roberson 2021-1-24
You appear to have functions named u1 and u2 and u3 that each take t as a parameter, but you have not posted the code for those functions.

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回答（1 个）

Sam Chak
Sam Chak 2022-8-20
Ran in:
Hi @af af
Not sure what are PID controllers for the Malaria dynamics. However, by the mathematical manipulation, you can probably propose as shown below to keep the disease spread under control.
tspan = [0 10];
y0 = zeros(1, 7);
[T, Y] = ode45(@malariaSEIRS, tspan, y0);
plot(T, Y), grid, xlabel('Days')
legend('S_h', 'E_h', 'I_h', 'R_h', 'S_v', 'E_v', 'I_v', 'location', 'East')
Y(end, :)
ans = 1×7
0.0001 1.5163 0.4067 0.0021 0.9990 125.2982 0.8853
function dydt = malariaSEIRS(t, y)
dydt = zeros(7, 1);
% parameters
phi = 0.502;
epsilon = 0.2;
beta = 0.8333;
landa = 0.09;
muh = 0.00004;
muv = 0.1429;
k = 0.7902;
a1 = 1/17;
a2 = 1/18;
lambdah = 0.2;
lambdav = 1000;
tau = 0.01 - 0.7;
psi = 0.05;
b = 0.005;
p = 0.25;
Sh = 1100;
Eh = 200;
Ih = 400;
Rh = 0;
Sv = 800;
Ev = 250;
Iv = 80;
Nh = Sh + Eh + Ih + Rh;
% Nv = Sv + Ev + Iv;
betam = beta*epsilon*phi*Iv/Nh;
landav = landa*epsilon*phi*Ih/Nh;
% states
Sh = y(1);
Eh = y(2);
Ih = y(3);
Rh = y(4);
Sv = y(5);
Ev = y(6);
Iv = y(7);
% u1, u2, u3
k3 = 1; % adjust this parameter
u3 = ((k3 - muv)*Iv + a2*Ev)/p;
u2 = 0;
k1 = 1; % adjust this parameter
u1 = (- (k1 - p*u3 - muv - 1*landav)*Sv - lambdav)/landav;
% Malaria dynamics
dydt(1) = lambdah + (k*Rh) - (1 - u1)*betam*Sh - muh*Sh;
dydt(2) = (1 - u1)*betam*Sh - (a1 + muh)*Eh;
dydt(3) = a1*Eh - (b + tau*u2)*Ih - (psi + muh)*Ih;
dydt(4) = (b + tau*u2)*Ih - (k + muh)*Rh;
dydt(5) = lambdav - (1 - u1)*landav*Sv - p*u3*Sv - muv*Sv;
dydt(6) = (1 - u1)*landav*Sv - p*u3*Ev - (a2 + muv)*Ev;
dydt(7) = a2*Ev - p*u3*Iv - muv*Iv;
end

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