Can you simulate the following article?(Only the first formula: malaria epidemic dynamics) article name: Control of malaria outbreak using a nonlinear robust strategy with adaptive gains

Can you simulate the following article?(Only the first formula: malaria epidemic dynamics)

article name: Control of malaria outbreak using a nonlinear robust strategy with adaptive gains

[Walter Roberson]

Yes, if I were given the values of all of the variables and of the function u1 and given boundary conditions, and it was clarified whether the derivative of S was with respect to t or if t is constant for the system.

I would probably use ode45

[af af]

I put the article file

[Walter Roberson]

Some things like still look to be missing, and it has not been clarified whether the derivative is with respect to t or not.

is still not defined. It needs to be defined before we can be certain that it is possible to use ode45.

Knowing the exact values of the constants such as is not important to answer the question asked, which was whether I could simulate that formula. I offerered an extra answer as well, namely that you could simulate the system using ode45() . I recommend you read the documentation on that.

Answer 1

[Walter Roberson]

P.R_h      = rand;        %unknown value, unknown unit
P.t        = randn() * 10; %unknown value, unknown unit

P.lambda_h = 0.2;         %per day
P.kappa    = 0.7902;      %per day
P.Beta_m   = 0.8333;      %probability
P.u_h      = 0.00004;     %per day

tspan = [0 10];
Sh0 = rand;               %unknown initial condition
[x, Sh] = ode45(@(x,Sh)Sh_fun(x,Sh,P), tspan, Sh0 );

plot(x, Sh);

function dS_h = Sh_fun(x, S_h, P)
     dS_h = P.lambda_h + P.kappa .* P.R_h - (1-u_1(P.t)).*P.Beta_m .* S_h - P.u_h .* S_h;
end

function u1t = u_1(t)
   u1t = sin(t*7*pi).^2 - exp(-t);     %function u_1 is not defined so make something up
end

Notice that the t being passed to u_1 has nothing to do with the integration: it is just some parameter whose value you did not specify. t is not the variable of integration of S_h -- if it were then there would have had to have been a in the definition of

[af af]

thank you

[af af]

Can the pid controller be set to malaria dynamics?

[Walter Roberson]

I have no idea.

[af af]

How to implement Ehd in Simulink as shown below?

Eh0=200, Ehf=0, a=0.055, t=100,

Ehd=(Eh0-Ehf)*exp(-at)+Ehf

Where is the problem in Simulink below?