Help with coding a model

Greetings,

I am currently trying to simulate an SI (SIR) model but everytime I get a new error and I do not know how to solve it from now on, could any one please help me?

The model is simple as the following:

With beta = 0.007

gamma = 0.01

L = 80

And

Sigma = 0.115129254649702

I tried using Euler method and ode45 but with no luck, I am a bit confused on how to discretize just over time and inside the integral I should descritize over space

Here is my current code

syms x

L=80;

y=[0 L];

j = [0,L];

days = 10;

tspan = [1 10];

gamma=10^-2;

R_0 = 0.7;

beta=R_0*gamma;

epsilon = 0.0001;

sigma = -log(epsilon)/L;

Z0 = 0.2;

S0 = 1 - Z0;

[t,Z] = ode45(@(t,Z) odefun(Z,x,y,L,sigma,beta,gamma,days),tspan,Z0);

grid on;

hold on

function dZdt = odefun(Z,x,y,L,sigma,beta,gamma,days)

dZdt = zeros(L,days);

dZdt = beta*(1-Z)*int(exp(-sigma*abs(x-y))*Z(y),y,0,L) - gamma*Z;

end

Thank you in advance!

Have a nice day

Answer 1

[Davide Masiello]

I think this could be the solution to your problem

% Parameters
L       = 80;
gamma   = 1e-2;
R_0     = 0.7;
beta    = R_0*gamma;
epsilon = 0.0001;
sigma   = -log(epsilon)/L;

% Time discretization
days    = 10;
tspan   = [1 days];

% Space discretization
y       = linspace(0,L,100); 

% Intial conditions 
z0      = 0.2*ones(size(y));

[t,Z] = ode45(@(t,z) odefun(t,z,y,sigma,beta,gamma),tspan,z0);

plot(y,Z) % plot of Z vs space at various times
xlabel('y')
ylabel('Z')
legend([repmat('t = ',length(t),1),num2str(t)],'Location','EastOutside')

function dzdt = odefun(t,z,y,sigma,beta,gamma)
xmy  = abs(y-y');
dzdt = beta*(1-z).*trapz(y,exp(-sigma*xmy).*z',2)-gamma*z;
end

[iheb kharab]

Hi Davide,

Yes, this is exactly what I was looking for! Thank you so much.

Kind regards,

Iheb