SIR model using fsolve and Euler 3PDF

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Faraz Vossoughian
Faraz Vossoughian 2020-4-15
评论： Ameer Hamza 2020-4-16
Hi ive been asked to solve SIR model using fsolve command in MATLAB, and Euler 3 point backward. Im really confused on how to proceed, please help. This is what i have so far. I created a function for 3PDF schme but im not sure how to proceed with fsolve and solve the system of nonlinear odes. The SIR model is shown as and 3Dpf scheme is formulated as
clc
clear all
gamma=1/7;
beta=1/3;
ode1= @(R,S,I) -(beta*I*S)/(S+I+R);
ode2= @(R,S,I) (beta*I*S)/(S+I+R)-I*gamma;
ode3= @(I) gamma*I;
R0=0;
I0=10;
S0=8e6;
odes={ode1;ode2;ode3}
fun = @root2d;
x0 = [0,0];
x = fsolve(fun,x0)
function [xs,yb] = ThreePointBDF(f,x0, xmax, h, y0)
% This function should return the numerical solution of y at x = xmax.
% (It should not return the entire time history of y.)
% TO BE COMPLETED
xs=x0:h:xmax;
y=zeros(1,length(xs));
y(1)=y0;
yb(1)=y0+f(x0,y0)*h;
for i=1:length(xs)-1
y(i+1)=y(i)+h*f(xs(i),y(i));
yb(i+1)=(4/3*y(i+1)-1/3*yb(i))+2*h/3*f(xs(i+1),y(i+1));
end
end

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回答（1 个）

Ameer Hamza
Ameer Hamza 2020-4-15
You need to use ode45 to solve the system of ODEs. Study the following code to see how it is done.
clc
gamma=1/7;
beta=1/3;
R0=0;
I0=10;
S0=8e6;
dsdt = @(S,I,R) -(beta*I.*S)./(S+I+R);
didt = @(S,I,R) (beta*I.*S)./(S+I+R)-I*gamma;
drdt = @(S,I,R) gamma*I;
dXdt = @(R,S,I) [dsdt(R,S,I); didt(R,S,I); drdt(R,S,I)];
IC = [8000000; 10; 0];
[t, x] = ode45(@(t,X) dXdt(X(1),X(2),X(3)), [0 10], IC);
s_sol = x(:,1);
i_sol = x(:,2);
r_sol = x(:,3);
subplot(3,1,1);
plot(t, s_sol);
title('S');
subplot(3,1,2);
plot(t, i_sol);
title('I');
subplot(3,1,3);
plot(t, r_sol);
title('R');
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Faraz Vossoughian
Faraz Vossoughian 2020-4-15
i have been asked to use this in conjuction with fsolve to solve non linear ode system SIR model. and im not sure how to implement it
Ameer Hamza
Ameer Hamza 2020-4-16
This seems like an iterative formula. I don't know what solving it with fsolve() even means.

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