How to use ode45 to plot this code?

Hello, I have to use ode45 to plot I on the same figure as the other way I plotted I (using a for loop). I tried doing it this way but the error that keeps coming up is that "Vectors must be the same length". Do you have any suggestions in how to fix that? Thank you.

clc
clear
N=1000;
del_T=0.01; %delta T
B=2; %B=Beta
g=0.5; %g=gamma
R_o=4; %R not
S(1)=999;
I(1)=1;
R(1)=0;
t=0:del_T:30;
for k= 1:length(t)-1
    S(1+k)=S(k)-(del_T*B*I(k).*(S(k)/N));
    I(1+k)=I(k) + ((B*I(k)*S(k)*del_T)./N)-(g*I(k)*del_T);
    R(1+k)=R(k) + g*I(k)*del_T;
     tspan = [0 30];
    y0 = [S(1) I(1) R(1)];
    [t,I_ode]= ode45(@(t,I_ode)odefun(t,I_ode,k,B,g,N,del_T,S,I,R), tspan, y0);
end
plot(t, I)
hold on;
plot (t,I_ode)
function I_ode= odefun(t,I_ode,k,B,g,N,del_T,S, I,R)
    I_ode=zeros(3,1);
    dSdt= S(k)-(del_T*B*I(k).*(S(k)/N));
    dIdt=I(k) + ((B*I(k)*S(k)*del_T)./N)-(g*I(k)*del_T);
    dRdt=R(k) + g*I(k)*del_T;
end

Answer 1

[Alan Stevens]

You have mixed up doing your own iterations with allowing ode45 to do its iterations! For ode45, just use the following

N=1000;
del_T=1; %delta T
B=2; %B=Beta
g=0.5; %g=gamma
R_o=4; %R not
S=999;
I=1;
R=0;
tspan = [0 30];
y0 = [S I R];
[t,y]= ode45(@(t,y)odefun(t,y,B,g,N), tspan, y0);
S = y(:,1); I = y(:,2); R = y(:,3);
plot(t, y)
xlabel('time'), ylabel('S, I and R')
legend('S','I','R')

function I_ode= odefun(~,y,B,g,N)
    S = y(1); I = y(2); R = y(3);
    dSdt= -B*I.*S/N;
    dIdt= B*I*S./N-g*I;
    dRdt= g*I;
    I_ode = [dSdt; dIdt; dRdt];
end

[Ethan Hoang]

Your fixtures to my code worked! Thank you very much.