Predator/Prey Model questions

I'm trying to create a predator prey model with three different populations.

I was able to construct this using my notes/online tutorials, but I do not understand what all of this does (nor if I did this correctly). In my notes/ online tutorials, it seems p(1) would be the first population. I don't see where this is set up though and how it is updated. If anyone could explain how the computer reads these lines of , I'd greatly appreciate it.

function population
%initial conditions
h0=100; i0=1; v0=1;
IC=[h0,i0,v0];
t = [0 365];

B=0.07; 
Ri=0.01; 
Rv=0.01; 
Di=0.03; 
Dv=1; 
Bv=0.03; 
Rr=0.001;

[t,p]= ode15s(@RHS, t,IC );
figure(1)
plot(t ,p(:,1),'linewidth',2,'color','b')
hold on
plot(t ,p(:,2),'linewidth',2,'color','g')
hold on
plot(t ,p(:,3),'linewidth',2,'color','r')
grid on;
xlabel('time', 'FontSize', 20);
ylabel('Population', 'FontSize', 20);




function dpdt= RHS(t,p)
 
  
   
    dpdt_1=(B*p(1)) - (Rv*p(1)*p(3)) - (Ri*p(1)*p(2)) + (Rr*p(2));
    dpdt_2=(Ri*p(1)*p(2)) - (Di*p(2)) - (Rr*p(2));
    dpdt_3=(Bv*(p(1)+p(2))*p(3))- (Dv*p(3));
    dpdt=[dpdt_1;dpdt_2;dpdt_3];
end
end 

Answer 1

[William Rose]

@Nicholas Carr, line

[t,p]= ode15s(@RHS, t,IC );

is where the action is in this script.

Outputs: p() is Nx3array with populations p1, p2, p3, at the N times given in the Nx1 vector t().

Inputs:

• IC() is the vector of initial conditions. Therefore the values of [p1, p2, p3] at the initial time (t=0) are the values given in IC. Those were defined at the top to be IC=[h0, i0, v0].
• RHS() is a function that returns a 3-element vector whose values are the time derivatives [dp1/dt, dp2/dt, dp3/dt].
• t=[0,365] is the time range for integraiton.

[Nicholas Carr]

Excellent, that all makes sense now. Thanks bud I appreciate the help