ODE45 specific time point settings

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Hello!
I'm trying to stimulate BIG model in different situations (Beta-cells , insulin , glucose).
The following function is very simple. I'm able to change the parameter 's' at t>100.
%%% BIG Model %%%
function yprime = big(t,y)
s=1;
delta=1;
q=1;
if t>100
s=0.2;
end
yprime = zeros(3,1);
yprime(1) = m - s*y(2)*y(1);%dG/d
yprime(2) = (q * y(3) * (y(1))^2) - delta * y(2); %dI/dt
yprime(3) = y(3)*0.01*(y(1)-5);%dB/dt
The second thing that I need to do is to change m=2 at t=90, t=110, t=200 (rest of the time m=1)
The problem is that the ODE is choosing the time points by itself and it skips these specific time point. How can I overcome this?
This is the code that i'm using to solve this.
clear all
clc
[t,y] = ode45(@(t,y) big(t,y) , [0:1:400] ,[5,1/5,1/125]);
subplot(1,3,1)
plot(t,y(:,1))
title('Glucose')
xlabel('Time')
subplot(1,3,2)
plot(t,y(:,2))
title('Insulin')
xlabel('Time')
subplot(1,3,3)
plot(t,y(:,3))
title('Beta-Cells')
xlabel('Time')

Accepted Answer

Star Strider
Star Strider on 12 Jun 2020
I verified that this version works, however I do not see any significant change in the integrated results.
These added lines:
tcnd = (((t>=90) & (t<91)) | ((t>=110) & (t<111)) | ((t>=200) & (t<201)));
m = tcnd*2 + (~tcnd)*1;
‘toggle’ ‘m’ between ‘1’ and ‘2’ at the appropriate times. An additional fprintf call allows verification.
The (Slightly Revised) Code —
function yprime = big(t,y)
s=1;
delta=1;
q=1;
if t>100
s=0.2;
end
tcnd = (((t>=90) & (t<91)) | ((t>=110) & (t<111)) | ((t>=200) & (t<201)));
m = tcnd*2 + (~tcnd)*1;
% fprintf('t = %f\t\tm = %d\n',t,m) % Un-Comment To See dm’ At Each Time
yprime = zeros(3,1);
yprime(1) = m - s*y(2)*y(1);%dG/d
yprime(2) = (q * y(3) * (y(1))^2) - delta * y(2); %dI/dt
yprime(3) = y(3)*0.01*(y(1)-5);%dB/dt
end
The Plot —
The only discernable difference are the ‘spikes’.
  6 Comments
Eran Sandman
Eran Sandman on 16 Jun 2020
Evenutally i changed the conditions of 't' to nearby points which likley the intergration goes through them. So it worked well.
Star Strider
Star Strider on 16 Jun 2020
I’m happy you got it sorted.
I still don’t understand what the problem is with ‘s’. In spite of my experience with metabolic models (specifically glucose regulatory models), I don’t recognise the one you’re using.

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More Answers (2)

darova
darova on 12 Jun 2020
Try tolerance
function yprime = big(t,y)
m = 1;
if any( abs([90 110 200]-t)<0.5 )
m = 2;
end

Boxn Hen
Boxn Hen on 12 Jun 2020
Do you change m at one point like t=90 ?Ode steps small size ,if the tspan is [0,1] and you set m=1 when t=0,while m=2 in other time,it will be meaningless.What I experience is effective if you change m for a period.
function yprime = big2(t,y)
s=1;
delta=1;
q=1;
m=1;
if t>100
s=0.2;
end
if t>90
m=2;
end
yprime = zeros(3,1);
yprime(1) = m - s*y(2)*y(1);%dG/d
yprime(2) = (q * y(3) * (y(1))^2) - delta * y(2); %dI/dt
yprime(3) = y(3)*0.01*(y(1)-5);%dB/dt
end

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