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Differential equation in matlab

1

$begingroup$

A pathogen population ($P(t)$) under the effect of a drug($A(t)$) is modelled as

$dPover dt=rP-E_maxA^nover C_50^n+A^nP$ and $A(t)$ is modelled as

$A(t)=Dover V(e^-k(t-t_0)-e^-k_a(t-t_0))$.

From literature I know the values of $D,V,t_0$(lag time), $k,k_a$. So, $A(t)$ can be obtained at the respective time points the ODE is run.
$r,E_max,n,C_50$ are also known.

I want to solve the ODE $dPover dt$ using ode45 of Matlab. (Without obtaining the analytical solution of $P(t)$ as this is only a simplified system and the original system cannot be solved analytically).

Can someone please let me know if the below code is right in solving $P(t)$. I am not sure about the way $A(t)$ is included into the ODE equation.

y0=10;
[t,y]=ode45(@Model,1:200,y0);

function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end

ordinary-differential-equations matlab mathematical-modeling

share|cite|improve this question

asked Mar 25 at 10:17

sam_roxsam_rox

51821020

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Matlab has a very comprehensive help with several examples. I urge you to check it.
  $endgroup$
  – Jon
  Mar 25 at 11:06
  

  
  
  
  

add a comment | 

1

$begingroup$

A pathogen population ($P(t)$) under the effect of a drug($A(t)$) is modelled as

$dPover dt=rP-E_maxA^nover C_50^n+A^nP$ and $A(t)$ is modelled as

$A(t)=Dover V(e^-k(t-t_0)-e^-k_a(t-t_0))$.

From literature I know the values of $D,V,t_0$(lag time), $k,k_a$. So, $A(t)$ can be obtained at the respective time points the ODE is run.
$r,E_max,n,C_50$ are also known.

I want to solve the ODE $dPover dt$ using ode45 of Matlab. (Without obtaining the analytical solution of $P(t)$ as this is only a simplified system and the original system cannot be solved analytically).

Can someone please let me know if the below code is right in solving $P(t)$. I am not sure about the way $A(t)$ is included into the ODE equation.

y0=10;
[t,y]=ode45(@Model,1:200,y0);

function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end

ordinary-differential-equations matlab mathematical-modeling

share|cite|improve this question

asked Mar 25 at 10:17

sam_roxsam_rox

51821020

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Matlab has a very comprehensive help with several examples. I urge you to check it.
  $endgroup$
  – Jon
  Mar 25 at 11:06
  

  
  
  
  

add a comment | 

$begingroup$

A pathogen population ($P(t)$) under the effect of a drug($A(t)$) is modelled as

$dPover dt=rP-E_maxA^nover C_50^n+A^nP$ and $A(t)$ is modelled as

$A(t)=Dover V(e^-k(t-t_0)-e^-k_a(t-t_0))$.

From literature I know the values of $D,V,t_0$(lag time), $k,k_a$. So, $A(t)$ can be obtained at the respective time points the ODE is run.
$r,E_max,n,C_50$ are also known.

I want to solve the ODE $dPover dt$ using ode45 of Matlab. (Without obtaining the analytical solution of $P(t)$ as this is only a simplified system and the original system cannot be solved analytically).

Can someone please let me know if the below code is right in solving $P(t)$. I am not sure about the way $A(t)$ is included into the ODE equation.

y0=10;
[t,y]=ode45(@Model,1:200,y0);

function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end

ordinary-differential-equations matlab mathematical-modeling

share|cite|improve this question

asked Mar 25 at 10:17

sam_roxsam_rox

51821020

$endgroup$

y0=10;
[t,y]=ode45(@Model,1:200,y0);

function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end

share|cite|improve this question

asked Mar 25 at 10:17

sam_roxsam_rox

51821020

share|cite|improve this question

asked Mar 25 at 10:17

sam_roxsam_rox

51821020

asked Mar 25 at 10:17

sam_roxsam_rox

51821020

asked Mar 25 at 10:17

sam_roxsam_rox

51821020

2 Answers
2

active

oldest

votes

1

$begingroup$

Your time vector likely has too large steps for solver. Try replace

1:200

with

linspace(0,0.125,256)

share|cite|improve this answer

answered Mar 25 at 11:57

mathreadlermathreadler

15.5k72263

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  thank you for the answer.
  $endgroup$
  – sam_rox
  Mar 25 at 13:07
  

  
  
  
  

add a comment | 

0

$begingroup$

I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.

share|cite|improve this answer

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,178215

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
  $endgroup$
  – mathreadler
  Mar 25 at 12:00
  
  

  
  
  
  

add a comment | 

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1

$begingroup$

Your time vector likely has too large steps for solver. Try replace

1:200

with

linspace(0,0.125,256)

share|cite|improve this answer

answered Mar 25 at 11:57

mathreadlermathreadler

15.5k72263

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  thank you for the answer.
  $endgroup$
  – sam_rox
  Mar 25 at 13:07
  

  
  
  
  

add a comment | 

1

$begingroup$

Your time vector likely has too large steps for solver. Try replace

1:200

with

linspace(0,0.125,256)

share|cite|improve this answer

answered Mar 25 at 11:57

mathreadlermathreadler

15.5k72263

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  thank you for the answer.
  $endgroup$
  – sam_rox
  Mar 25 at 13:07
  

  
  
  
  

add a comment | 

$begingroup$

Your time vector likely has too large steps for solver. Try replace

1:200

with

linspace(0,0.125,256)

share|cite|improve this answer

answered Mar 25 at 11:57

mathreadlermathreadler

15.5k72263

$endgroup$

1:200

linspace(0,0.125,256)

share|cite|improve this answer

answered Mar 25 at 11:57

mathreadlermathreadler

15.5k72263

answered Mar 25 at 11:57

mathreadlermathreadler

15.5k72263

answered Mar 25 at 11:57

mathreadlermathreadler

15.5k72263

0

$begingroup$

I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.

share|cite|improve this answer

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,178215

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
  $endgroup$
  – mathreadler
  Mar 25 at 12:00
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.

share|cite|improve this answer

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,178215

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
  $endgroup$
  – mathreadler
  Mar 25 at 12:00
  
  

  
  
  
  

add a comment | 

$begingroup$

I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.

share|cite|improve this answer

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,178215

$endgroup$

share|cite|improve this answer

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,178215

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,178215

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,178215