Differential equation in matlab The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Stochastic predator-preymatlab differential equationSolving 2nd order ODE with 2 independent parameters(over finite intervals), with bounds on solutionAnalytic solution to the one-compartment modelMatlab differential equation verificationIncluding a time delay term for a differential equationFinding parameters using two data sets for the same ODE systemmass balance from a system of nonlinear differential equationsDeciding the parameter value in a ODE systemHow can I solve/integerate the One-To-One kinetic binding model system of differential equations analytically?

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Differential equation in matlab



The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Stochastic predator-preymatlab differential equationSolving 2nd order ODE with 2 independent parameters(over finite intervals), with bounds on solutionAnalytic solution to the one-compartment modelMatlab differential equation verificationIncluding a time delay term for a differential equationFinding parameters using two data sets for the same ODE systemmass balance from a system of nonlinear differential equationsDeciding the parameter value in a ODE systemHow can I solve/integerate the One-To-One kinetic binding model system of differential equations analytically?










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









share|cite|improve this question









$endgroup$











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















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









share|cite|improve this question









$endgroup$











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













1












1








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









share|cite|improve this question









$endgroup$




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













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 25 at 10:17









sam_roxsam_rox

51821020




51821020











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
















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















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




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










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)


enter image description here






share|cite|improve this answer









$endgroup$












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


















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.



enter image description here






share|cite|improve this answer









$endgroup$








  • 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












Your Answer








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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






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)


enter image description here






share|cite|improve this answer









$endgroup$












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















1












$begingroup$

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



1:200


with



linspace(0,0.125,256)


enter image description here






share|cite|improve this answer









$endgroup$












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













1












1








1





$begingroup$

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



1:200


with



linspace(0,0.125,256)


enter image description here






share|cite|improve this answer









$endgroup$



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



1:200


with



linspace(0,0.125,256)


enter image description here







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Mar 25 at 11:57









mathreadlermathreadler

15.5k72263




15.5k72263











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
















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















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




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











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.



enter image description here






share|cite|improve this answer









$endgroup$








  • 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
















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.



enter image description here






share|cite|improve this answer









$endgroup$








  • 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














0












0








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.



enter image description here






share|cite|improve this answer









$endgroup$



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.



enter image description here







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Mar 25 at 11:12









PierreCarrePierreCarre

2,178215




2,178215







  • 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













  • 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








1




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





$begingroup$
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


















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