I have an ODE system defining a mathematical model of a biological system, say

$$ \frac{da}{dt}=f_1(a,b,\ldots,z,p)\\ \frac{db}{dt}=f_2(a,b,\ldots,z,p)\\ \cdots\\ \frac{dz}{dt}=f_n(a,b,\ldots,z,p) $$

with state variables, $a,b,\ldots,z$, and parameter vector, $p$.

In the end, I need to calculate a scalar model response, $f$, defined as

$$ f(p)=\int_0^{t_\text{end}}dt \left(a(t)+b(t)\right)+\int_0^{t_\text{end}}dt \left(x(t)+z(t)\right) $$

Question: what is the best way to calculate $f(p)$ apart from numerical integration once the time-courses are calculated?


The common way of tracking such properties is indeed to add an additional ODE to the system, here: $$\frac{df}{dt}=a(t)+b(t)+x(t)+z(t)$$ with initial condition $$f(0)=0.$$ If this is not possible, then a smart choice of output times e.g. quadrature points in t for an integration afterwards is recommend.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.