I have the following pair of nonlinear ordinary differential equations
m'[t] == gamma*v[t]*m[t] - mu*m[t]; v'[t] == v[t]*(k - epsilon - mu) - v[t]^2*k + m[t]*l - m[t]^2*l - m[t]*v[t]*(k + l + gamma);
So there are five parameters gamma, epsilon, mu, k and l. Now I would like to estimate these parameters from data that is only related to the function
m[t]. I have tried using
ParametricNDSolveValue together with
FindFit as usual. The problem what arises is that
ParametricNDSolveValue gives me a function with two variables
v and four parameters. I'm not sure how to write the
FindFit so it understands that the data is only for
m and not for
v at all.
If I only had one differential equation with five parameters, I could easily do the fitting because then it's just a straightforward application of
FindFit. However, as I have two differential equations depending on each other, I cannot do this.