Solving system ODEs with one unknown variable coefficient.
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Hi all, I am trying to solve this system of ODEs: $$ S'(a)= {\tau}R(a)-\lambda(a)S(a)\\ I'(a)=\lambda(a)S(a)-{\gamma}I(a)+rL(a)\\ R'(a)=(1-q)\gammaI(a)-{\tau}R(a)\\ L'(a)=q\gammaI(a)-rL(a) $$
I know the value of all the parameters apart from $\lambda$ which is more over a-dependent. I have tried to solve it analitically using this solve but it seems not possible. So I want to tried with a numerical approach but I don't know how to procede because of the presence of this $\lambda(a)$. Do you have any hints-suggestion ?
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Torsten
on 2 Dec 2015
Even if an analytical solution existed for your linear ODE system with variable coefficients, it would be so complicated that it does not help for interpretation.
A numerical solution is only possible if you supply an explicit function lambda=lambda(a).
Best wishes
Torsten.
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