I have a system of differential equation to solve, but it's a mixed system of ODE and SDE. I'm not sure whether there is any way to solve this kind of system or not. My equations are:
s'[t] == -a s[t] i[t]
di[t] == (a s[t] i[t] - µ i[t] + c (1 - s[t] -i[t]) i[t]) dt + σ dB
i[0]=.5
s[0]=.5
with the parameters a,c,σ,µ
greater than 0. Is there any known way to solve this numerically?
{ s'[t] == -a s[t] i[t], i'[t] == (a s[t] i[t] - \[Micro] i[t] + c (1 - s[t] - i[t]) i[t]) + \[Sigma] B'[t], i[0] == .5, s[0] == .5 }
$\endgroup$ – rhermans May 31 '18 at 18:42B'[t]
? $\endgroup$ – rhermans May 31 '18 at 18:43