# Numerically solving a system of partial integro-differential equations in Matlab

Given the following system of partial integro-differential equations $$\frac{dX(t)}{dt}=\Lambda-\mu X(t)-\beta X(t)Z(t),\\ \frac{\partial Y(t,\omega)}{\partial t}+\frac{\partial Y(t,\omega)}{\partial \omega}=-\delta(\omega) Y(t,\omega),\\ \frac{dZ(t)}{dt}=-\gamma Z(t)+(N-Z(t))\int^{\infty}_{0}\kappa (\omega)Y(t,\omega)d\omega$$ with the boundary condition $$Y(t,0)=\beta X(t)Z(t)$$ and initial conditions $$X(0)=X_{0},Y(0,\omega)= \sigma(\omega),Z(0)=Z_{0}$$ where all parameters $\Lambda, \mu, \beta, \delta(\omega), \gamma, N, \kappa(\omega), X_{0},Z_{0}$ are positive.

How does one numerically compute a solution for this on Matlab?

Note : I was asked to repost this question in scicomp.se -

Numerically solving a system of partial integro-differential equations in Matlab