  We study a stochastic epidemic model with multiple patches (locations), where
individuals in each patch are categorized into three compartments, Susceptible,
Infected and Recovered/Removed, and may migrate from one patch to another in
any of the compartments. Each individual is associated with a random
infectivity function which dictates the force of infectivity while the
interactive infection process depends on the age of infection (elapsed time
since infection). We prove a functional law of large number for the epidemic
evolution dynamics including the aggregate infectivity process, the numbers of
susceptible and recovered individuals as well as the number of infected
individuals at each time that have been infected for a certain amount of time.
From the limits, we derive a PDE model for the density of the number of
infected individuals with respect to the infection age, which is a systems of
linear PDE equations with a boundary condition that is determined by a set of
integral equations.
