Abstract
We study a non-Markovian individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity while satisfying certain growth condition.
Each individual is associated with a random infectivity function, which depends on the age of infection.
The rate of infection at each location takes an averaging effect of infectivity from all the locations.
The epidemic dynamics in each location is described by the total force of infection, the number of susceptible individuals,
the number of infected individuals that are infected at each time and have been infected for a certain amount of time, as well as the number of recovered individuals. The processes can be described using a time-space representation.
We prove a functional law of large numbers for these time-space processes, and in the limit, we obtain a set of time-space integral equations together with the limit of the number of infected individuals tracking the age of infection as a time-age-space integral equation.
Joint work with G. Pang (Rice Univ)