Epidemic modeling: Diffusion approximation vs. stochastic differential equations allowing reflection

Abstract

A birth–death process is considered as an epidemic model with recovery and transmittance from outside. The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differential equation taking values in [Formula: see text]. For intermediate size or semilarge populations, the fraction of infected individuals is approximated by a diffusion formulated as a stochastic differential equation. That diffusion approximation however needs to be killed at the boundary [Formula: see text]. An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.