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

摘要

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[0,1].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{0}U{1}.An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.