Poisson integral type quarantine in a stochastic SIR system.

Abstract

We propose a SIR system that includes a Poisson measure term to model the quarantine of infected individuals. An inequality concerning the term representing the transmission rate is given to establish the stochastic stability of the disease free equilibrium. It is further shown that if R0 > 1 then the long-run behavior the system will reside within a neighborhood of the equilibrium in the underlying deterministic version of this system.