Modeling Stochastic Anomalies in an SIS and SIRS System

TL;DR

This paper introduces a stochastic SIS and SIRS epidemiological model incorporating Poisson measures to simulate anomalies like quarantine, providing stability conditions for disease-free states.

Contribution

It presents a novel stochastic modeling approach with Poisson measures for SIS and SIRS systems, including stability analysis of disease-free equilibria.

Findings

Derived stability conditions for disease-free equilibrium.

Modeled quarantine as a stochastic anomaly.

Extended classical models with Poisson measure terms.

Abstract

I propose a stochastic SIS and SIRS system to include a Poisson measure term to model anomalies in the dynamics. In particular the positive integrand in the Poisson term is intended to model quarantine. Conditions are given for the stability of the disease free equilibrium for both systems.