Stability Criteria for SIS Epidemiological Models under Switching Policies

TL;DR

This paper introduces a stability analysis framework for SIS epidemiological models with switching parameters, using joint spectral radius as a threshold, and provides conditions for persistence and periodic orbits.

Contribution

It extends SIS models to include switching parameters and establishes stability criteria using joint spectral radius, a novel approach in epidemiological modeling.

Findings

Joint spectral radius serves as a threshold for stability.

Conditions for disease persistence and periodic orbits are derived.

Results include stochastic switched model analysis.

Abstract

We study the spread of disease in an SIS model. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold parameter for this model in the spirit of the basic reproduction number for time-invariant models. We also present conditions for persistence and the existence of periodic orbits for the switched model and results for a stochastic switched model.