On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate

TL;DR

This paper analyzes a modified SIR epidemiological model where the infection rate depends on recovered individuals, revealing complex stability phenomena like multistability and multiple equilibria, which differ from classical models.

Contribution

It introduces conditions for the existence, uniqueness, and stability of equilibria in a recovery-dependent infection rate SIR model, highlighting novel multistability behaviors.

Findings

Multiple endemic stable equilibria can occur

Conditions for local and global stability are established

Examples illustrate complex equilibrium structures

Abstract

We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also the stability of the disease-free equilibrium. We show that, in contrast with classical SIR models, a system with a recovery-dependent infection rate can have multiple endemic stable equilibria (multistability) and multiple stable and unstable saddle points of equilibria. We establish conditions for the occurrence of these phenomena and illustrate the results with some examples.