Effects of anti-infection behavior on the equilibrium states of an infectious disease

TL;DR

This paper introduces a mathematical model integrating anti-infection behaviors into an SIR framework, revealing complex equilibrium states that inform strategic disease control.

Contribution

It develops a novel epidemiological model incorporating behavior adoption dynamics and analyzes its equilibrium states, highlighting complex stability scenarios.

Findings

Coexistence of two locally stable endemic equilibria.

Presence of stable disease-free and endemic equilibrium coexistence.

Existence of a stable continuum of endemic equilibrium points.

Abstract

We propose a mathematical model to analyze the effects of anti-infection behavior on the equilibrium states of an infectious disease. The anti-infection behavior is incorporated into a classical epidemiological SIR model, by considering the behavior adoption rate across the population as an additional variable. We consider also the effects on the adoption rate produced by the disease evolution, using a dynamic payoff function and an additional differential equation. The equilibrium states of the proposed model have remarkable characteristics: possible coexistence of two locally stable endemic equilibria, the coexistence of locally stable endemic and disease-free equilibria, and even the possibility of a stable continuum of endemic equilibrium points. We show how some of the results obtained may be used to support strategic planning leading to effective control of the disease in the long-term.