Global stability of a network-based SIRS epidemic model with nonmonotone incidence rate

TL;DR

This paper analyzes the global stability of a network-based SIRS epidemic model incorporating nonmonotone incidence rates, revealing conditions for disease extinction or persistence and demonstrating the impact of behavioral effects on epidemic dynamics.

Contribution

It introduces a novel analysis of a network-based SIRS model with nonmonotone incidence, deriving epidemic thresholds and stability conditions considering behavioral inhibitory effects.

Findings

Disease-free equilibrium is globally stable when R0<1.

Endemic equilibrium is globally stable for large inhibitory factor α.

Larger α accelerates disease extinction and lowers infection levels.

Abstract

This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral change of the susceptible individuals when the number of infective individuals on heterogeneous networks is getting larger. Using the analytical method, epidemic threshold $R_0$ is obtained. When $R_0$ is less than one, we prove the disease-free equilibrium is globally asymptotically stable and the disease dies out, while $R_0$ is greater than one, there exists a unique endemic equilibrium. By constructing a suitable Lyapunov function, we also prove the endemic equilibrium is globally asymptotically stable if the inhibitory factor $\alpha$ is sufficiently large. Numerical experiments are also given to support the theoretical results. It is shown both theoretically and numerically a larger $\alpha$ can accelerate the extinction of the disease and reduce the level of disease.