Recurrent epidemic waves in a delayed epidemic model with quarantine

Toshikazu Kuniya

doi:10.1080/17513758.2022.2111468

Recurrent epidemic waves in a delayed epidemic model with quarantine

J Biol Dyn. 2022 Dec;16(1):619-639. doi: 10.1080/17513758.2022.2111468.

Author

Toshikazu Kuniya¹

Affiliation

¹ Graduate School of System Informatics, Kobe University, Kobe, Japan.

PMID: 35950789
DOI: 10.1080/17513758.2022.2111468

Abstract

In this paper, we are concerned with an epidemic model with quarantine and distributed time delay. We define the basic reproduction number $R_{0}$ and show that if $R_{0} \leq 1$ , then the disease-free equilibrium is globally asymptotically stable, whereas if $R_{0} > 1$ , then it is unstable and there exists a unique endemic equilibrium. We obtain sufficient conditions for a Hopf bifurcation that induces a nontrivial periodic solution which represents recurrent epidemic waves. By numerical simulations, we illustrate stability and instability parameter regions. Our results suggest that the quarantine and time delay play important roles in the occurrence of recurrent epidemic waves.

Keywords: 34K13; 34K20; 37N25; 92D30; Epidemic model; Hopf bifurcation; basic reproduction number; quarantine; time delay.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Basic Reproduction Number
Computer Simulation
Epidemics*
Models, Biological
Quarantine*