Recurrent epidemic waves in a delayed epidemic model with quarantine

ABSTRACT

In this paper, we are concerned with an epidemic model with quarantine and distributed time delay. We define the basic reproduction number ${\mathcal{R}}_0$ and show that if ${\mathcal{R}}_0\le 1$, then the disease-free equilibrium is globally asymptotically stable, whereas if ${\mathcal{R}}_0>1$, 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:

• Epidemic model
• quarantine
• basic reproduction number
• time delay
• Hopf bifurcation

AMS CLASSIFICATIONS:

• 34K13
• 34K20
• 37N25
• 92D30

Acknowledgments

The author would like to thank the associate editor and anonymous reviewers for their helpful comments that allowed me to improve the manuscript.

Disclosure statement

The author reports there are no competing interests to declare(s).

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science (JSPS) [grant number 19K14594] and the Japan Agency for Medical Research and Development (AMED) [grant number JP20fk0108535].