Annals of Mathematical Sciences and Applications

Volume 6 (2021)

Number 2

Lyapunov functionals for some distributed delay models in epidemiology

Pages: 145 – 172

DOI: https://dx.doi.org/10.4310/AMSA.2021.v6.n2.a2

Authors

Kai-Yang Liu (Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan)

Chang-Hong Wu (Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan)

Abstract

In this paper, we give a brief survey of Lyapunov functionals for compartmental epidemic models with distributed time delays based on the SIR model proposed by Beretta and Takeuchi (J. Math. Biol., 1995). We then consider various models with an exposed compartment such as SEIR, SEIQR, SEIAR, and SEIS models. Based on the suitable construction of Lyapunov functionals, we establish the global stability of the disease free equilibrium and endemic equilibrium (if it exists) for these models.

Keywords

epidemic models, distributed delay, Lyapunov functional, global stability

2010 Mathematics Subject Classification

Primary 34K20, 34K25. Secondary 92D30.

Full Text (PDF format)

This work was partly supported from the Young Scholar Fellowship Program by Ministry of Science and Technology (MOST) in Taiwan, under Grant MOST 110-2636-M-009-006.

Received 15 May 2021

Accepted 5 June 2021

Published 18 October 2021