Annals of Mathematical Sciences and Applications
Volume 6 (2021)
Lyapunov functionals for some distributed delay models in epidemiology
Pages: 145 – 172
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.
epidemic models, distributed delay, Lyapunov functional, global stability
2010 Mathematics Subject Classification
Primary 34K20, 34K25. Secondary 92D30.
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