Lyapunov functionals for some distributed delay models in epidemiology. (English) Zbl 1477.92025

Summary: 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 E. Beretta and Y. Takeuchi [J. Math. Biol. 33, No. 3, 250–260 (1995; Zbl 0811.92019)]. 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.


92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations


Zbl 0811.92019
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