Global stability for delay SIR and SEIR epidemic models with saturated incidence rates. (English) Zbl 1243.34115

Abta, Abdelhadi; Kaddar, Abdelilah; Alaoui, Hamad Talibi

Electron. J. Differ. Equ. 2012, Paper No. 23, 13 p. (2012).

Summary: We propose a comparison of a delayed SIR model and its corresponding SEIR model in terms of global stability. We consider a saturated incidence rate and we determine, using Lyapunov functionals, conditions by which the disease-free equilibrium and the endemic equilibrium are globally asymptotically stable. Also some numerical simulations are given to compare a global behaviour of a delayed SIR model and its corresponding SEIR model.

MSC:

34K60	Qualitative investigation and simulation of models involving functional-differential equations
34D23	Global stability of solutions to ordinary differential equations
34K20	Stability theory of functional-differential equations
34C60	Qualitative investigation and simulation of ordinary differential equation models
92D30	Epidemiology

Keywords:

SIR epidemic model; SEIR epidemic model; incidence rate; delay differential equations; Lyapunov function; global stability