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