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Globally Asymptotical Stability of a Delayed SEIR Epidemic Model with Saturation Incidence Rate and Vaccination

Xueliang Zhang

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Abstract

This paper deals with the global analysis of a delayed SEIR epidemic model with saturation incidence rate and vaccination strategy.By constructing suitable Lyapunov functionals and using LaSalle-type theorems for delayed differential equations,we will prove that when the basic reproduction ratio is less than unity,then the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is great than unity, a unique endemic equilibrium exists and is globally asymptotically stable.

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What this paper is about

This paper deals with the global analysis of a delayed SEIR epidemic model with saturation incidence rate and vaccination strategy.By constructing suitable Lyapunov functionals and using LaSalle-type theorems for delayed differential equations,we will prove that when the basic reproduction ratio is less than unity,then the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is great than unity, a unique endemic equilibrium exists and is globally asymptotically stable.

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Available abstract

This paper deals with the global analysis of a delayed SEIR epidemic model with saturation incidence rate and vaccination strategy.By constructing suitable Lyapunov functionals and using LaSalle-type theorems for delayed differential equations,we will prove that when the basic reproduction ratio is less than unity,then the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is great than unity, a unique endemic equilibrium exists and is globally asymptotically stable.

Key concepts: Mathematics, Epidemic model, Basic reproduction number, Stability theory, Saturation (graph theory), Lyapunov function, Applied mathematics, Invariance principle

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