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2014•Unpublished venueRequires access

Analysis of an epidemic model with population dynamics and nonlinear incidence rate βI~PS/1+αI~P

Le Yi Shi

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Abstract

In this paper,a class of epidemic models with nonlinear incidence rate βIPS/1+αIP is studied,where we introduce population dynamics.The positive invariant set of the model is discussed by using qualitative theory of differential equations,and the existence and stability of the endemic steady state and the disease-free steady state are analyzed.We obtain the sufficient conditions for the global asymptotic stability of the models.Finally the biological significance is discussed.

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What this paper is about

In this paper,a class of epidemic models with nonlinear incidence rate βIPS/1+αIP is studied,where we introduce population dynamics.The positive invariant set of the model is discussed by using qualitative theory of differential equations,and the existence and stability of the endemic steady state and the disease-free steady state are analyzed.We obtain the sufficient conditions for the global asymptotic stability of the models.Finally the biological significance is discussed.

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Available abstract

In this paper,a class of epidemic models with nonlinear incidence rate βIPS/1+αIP is studied,where we introduce population dynamics.The positive invariant set of the model is discussed by using qualitative theory of differential equations,and the existence and stability of the endemic steady state and the disease-free steady state are analyzed.We obtain the sufficient conditions for the global asymptotic stability of the models.Finally the biological significance is discussed.

Key concepts: Epidemic model, Nonlinear system, Invariant (physics), Exponential stability, Population, Steady state (chemistry), Stability (learning theory), Dynamics (music)

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