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2009•Journal of Nanchang UniversityRequires access

Global Analysis of a SEIR Epidemic Model with Nonlinear Incidence Rate under Vaccination

Wei Wang

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Abstract

The global analysis of a SEIR epidemic model with nonlinear incidence rate under vaccination is studied.The conditions and threshold to the existence of equilibriums are found.By Liapunov-Lasalle invariant theorem,the globally asymptotic stability of disease-free equilibrium is proved.By Hurwitz criterion,the sufficient condition of locally asymptotic stability of endemic equilibrium is obtained.And the sufficient condition under which endemic equilibrium is globally asymptotic stability is given by the theory about asymptotically orbital stability in differential equations and compound matrix.

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What this paper is about

The global analysis of a SEIR epidemic model with nonlinear incidence rate under vaccination is studied.The conditions and threshold to the existence of equilibriums are found.By Liapunov-Lasalle invariant theorem,the globally asymptotic stability of disease-free equilibrium is proved.By Hurwitz criterion,the sufficient condition of locally asymptotic stability of endemic equilibrium is obtained.And the sufficient condition under which endemic equilibrium is globally asymptotic stability is given by the theory about asymptotically orbital stability in differential equations and compound matrix.

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Available abstract

The global analysis of a SEIR epidemic model with nonlinear incidence rate under vaccination is studied.The conditions and threshold to the existence of equilibriums are found.By Liapunov-Lasalle invariant theorem,the globally asymptotic stability of disease-free equilibrium is proved.By Hurwitz criterion,the sufficient condition of locally asymptotic stability of endemic equilibrium is obtained.And the sufficient condition under which endemic equilibrium is globally asymptotic stability is given by the theory about asymptotically orbital stability in differential equations and compound matrix.

Key concepts: Exponential stability, Mathematics, Epidemic model, Nonlinear system, Invariant (physics), Stability theory, Applied mathematics, Stability (learning theory)

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