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2007•Journal of BiomathematicsRequires access

Exponential Stability of an Epidemic Model with Time Delays

Zhenhua Huang

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Abstract

This is a study of dynamic behavior of an SEIRS epidemic model by using analytic technique.It is shown that disease-free equilibrium is globally exponentially stable if the reproduction number is smaller than one.When the reproduction number is greater than one, a sufficient condition has been obtained to guarantee the local exponential stability of endemic equilibrium.And,an example is given to illustrate the new results.

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What this paper is about

This is a study of dynamic behavior of an SEIRS epidemic model by using analytic technique.It is shown that disease-free equilibrium is globally exponentially stable if the reproduction number is smaller than one.When the reproduction number is greater than one, a sufficient condition has been obtained to guarantee the local exponential stability of endemic equilibrium.And,an example is given to illustrate the new results.

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Available abstract

This is a study of dynamic behavior of an SEIRS epidemic model by using analytic technique.It is shown that disease-free equilibrium is globally exponentially stable if the reproduction number is smaller than one.When the reproduction number is greater than one, a sufficient condition has been obtained to guarantee the local exponential stability of endemic equilibrium.And,an example is given to illustrate the new results.

Key concepts: Exponential stability, Exponential growth, Stability (learning theory), Epidemic model, Mathematics, Basic reproduction number, Applied mathematics, Exponential function

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