Global stability of a class of discreteage-structured SIS models with immigration

Yicang Zhou; Zhien Ma

doi:10.3934/mbe.2009.6.409

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2009, Volume 6, Issue 2: 409-425. Doi: 10.3934/mbe.2009.6.409

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Global stability of a class of discrete age-structured SIS models with immigration

Yicang Zhou^1, and
Zhien Ma^1,

1.
Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049

Received: December 2007

Revised: September 2008

Published: February 2009

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Abstract

Immigration has an important influence on the growth of population and the transmission dynamics of infectious diseases. A discrete age-structured epidemic SIS model with immigration is formulated and its dynamical behavior is studied in this paper. It is found that population growth will be determined by the reproductive number and the immigration rate. In the simple case without infected immigration, the basic reproductive number is defined, and the global stability of equilibria is investigated. In the case with infected immigration, there is no disease-free equilibrium, and there always exists an endemic equilibrium, and the global stability conditions of the unique endemic equilibrium is obtained.

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Mathematics Subject Classification: Primary: 92D30; Secondary: 39A11.

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