American Institute of Mathematical Sciences

Advanced
2009, 6(2): 409-425. doi: 10.3934/mbe.2009.6.409

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  March 2009

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.
Keywords: Age-structure, infectious disease, discrete model, stability..
Mathematics Subject Classification: Primary: 92D30; Secondary: 39A1.
Citation: Yicang Zhou, Zhien Ma. Global stability of a class of discrete age-structured SIS models with immigration. Mathematical Biosciences & Engineering, 2009, 6 (2) : 409-425. doi: 10.3934/mbe.2009.6.409
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