Stability analysis for SIS epidemic models with vaccination and constant population size

Jianquan Li; Zhien Ma

doi:10.3934/dcdsb.2004.4.635

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2004, Volume 4, Issue 3: 635-642. Doi: 10.3934/dcdsb.2004.4.635

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Stability analysis for SIS epidemic models with vaccination and constant population size

Jianquan Li^1, and
Zhien Ma^2,

1.
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049
2.
Department of Applied Mathematics, College of Science, Xian Jiaotong University, Xian 710049

Received: July 31, 2002

Revised: October 31, 2003

Published: July 2005

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Abstract

This paper investigates two types of SIS epidemic model with vaccination and constant population size to determine to the thresholds, equilibria, and stabilities. One of SIS models is a delay differential equations, in which the period of immunity due to vaccination is a constant. Another is an ordinary differential equations, in which the loss of immunity due to vaccination is in the exponent form. We find all of their thresholds respectively, and compare them. The disease-free equilibrium is globally asymptotically stable if the threshold is not greater than one; the endemic equilibrium is globally asymptotically stable if the threshold is greater than one.

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Mathematics Subject Classification: 34D23, 92D30.

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