Global dynamics of a discrete age-structured SIR epidemic model with applications to measles vaccination strategies
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Published on: April 26, 2009
Linhua Zhou1, Yan Wang2, Yanyu Xiao3
1Department of Applied Mathematics, Changchun University of Science and Technology, Changchun, Jilin 140022, PR China.
Abstract:
We investigate an SIR epidemic model with discrete age groups to understand the transmission dynamics of an infectious disease in a host population with an age structure. We derive the basic reproduction number R0 and show that it is a sharp threshold parameter. If R0≤1, the disease-free equilibrium E0 is globally stable. If R0>1,E0 is unstable, the model is uniformly persistent, and an endemic equilibrium exists. The global stability of the endemic equilibrium when R0>1 is established under a sufficient condition. The model is then used to analyze the measles data in India and evaluate the effectiveness of several vaccination strategies for the control of measles epidemics in India.
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