Global dynamics of a discrete age-structured SIR epidemic model with applications to measles vaccination strategies

Linhua Zhou; Yan Wang; Yanyu Xiao; Michael Y Li

doi:10.1016/j.mbs.2018.12.003

Global dynamics of a discrete age-structured SIR epidemic model with applications to measles vaccination strategies

Math Biosci. 2019 Feb:308:27-37. doi: 10.1016/j.mbs.2018.12.003. Epub 2018 Dec 7.

Authors

Linhua Zhou¹, Yan Wang², Yanyu Xiao³, Michael Y Li⁴

Affiliations

¹ Department of Applied Mathematics, Changchun University of Science and Technology, Changchun, Jilin 140022, PR China. Electronic address: zhoulh@cust.edu.cn.
² School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116023, PR China. Electronic address: wangy891@dlut.edu.cn.
³ Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, USA. Electronic address: yanyu.xiao@uc.edu.
⁴ Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada. Electronic address: myli@ualberta.ca.

PMID: 30529600
DOI: 10.1016/j.mbs.2018.12.003

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.

Keywords: Discrete age structure; Epidemic models; Global stability; Measles vaccination.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Basic Reproduction Number
Child
Child, Preschool
Endemic Diseases / statistics & numerical data
Epidemics* / statistics & numerical data
Humans
India
Infant
Measles* / prevention & control
Models, Biological*
Vaccination* / methods
Vaccination* / statistics & numerical data