The stability analysis of an epidemic model with age-structure in the exposed and infectious classes
Abstract
In this paper, we propose an epidemic model with age-structure in the exposed and infectious classes for a disease like hepatitis-B. Asymptotic smoothness of semi-flow generated by the model is studied. By calculating the basic reproduction number and analyzing the characteristic equation, we study the local stability of disease-free and endemic steady states. By using Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable; if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable.
- Published
- 12 May 2017
- Volume
- 2017 (2017)
- License
- CC BY 3.0
Copyright © 2017 Yuji Li, Rui Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
Y. Li, R. Xu, The stability analysis of an epidemic model with age-structure in the exposed and infectious classes, Commun. Math. Biol. Neurosci. 2017 (2017), 12.
BibTeX
@article{Li2017,
author = {Li, Yuji and Xu, Rui},
title = {The stability analysis of an epidemic model with age-structure in the exposed and infectious classes},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2017},
year = {2017},
pages = {12},
doi = {}
}