The stability analysis of an epidemic model with age-structure in the exposed and infectious classes

Yuji Li, Rui Xu

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.

https://doi.org/10.28919/cmbn/3337


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Published: 2017-05-12

How to Cite this Article:

Yuji Li, Rui Xu, The stability analysis of an epidemic model with age-structure in the exposed and infectious classes, Communications in Mathematical Biology and Neuroscience, Vol 2017 (2017), Article ID 12

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.

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