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.

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