Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, China
Copyright © 2013 Xiaoyan Wang et al. 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.
A coepidemic arises when the spread of one infectious disease stimulates the spread of
another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV)
and tuberculosis (TB). The density of individuals infected with latent tuberculosis is structured by age
since latency. The host population is divided into five subclasses of susceptibles, latent TB, active TB
(without HIV), HIV infectives (without TB), and coinfection class (infected by both TB and HIV). The
model exhibits three boundary equilibria, namely, disease free equilibrium, TB dominated equilibrium, and
HIV dominated equilibrium. We discuss the local or global stabilities of boundary equilibria. We
prove the persistence of our model. Our simple model of two synergistic infectious disease epidemics
illustrates the importance of including the effects of each disease on the transmission and progression
of the other disease. We simulate the dynamic behaviors of our model and give medicine explanations.