Analysis of an age-structured model for HIV-TB co-infection

Abstract

<p style='text-indent:20px;'>According to the report of the WHO, there is a strong relationship between AIDS and tuberculosis (TB). Therefore, it is very important to study how to control TB in the context of the global AIDS epidemic. In this paper, we establish an age structured mathematical model of HIV-TB co-infection to study the transmission dynamics of this co-infection, and consider awareness in the modeling. We give the basic reproduction numbers for each of the two diseases and find four equilibria, namely, disease-free equilibrium, TB-free equilibrium, HIV-free equilibrium and endemic disease equilibrium. Then we discuss the local stability of the equilibria according to the range of values of the two basic reproduction numbers, and find the endemic equilibrium is unstable. We also discuss the global stability of the disease-free equilibrium and the TB-free equilibrium. Based on the new HIV-positive cases and TB cases data in China, the best-fit parameter values and initial values of the model are identified by the MCMC algorithm. Then we perform uncertainty and sensitivity analysis to identify the parameters that have significant impact on the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_{T} $\end{document}</tex-math></inline-formula>. Finally, combined with the established model, we give some measures that may help China achieve the goal of WHO of reducing the incidence of TB by 80% by 2030 compared to 2015.</p>