Dynamical analysis of HIV-TB co-infection transmission model in the presence of treatment for TB

Abstract

The immense disease burden of tuberculosis (TB) infection is well-documented, particularly among those co-infected with HIV and TB. To better understand the transmission dynamics of HIV-TB co-infection in the absence of readily available HIV treatment, we develop a deterministic compartmental co-infection model. Our model helps to identify the effects of TB infection on the co-infection dynamics of the two diseases, especially when treatment for TB is readily available. We find that susceptibility to TB reinfection after a previous infection leads to backward bifurcation in the TB-only model when the associated reproduction number $(R_0)$ is less than unity. However, when we make the susceptibility to TB re-infection insignificant in the model, the disease-free equilibrium of the TB-only model is locally asymptotically stable when the associated $R_0$ is less than unity. We conduct sensitivity and uncertainty analyses to identify the key parameters driving TB infection dynamics, using the $R_0$ as the response function. We discover that the transmission rate for TB, the modification parameters accounting for the infectiousness of infected individuals with TB-only, and the treatment rates for singly infected individuals with latently infected TB are the top drivers of TB infection in the given population. Our numerical simulations suggest that concentrating treatment on TB-infected individuals in the diagnosed latently infected stage (singly or dually infected with HIV) could effectively reduce the co-infection disease burden and HIV incidence in the population under study.