Controlling Co-Epidemics: Analysis of HIV and Tuberculosis Infection Dynamics

A co–epidemic 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). We develop two variants of a co–epidemic model of two diseases. We calculate the basic reproduction number (R0), the disease–free equilibrium, and the quasi–disease–free equilibria, which we define as the existence of one disease along with the complete eradication of the other disease, and the co–infection equilibria for specific conditions. We determine stability criteria for the disease–free and quasi–disease–free equilibria. We present an illustrative numerical analysis of the HIV–TB co–epidemics in India that we use to explore the effects of hypothetical prevention and treatment scenarios. Our numerical analysis demonstrates that exclusively treating HIV or TB may reduce the targeted epidemic, but can subsequently exacerbate the other epidemic. Our analyses suggest that coordinated treatment efforts that include highly active antiretroviral therapy for HIV, latent TB prophylaxis, and active TB treatment may be necessary to slow the HIV–TB co–epidemic. However, treatment alone may not be sufficient to eradicate both diseases. Increased disease prevention efforts (for example, those that promote condom use) may also be needed to extinguish this co–epidemic. 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.