Mathematical model for transmission dynamics of HIV and tuberculosis co-infection in Kogi State, Nigeria

Abstract

In this work, we formulated a deterministic co-infection mathematical model made up of a system of nonlinear differential equations and rigorously analyzed it so as to gain insight into the transmission dynamics of each of the diseases as they were co-circulating in the population. We investigated the existence and stability of equilibria of the co-infection model and we subjected the model to rigorous analysis. The analysis of the sub-models (HIV only and TB-only models) and that of the co-infection model revealed that their disease-free equilibrium are locally and globally asymptotically stable when their reproduction numbers were each less than unity, showing that the diseases can be put under control under these conditions. We carried out sensitivity analysis of the co-infection model, using data relevant to Kogi state of Nigeria, which revealed that the top ranked parameters that drive the tuberculosis infection (with respect to the associated response function RT) is (u1), the control measure, educational awareness for the susceptible to always cover their mouth when coughing, sneezing and the need for the infants to be inoculated against the disease, while the top ranked parameter that drive the HIV infection (with respect to the associated response function RH) is (u2), the educational awareness campaign measure for the susceptible individuals to practice safe sexual activities, the need to avoid contacts with bodily fluids of infected patients and the prevention of vertical transmission of the disease. From the simulation of the co-infection model, the phenomenon of competitive exclusion occur where the disease with higher reproduction number drives out that with lesser one; furthermore, it was revealed that increasing the treatment rates of the individuals co-infected with TB and HIV could bring down the burden of the two diseases significantly, while increasing the control measures (u1) and (u2) leads to significant reduction in the cumulative co-infection new cases of mixed infection in the population.