Dynamics of tuberculosis in HIV–HCV co-infected cases

Abstract

This work presents a compartmental mathematical model describing transmission and spread of tuberculosis (TB) in HIV–HCV co-infected cases. The novelty of this work comes through mathematical modeling of the dynamics of TB not only in HIV but also in HIV–HCV co-infected cases. We analyze the formulated model by proving the existence of disease-free equilibrium solution. We calculate the basic reproduction number [Formula: see text], of the model and construct Lyapunov–Lasalle candidate function to explore the global asymptotic stability of the disease-free equilibrium solution. Result from the mathematical analysis indicates that the disease-free equilibrium solution is globally asymptotically stable if [Formula: see text]. The existence of unique endemic equilibrium solution is established through numerical investigation. Further, the model is reformulated as an optimal control problem, considering time-dependent controls (vaccination and public health education) to minimize the spread of tuberculosis in HIV–HCV co-infected cases, using Pontryagin’s maximum principle. Numerical simulations and cost-effectiveness analysis are carried out which reveal that vaccination combined with public health education would reduce the spread of tuberculosis when HIV–HCV co-infected cases have been successfully controlled in the population.