Optimal control of intervention strategies in malaria–tuberculosis co-infection with relapse

Abstract

A model which incorporates some of the basic epidemiological features of the co-dynamics of malaria and tuberculosis (TB) is formulated and the effectiveness of current intervention strategies of these two diseases is analyzed. The malaria-only and TB-only models are considered first. Global stability disease-free steady states of the two sub-models does not hold due to the co-existence of stable disease-free with stable endemic equilibria, a phenomenon known as backward bifurcation. The dynamics of the dual malaria–TB model with intervention strategies are also analyzed. Numerical simulations of the malaria–TB model are carried out to determine whether the two diseases can co-exist. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance to disease transmission.