Dynamical Analysis of a New Epidemiological Model for the Control of Malaria–Tuberculosis Co-infection in Nigeria

The main focus of this work is the formulation of a deterministic mathematical model governed by a system of non-linear differential equations to investigate the dynamics of co-infection between tuberculosis and malaria. A thorough analysis of the model shows that the co-infection model exhibits the phenomenon of backward bifurcation when the reproduction number of the diseases were less than unity. To determine the key parameters that greatly influenced the spread of the diseases, we conducted sensitivity analysis of the reproduction number. Real life data pertaining to the two diseases were gathered and fitted to our model through which key parameter values embedded in the model were estimated. Using these parameter values, we conducted numerical simulations of the co-infection model. The results from the simulation showed that an increase in the rate of contact and the rate at which the individuals in the exposed classes proceed to the infected classes will cause the prevalence of these diseases to rise in the human population. On the other hand, expectedly, it was discovered that a rise in the treatment rates for those singly infected with malaria and TB, as well as those with their co-infection, will ultimately decrease the burden of Malaria-TB co-infection. We proceeded to develop predictive tool through which forecast is made about the endemicity of the diseases under varying prevailing circumstances.