Modeling visceral leishmaniasis and tuberculosis co-infection dynamics - Egbelowo, Oluwaseun F.; Munyakazi, Justin B.; Dlamini, Phumlani G.; Osaye, Fadekemi J.; Simelane, Simphiwe M. (Frontiers in Applied Mathematics and Statistics, 2023)
The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) in a patient pose a major public health challenge. In this paper, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by analyzing the VL and TB sub-models separately. For any infectious disease, the basic reproduction number is the average number of secondary cases that would be generated by a totally susceptible population. When the associated reproduction number (R1) for the TB-only model and reproduction number (R2) for the VL-only are less than unity respectively, the model exhibits bifurcation. Also, if max{R1,R2} = R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2} = R2, and choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model also exhibits the phenomenon of backward bifurcation when R0 = 1. The thresholds and equilibria quantities for the models are determined and stabilities are analyzed. Finally, some numerical simulations are given to show the reliability of our theoretical results.