Stability Analysis of Multi-Infections (Malaria, Zika-Virus and Elephantiasis) Model

The paper presents a multi-infections system model to study the transmission dynamics of Malaria, Zika-Virus and Elephantiasis in an endemic region such as Kedougou in the Southeastern part of Senegal and other parts of the world where it is possible to have multi-infections of the three diseases simultaneously. We performed the disease-free equilibrium and it is shown to be globally asymptotically stable when the associated threshold known as the basic reproduction number for the model is less than unity. Investigation on the existence and stability of equilibria is also performed, the model is found to exhibit backward bifurcation so that for less than unity is not sufficient to eradicate the disease from the population and there is the need to lower below a certain threshold for effective disease control. Sensitivity analysis is performed to determine parameters that have high influence on the basic reproduction number.