A COMPARISON OF FOUR CONTROL SCENARIOS THAT INCLUDE IVERMECTIN USAGE FOR MALARIA INFECTIONS BASED ON MATHEMATICAL MODELLING

Abstract

Malaria, a deadly infectious disease that is transmitted through bites of infected female mosquitoes is still a global concern despite the aged long control interventions, most of which hardly target outdoor feeding mosquitoes. To fill this gap in this paper, a model for the dynamics of malaria in the presence of cattle is developed based on mathematical equations and analysed rigorously under four different combinations formed as control strategies using three intervention tools which includes the use of an endectocide known as ivermectin. Estimate of the model reproduction number was obtained by the next generation matrix method and was used to analyse the stability of the equilibrium points. By the Routh-Hurwitz criteria, the disease-free equilibrium point was found to be asymptotically stable for R₀ < 1 and unstable provided R₀ > 1. Analysis of the stability of the endemic equilibrium carried out based on the Centre Manifold theorem also suggests that at R₀  = 1 the malaria model exhibits a forward bifurcation. The most effective combination as a strategy is also identified based on the numerical simulations and bar charts constructed using data obtained from the plots.