Mathematical Analysis of a Malaria model with vaccination, treatment and vector control using Sterile-insect technique

Abstract

In this work, a mathematical model for malaria transmission is developed using a system of nonlinear
ordinary differential equations. The model incorporates three control strategies: vaccination, treatment,
and sterile insect technique. Analytical results demonstrate that the malaria-free equilibrium is both locally and globally asymptotically stable when the basic reproduction number, R0 is less than one, and unstable when R0 > 1. The existence of an endemic equilibrium is investigated, and conditions for the occurrence of forward or backward bifurcation are derived. Numerical simulations and graphical illustrations are provided to demonstrate the disease dynamics under various control scenarios. The findings reveal that the combined application of all three control measures is more effective in reducing malaria transmission than any individual or pairwise combination of interventions.