Modeling and Analysis of HIV and Cholera Direct Transmission with Optimal Control

Abstract

In this study, a mathematical model of the human immunodeficiency virus (HIV) and cholera co infection is constructed and analyzed. The disease-free equilibrium of the co-infection model is both locally and globally asymptotically stable if R01. The only cholera model and only the HIV model show forward bifurcation if the corresponding reproduction numbers attain a value one. The disease-free equilibria of only the cholera and only the HIV models is locally and globally asymptotically if R00 show that the increase of one infection contributes to the increase of other infection. Pontryagin’s maximum principle is applied to construct Hamiltonian function, and optimal controls are computed. The optimal system is solved numerically using forward and backward sweep method of Runge Kutta’s fourth-order methods. The numerical simulations are plotted using MATLAB.