Effects of PrEP on the HIV/AIDS dynamics with of immigration of infectives

Abstract

In this work a six compartmental model is formulated to study the effect of PrEP and the direct inflow of HIV infective immigrants on the spread of HIV/AIDS. The positivity and the equilibrium points were analyzed; the Basic Reproduction number 0 R was generated, the local and global stability of the Disease-Free Equilibrium of the model was established and there exists a feasible region where the model is well posed, a unique Disease-Free Equilibrium point exist in the absence of HIV infective immigrants which is locally and globally asymptotically stable if 1 0 R . Sensitivity index of key parameters revealed that c (number of sexual partners) makes the disease more endemic. Numerical simulation suggests that PrEP reduces the number of HIV infection despite the presence of constant inflow of infective immigrants and rigorous adherence to PrEP and treatment reduces the transmission of HIV/AIDS infection among high-risk population and can slow down the spread of infection.