MATHEMATICAL ANALYSIS OF THE IMPACT OF SEX WORKERS’ RISK BEHAVIOUR ON THE DYNAMICS OF HIV TRANSMISSION

Abstract

This paper presents an SI model to study the impact of risk behaviours on HIV transmission among sex workers and their clients, divided into high, medium, and low-risk groups. Fundamental properties are established, and the basic reproduction number  is computed. Local and global stability are analyzed using Varga’s theorem and the Lyapunov method. Numerical simulations show that migrations of high-risk individuals to lower-risk groups strongly affect HIV spread. The model highlights the importance of awareness and counselling to reduce risky behaviours and limit transmission in key populations.