Mathematical analysis of sex-structured population model of HIV infection in Kenya

Abstract

In this paper, we develop a mathematical model describing the dynamics of HIV transmission by incorporating sexual orientation of individuals. Equilibrium points and the basic reproduction number are derived. The basic reproduction number provides a threshold that determines whether or not the disease fades away. The model, described by non-linear ODEs, shows existence of unique disease-free and disease-persistent equilibria. Least squares curve fitting is presented to quantitatively investigate the trend of infection within each gender. The results are indicative of a higher infectivity in the female population. We further investigated the effect of the introduction of pre-exposure prophylaxis (PrEP) on the dynamics of the HIV. Our results show that the introduction of PrEP has had a positive effect on the limitation of spread of HIV. Sensitivity analysis results show that control of effective contacts can result in control of the disease across gender divide. The model provides a unique opportunity to influence policy on HIV treatment and management.