Transmission dynamics of HIV/AIDS with screening and non-linear incidence

Abstract

This paper examines the transmission dynamics of HIV/AIDS with screening using non-linear incidence. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However numerical results suggest that screening of unaware infectives has the effect of reducing the transmission dynamics of HIV/AIDS. Also, the effect of non-linear incidence parameters showed that transmission dynamics of HIV/AIDS will be lowered when infectives after becoming aware of their infection, do not take part in sexual interaction or use preventive measures to prevent the spreading of the infection. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the transmission dynamics of HIV/AIDS with screening using non-linear incidence.

Keywords: HIV/AIDS, Screening, Non-linear incidence, Reproduction number, Stability