Modelling the Effect of Screening and Treatment on Transmission of HIV/AIDS Infection in a Population

Abstract

This paper examines the effect of screening and treatment on the transmission of HIV/AIDS infection in a population. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The effective reproduction number of the normalised model system (3) was obtained by using the next generation operator method. The results show that the disease free equilibrium is locally stable by using Routh Hurwitz criteria 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. Using Lyapunov method, endemic equilibrium is globally stable under certain conditions. However, analysis shows that, screening of unaware HIV infectives and treatment of screened HIV infectives have the effect of reducing the transmission of the disease. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the voluntary screening and treatment of the screened infectives and full blown AIDS victims.