A Mathematical Delay Model for Control of the Spread of HIV/AIDS in a Homogeneous Population
Emily Nelima Simiyu *
Department of Pure and Applied Mathematics, Maseno University, Box 333 Maseno, Kenya.
David O. Ambogo
Department of Pure and Applied Mathematics, Maseno University, Box 333 Maseno, Kenya.
Richard O. Opiyo
Department of Pure and Applied Mathematics, Maseno University, Box 333 Maseno, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we have considered a Delay Differential Equations model describing HIV-AIDS transmission incorporating time lags \(\tau\)1, and \(\tau\)2 and use of Prophylaxis . The formulated model has been analysed in which the Stationary points have been shown to be asymptotically Stable. Numerical Simulations have been carried out to determine the effects of time lags and Prophylaxis use. our results shows that when R\(\tau\) < 1, HIV is controlled in the population and vice versa. Numerical simulations were carried out to determine the impact of time delay and Prophylaxis use on the control of HIV. Our results demonstrate that optimal use of Prophylaxis and minimal time delay within 3 days resulted in R\(\tau\) < 1, hence resulting in predominance in the uninfected (Susceptibles), coupled with the diminishing of the Exposed, Infected and AIDS individuals. The findings imply that prophylaxis use and time delay are key parameters in regulation of R\(\tau\) and therefore aids in the control of the spread of HIV/AIDS.
Keywords: Control, HIV/AIDS, prophylaxis, delay differential equations, stability