Abstract:
This paper is an investigation of the possible effects of vaccination and treatment on the dynamics of HIV-AIDS in a varying population. The devastating global impact of HIV has increased research efforts to find an effective vaccine, or drugs that would reduce the progression and transmission rate of the disease. Antiretro-viral drugs used in treatment, such as AZT (zidovudine), ddc (didieosyinosine) are presently used as a chemotherapy treatment of HIV-AIDS. The models discussed in this study are basically theoretical models since vaccination is not yet available, especially in the developing countries like Zimbabwe.
First, an SIR model was used to define the general sense of modeling an infectious disease. We then discussed the general AIDS model to describe the dynamics of the disease in a situation without any intervention programs in place. Stability analysis was looked at using mathematical analysis. A model when vaccination policy is in effect was also discussed. Critical conditions for the eradication of the disease were derived. For the sake of arguments, numerical simulations on the effect of vaccination were carried out for the cases when the proportion vaccinated is below and when it is above the critical proportion.
Next we assumed a case when treatment alone is used as a control strategy for the control of the disease and when a combination of treatment and vaccination was used. Stability analysis was carried out for each model and critical conditions were derived. With these critical values we would be able to know the minimum portion of susceptible individuals to be vaccinated and the infectives to be treated so that we can effectively control the dynamics of the disease.
