Noor Hidayat

Sensitivity analysis of the parameters of an HIV/AIDS model with condom campaign and antiretroviral therapy

In this article, we present a deterministic model for the transmission dynamics of HIV/AIDS in which condom campaign and antiretroviral therapy are both important for the disease management. We calculate the effective reproduction number using the next generation matrix method and investigate the local and global stability of the disease-free equilibrium of the model. Sensitivity analysis of the effective reproduction number with respect to the model parameters were carried out. Our result shows that efficacy rate of condom campaign, transmission rate for contact with the asymptomatic infective, progression rate from the asymptomatic infective to the pre-AIDS infective, transmission rate for contact with the pre-AIDS infective, ARV therapy rate, proportion of the susceptible receiving condom campaign and proportion of the pre-AIDS receiving ARV therapy are highly sensitive parameters that effect the transmission dynamics of HIV/AIDS infection.

Optimal strategy for controlling the spread of HIV dynamics with educational campaigns and antiretroviral therapy

A deterministic mathematical model with educational campaigns and ARV (Anti Retro Viral) therapy as control variables are formulated and analyzed using optimal control theory (the Pontryagins Maximum Principle). We formulate the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of the asymptomatic stage and pre-AIDS stage of HIV infection and in the spread of HIV using of educational campaigns and antiretroviral therapy are used as the control items. The numerical simulation of both the systems i.e. with control and without control, shows that the combination of the two strategies helps to reduce a significant difference in the number of individuals in the asymptomatic stage of HIV infection, the number of individuals in pre-AIDS stage, and the number of individuals with full-blown AIDS.