Abstract
The successful reduction in prevalence rates of HIV in many countries is attributed to control measures such as information and education campaigns (IEC), antiretroviral therapy (ART), and national, multinational and multilateral support providing official developmental assistance (ODAs) to combat HIV. However, control of HIV epidemics can be interrupted by limited random supply of ODAs, high poverty rates and low living standards. This study presents a stochastic HIV/AIDS model with treatment assessing the roles of IEC, the supply of ODAs and early treatment in HIV epidemics. The supply of ODAs is assessed via the availability of medical and financial resources leading more people to get tested and begin early ART. The basic reproduction number ($\mathfrak{R}_{0}$) for the dynamics is obtained, and other results for HIV control are obtained by conducting stability analysis for the stochastic SITRZ disease dynamics. Moreover, the model is applied to Uganda HIV/AIDS data, wherein linear regression is applied to predict the $\mathfrak{R}_{0}$ over time, and to determine the importance of ART treatment in the dynamics.
Highlights
HIV is the agent that causes AIDS
The impacts of information and education campaigns (IEC), the random supply of official developmental assistance (ODAs) and delayed antiretroviral therapy (ART) treatment on HIV/AIDS control are investigated via conducting a stochastic stability analysis of the system of differential equations for the HIV/AIDS epidemic
Derivation of the epidemic model in the absence of noise. It follows from the assumptions (A)–(G) in Model-Assumptions 2.1-2.8 above that a compartmental framework depicting the transitions between the different states of the population is given in Figure 2, and the deterministic HIV/AIDS epidemic dynamic model with treatment and information intervention follows immediately
Summary
HIV (human immunodeficiency virus) is the agent that causes AIDS (acquired immunodeficiency syndrome). Top multilateral organizations fighting against HIV/AIDS such as Global Fund [9], and PEPFAR [10] provide official development assistance (ODA)∗ [11], funding and supporting large and small scale projects globally designed to prevent and treat HIV/AIDS Such assistance in treatment or prevention has saved many lives against the disease [9,10,11,12]. Adding randomness in the supply of ODAs and poverty rates leads to a stochastic differential equation model for HIV/AIDS with treatment, multiple behaviorial changes, and time delays to onset of treatment and full blown AIDS. The impacts of IECs, the random supply of ODAs and delayed ART treatment on HIV/AIDS control are investigated via conducting a stochastic stability analysis of the system of differential equations for the HIV/AIDS epidemic.
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