A nonlinear multi-population behavioral model to assess the roles of education campaigns, random supply of aids, and delayed ART treatment in HIV/AIDS epidemics

Divine Wanduku; Divine Wanduku

doi:10.3934/mbe.2020354

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6791-6837. doi: 10.3934/mbe.2020354

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A nonlinear multi-population behavioral model to assess the roles of education campaigns, random supply of aids, and delayed ART treatment in HIV/AIDS epidemics

Divine Wanduku ^,

Department of Mathematical Sciences, Georgia Southern University, 65 Georgia Ave, Room 3309, Statesboro, Georgia, 30460, USA

Received: 24 May 2020 Accepted: 07 September 2020 Published: 09 October 2020

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.
- HIV/AIDS education campaigns,
- supply of HIV/AIDS aids,
- basic reproduction number,
- stochastic stability,
- linear regression,
- delayed ART treatment
Citation: Divine Wanduku. A nonlinear multi-population behavioral model to assess the roles of education campaigns, random supply of aids, and delayed ART treatment in HIV/AIDS epidemics[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6791-6837. doi: 10.3934/mbe.2020354

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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.

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