Mathematical analysis of HIV/AIDS prophylaxis treatment model

Abstract

Prophylaxis (PrEP) is considered one of the promising interventions against HIV infection as trials on various groups and sites have reported its significant effectiveness. From the studies done, analysis of the data collected shows that PrEP has the potential to help prevent HIV infections and slow the HIV epidemic. In this paper, a deterministic model that incorporates PrEP is developed to assess the impact of the use PrEP on the transmission of HIV/AIDS. Stability analysis of the model showed that DFE is locally and globally asymptotically stable when R p < 1. The EE exists and is locally and globally asymptotically stable when R p > 1. PrEP effectiveness is achieved if taken effectively, hence lack of adherence to PrEP substantially increases the risk of HIV infection among the high risk individuals.

Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment

“…The number of possible negative real roots of (25) depends on the signs of 0 , 1 , and 2 . This can be established by applying Descartes Rule of Signs as used in [11].…”

“…Global dynamics of delay distributed HIV infection models with differential drug efficacy in cocirculating target cells was investigated [3]. Recent work by [11] sought to mathematically analyze the potential of Prophylaxis treatment in preventing and slowing the spread of HIV/ AIDS in the population. In this study early use of Prophylaxis drug was shown to slow the rate of HIV transmission.…”

Dynamical Analysis Within-Host and Between-Host for HIV\AIDS with the Application of Optimal Control Strategy

“…Statistics for the last few years show an outbreak that affected 38.8 million and caused a mortality rate of 1.2 million in 2015, with the infection rate being relatively constant at 2.6 million per year from 2006 to 2015 [2]. Mathematical modeling of viral infections has led to enhance the understanding of virus dynamics and helped in predicting and controlling the spread of viral diseases such as HIV and hepatitis A, B, and C. The first epidemiological model on HIV was studied in 1985, followed by many studies [3][4][5][6][7][8][9]. Knox [3] studied the transmission of AIDS, while Anderson et al [4] described some preliminary attempts to formulate mathematical models of the transmission dynamics of HIV infection in homosexual communities.…”

“…Agosto et al [8] discussed recent data which suggest that contact-mediated transmission largely manifests itself in vivo as CD4+ T-cell depletion. A deterministic model that incorporates prophylaxis was developed by Tireito et al [9] to assess the impact of the use prophylaxis on the transmission of HIV/AIDS.…”