Mathematical Insights in Evaluating State Dependent Effectiveness of HIV Prevention Interventions

Abstract

Mathematical models have been used to simulate HIV transmission and to study the use of pre-exposure prophylaxis (PrEP) for HIV prevention. Often a single intervention outcome over 10 years has been used to evaluate the effectiveness of PrEP interventions. However, different metrics express a wide variation over time and often disagree in their forecast on the success of the intervention. We develop a deterministic mathematical model of HIV transmission and use it to evaluate the public-health impact of oral PrEP interventions. We study PrEP effectiveness with respect to different evaluation methods and analyze its dynamics over time. We compare four traditional indicators, based on cumulative number or fractions of infections prevented, on reduction in HIV prevalence or incidence and propose two additional methods which estimate the burden of the epidemic to the public-health system. We investigate the short and long term behavior of these indicators and the effects of key parameters on the expected benefits from PrEP use. Our findings suggest that public-health officials considering adopting PrEP in HIV prevention programs can make better informed decision by employing a set of complementing quantitative metrics.

Impact of Population Recruitment on the HIV Epidemics and the Effectiveness of HIV Prevention Interventions

“…Mathematical models have been extensively employed to provide insights into the effectiveness and cost-effectiveness of different prevention programs (Abbas et al 2007; Cremin et al 2013; Desai et al 2008; Dimitrov et al 2010, 2011, 2012; Grant et al 2010; Zhao et al 2013; Supervie et al 2010; Nichols et al 2013; Juusola et al 2012). Although focused on the intervention characteristics, such as efficacy mechanisms, roll out schedule, projected adherence and coverage these analyses necessarily model the demographic processes in the population such as births, sexual maturation, mortality and migration.…”

“…In this study, we additionally consider logistic recruitment assuming that the number of people who join the population increases with population size but saturates at specific level driven by resource limitations. We modify a model (Zhao et al 2013), previously used to project the impact of daily regimens of oral PrEP, to study the population dynamics and compare the efficacy of PrEP interventions under different recruitment assumptions. We demonstrate the impact of the recruitment assumptions using simple extensions of the classical SI model some of which have been already analyzed (Korobeinikov 2006; Hwang and Kuang 2003; Berezovsky et al 2005).…”

Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells

“…Recently, a cocktail of one or more RTIs and PIs is used to suppress the HIV replication and to prolong time to the onset of AIDS [2]. In the literature, a variety of mathematical models have been proposed to describe the HIV dynamics with target cells and the effect of antiviral treatment [2][3][4][5][6][7][8][9][10][11][12][13][14]. In these papers, it was assumed that all the infected cells have the same lifetime and produce the same amount of viruses.…”

“…Recently, many efforts have been devoted to the analysis of various mathematical models of HIV dynamics with two classes of target cells (see, e.g. [2,[7][8][9][10][11][12][13][14]). In [18], it is assumed that the virus has multiple classes of uninfected target cells.…”

“…In [18], it is assumed that the virus has multiple classes of uninfected target cells. However, in [2,[7][8][9][10][11][12][13][14]18] only short-lived infected cells have been considered. In [15], the model (1) was extended to take into consideration two cocirculating target cells, CD4 + T cells and macrophages as: 2 , v = Nδ(y 1 + y 2 ) + Ma(z 1 + z 2 ) − uv, (2) where x i , y i , z i , and v denote the concentration of uninfected target cells, short-lived infected cells, long-lived chronically infected cells, and free viruses, respectively, where i = 1, 2 correspond to the CD4 + T cells and macrophages, respectively.…”