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Hierarchical Modeling of the Effect of Pre-exposure Prophylaxis on HIV in the US

  • Renee Dale
  • Yingqing Chen
  • Hongyu HeEmail author
Chapter
  • 31 Downloads
Part of the Emerging Topics in Statistics and Biostatistics book series (ETSB)

Abstract

Pre-exposure chemical prophylaxis has been proposed as a way to slow the growth of the HIV epidemic in the US. This medication reduces the chances of an at-risk, susceptible individual acquiring HIV from an infected partner. The effectiveness of this preventative medication is dependent upon the population that uses it. Individuals susceptible to acquire HIV may engage in risky behaviors such as high partner number. We analyze the effectiveness of chemical prophylaxis on the populations involved in the HIV epidemic in the US using a hierarchical differential equation model. We create a system of nonlinear differential equations representing the system of populations involved in the HIV epidemic, focusing on susceptible and infected individuals. We stratify the susceptible population by behavior risk, and the infected population by behavior risk and HIV status awareness. We further define model parameters for both the national and the urban case, representing low and high sexual network densities. We apply a preventative medication protocol to the susceptible populations to understand the effectiveness. These parameter sets are used to study the predicted population dynamics over the next 5 years. Our results indicate that the undiagnosed high risk infected group is the largest contributor to the epidemic under both national and urban conditions. When medication that prevents contraction of HIV is applied to 35% of the high-risk susceptible population we observe a 40–50% reduction in the growth of the infected population. Little impact is observed when the medication is focused on the low-risk susceptible population. The simulations suggest that preventative medication effectiveness extends outside of the group that is taking the drug (herd immunity). Our model suggests that a strategy targeting the high-risk susceptible population would have the largest impact in the next 5 years. We also find that such a protocol has similar effects for the national as the urban case in our model, despite the smaller sexual network and lower transmission chance for rural areas.

Keywords

Hierarchical differential equations Nonlinear differential equations HIV Pre-exposure prophylaxis Mathematical modeling 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Biological SciencesLouisiana State UniversityBaton RougeUSA
  2. 2.Biostatistics ProgramFred Hutchinson Cancer Research CenterSeattleUSA
  3. 3.Math DepartmentLouisiana State UniversityBaton RougeUSA
  4. 4.Fred Hutchinson Cancer Research CenterSeattleUSA

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