HIV transmission rate modeling: a primer, review, and extension

Abstract

Several mathematical modeling studies based on the concept of "HIV transmission rates" have recently appeared in the literature. The transmission rate for a particular group of HIV-infected persons is defined as the mean number of secondary infections per member of the group per unit time. This article reviews the fundamental principles and mathematics of transmission rate models; explicates the relationship between these models, Bernoullian models of HIV transmission, and mathematical models based on the concept of the "reproductive rate of infection"; describes an extension of existing transmission rate models to better incorporate the positive impact of HIV treatment; and discusses the limitations of the transmission rate modeling approach. Results from the extended transmission rate model indicate that approximately 51.6% of new sexually-transmitted infections in the US are due to the transmission risk behaviors of infected persons who are unaware of their infection, including 10.9% due to persons in the acute phase of HIV infection. Findings from this study suggest that significant reductions in HIV incidence likely will require a combination of increased antibody testing, enhanced early detection of acute HIV infection, appropriate medical care and antiretroviral medicine adherence counseling, and behavioral risk reduction interventions.

Figure 1

Potential compartments (groups) in a comprehensive transmission rate model. Following Marks and colleagues (6), this schematic assumes that PLWH with CD4 cell counts less than 500 cells per mL are incapable of transmitting HIV to sex partners. Alternative models might substitute undetectable viral load for CD4 < 500 cells per mL or otherwise distinguish potential transmitters from non-transmitters.