Staged HIV transmission and treatment in a dynamic model with long-term partnerships

The transmission dynamics of HIV are closely tied to the duration and overlap of sexual partnerships. We develop an autonomous population model that can account for the possibilities of an infection from either a casual sexual partner or a long-term partner who was either infected at the start of the partnership or has been newly infected since the onset of the partnership. The impact of the long-term partnerships on the rate of infection is captured by calculating the expected values of the rate of infection from these extended contacts. The model includes three stages of infectiousness: acute, chronic, and virally suppressed. We calculate HIV incidence and the fraction of new infections attributed to casual contacts and long-term partnerships allowing for variability in condom usage, the effect of achieving and maintaining viral suppression, and early intervention by beginning HAART during the acute phase of infection. We present our results using data on MSM HIV transmission from the CDC in the U.S. While the acute stage is the most infectious, the majority of the new infections will be transmitted by long-term partners in the chronic stage when condom use is infrequent as is common in long-term relationships. Time series analysis of the solution, as well as parameter sensitivity analysis, are used to determine effective intervention strategies.

A sexually transmitted infection model with long-term partnerships in homogeneous and heterogenous populations

Population models for sexually transmitted infections frequently use a transmission model that assumes an inherent partnership length of zero. However, in a population with long-term partnerships, the infection status of the partners, the length of the partnership, and the exclusivity of the partnership significantly affect the rate of infection. We develop an autonomous population model that can account for the possibilities of an infection from either a casual sexual partner or a longtime partner who was either infected at the start of the partnership or was newly infected. The impact of the long-term partnerships on the rate of infection is captured by calculating the expected values of the rate of infection from these extended contacts. We present a new method to evaluate partner acquisition rates for casual or long-term partnerships which produces in a more realistic number of lifetime sexual partners. Results include a SI model with different infectiousness levels for the transmission of HIV and HSV-2 with acute and chronic/latent infection stages for homogeneous (MSM) and heterogeneous (WSM-MSW) groups. The accompanying reproduction number and sensitivity studies highlight the impact of both casual and long-term partnerships on infection spread. We construct an autonomous set of equations that handle issues usually ignored by autonomous equations and handled only through simulations or in a non-autonomous form. The autonomous formulation of the model allows for simple numerical computations while incorporating a combination of random instantaneous contacts between individuals and prolonged contacts between specific individuals.

A SIMULATION-BASED FRAMEWORK FOR ASSESSING THE FEASIBILITY OF RESPONDENT-DRIVEN SAMPLING FOR ESTIMATING CHARACTERISTICS IN POPULATIONS OF LESBIAN, GAY AND BISEXUAL OLDER ADULTS

Respondent-driven sampling (RDS) is a method for sampling from a target population by leveraging social connections. RDS is invaluable to the study of hard-to-reach populations. However, RDS is costly and can be infeasible. RDS is infeasible when RDS point estimators have small effective sample sizes (large design effects) or when RDS interval estimators have large confidence intervals relative to estimates obtained in previous studies or poor coverage. As a result, researchers need tools to assess whether or not estimation of certain characteristics of interest for specific populations is feasible in advance. In this paper, we develop a simulation-based framework for using pilot data-in the form of a convenience sample of aggregated, egocentric data and estimates of subpopulation sizes within the target population-to assess whether or not RDS is feasible for estimating characteristics of a target population. in doing so, we assume that more is known about egos than alters in the pilot data, which is often the case with aggregated, egocentric data in practice. We build on existing methods for estimating the structure of social networks from aggregated, egocentric sample data and estimates of subpopulation sizes within the target population. We apply this framework to assess the feasibility of estimating the proportion male, proportion bisexual, proportion depressed and proportion infected with HIV/AIDS within three spatially distinct target populations of older lesbian, gay and bisexual adults using pilot data from the caring and Aging with Pride Study and the Gallup Daily Tracking Survey. We conclude that using an RDS sample of 300 subjects is infeasible for estimating the proportion male, but feasible for estimating the proportion bisexual, proportion depressed and proportion infected with HIV/AIDS in all three target populations.