Saturation effects and the concurrency hypothesis: Insights from an analytic model

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.

Concurrency measures in the era of temporal network epidemiology: a review

Diseases spread over temporal networks of interaction events between individuals. Structures of these temporal networks hold the keys to understanding epidemic propagation. One early concept of the literature to aid in discussing these structures is concurrency-quantifying individuals' tendency to form time-overlapping 'partnerships'. Although conflicting evaluations and an overabundance of operational definitions have marred the history of concurrency, it remains important, especially in the area of sexually transmitted infections. Today, much of theoretical epidemiology uses more direct models of contact patterns, and there is an emerging body of literature trying to connect methods to the concurrency literature. In this review, we will cover the development of the concept of concurrency and these new approaches.

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.

Relational concurrency, stages of infection, and the evolution of HIV set point viral load

HIV viral load (VL) predicts both transmission potential and rate of disease progression. For reasons that are still not fully understood, the set point viral load (SPVL) established after acute infection varies across individuals and populations. Previous studies have suggested that population mean SPVL (MSPVL) has evolved near an optimum that reflects a trade-off between transmissibility and host survival. Sexual network structures affect rates of potential exposure during different within-host phases of infection marked by different transmission probabilities, and thus affect the number and timing of transmission events. These structures include relational concurrency, which has been argued to explain key differences in HIV burden across populations. We hypothesize that concurrency will alter the fitness landscape for SPVL in ways that differ from other network features whose impacts accrue at other times during infection. To quantitatively test this hypothesis, we developed a dynamic, stochastic, data-driven network model of HIV transmission, and evolution to assess the impact of key sexual network phenomena on MSPVL evolution. Experiments were repeated in sensitivity runs that made different assumptions about transmissibility during acute infection, SPVL heritability, and the functional form of the relationship between VL and transmissibility. For our main transmission model, scenarios yielded MSPVLs ranging from 4.4 to 4.75 log10 copies/ml, covering much of the observed empirical range. MSPVL evolved to be higher in populations with high concurrency and shorter relational durations, with values varying over a clinically significant range. In linear regression analyses on these and other predictors, main effects were significant (P < 0.05), as were interaction terms, indicating that effects are interdependent. We also noted a strong correlation between two key emergent properties measured at the end of the simulations-MSPVL and HIV prevalence-most clearly for phenomena that affect transmission networks early in infection. Controlling for prevalence, high concurrency yielded higher MSPVL than other network phenomena. Interestingly, we observed lower prevalence in runs in which SPVL heritability was zero, indicating the potential for viral evolution to exacerbate disease burden over time. Future efforts to understand empirical variation in MSPVL should consider local HIV burden and basic sexual behavioral and network structure.