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.