Improving adherence to a daily PrEP regimen is key when considering long-time partnerships.

A population model of HIV that includes susceptible individuals not taking the pre-exposure prophylaxis (PrEP), susceptible individuals taking daily PrEP, and infected individuals is developed for casual partnerships, as well as monogamous and non-monogamous long-term partnerships. Reflecting the reality of prescription availability and usage in the U.S., the PrEP taking susceptible population is a mix of individuals designated by the CDC as high and low risk for acquiring HIV. The rate of infection for non-monogamous long-term partnerships with differential susceptibility is challenging to calculate and requires Markov chain theory to represent the movement between susceptible populations before infection. The parameters associated with PrEP initiation, suspension and adherence impact both the reproduction number of the model and the elasticity indices of the reproduction model. A multi-parameter analysis reveals that increasing adherence has the largest effect on decreasing the number of new infections.