Stochastic analysis of pre-and postexposure prophylaxis against hiv infection

The events that occur following HIV exposure, preceding any detectable infection, are difficult to study experimentally. However, there is considerable evidence that these events can be influenced by the action of antiretroviral drugs, taken either as pre-or postexposure prophylaxis (PrEP and PEP, respectively). We present simple theoretical models of HIV dynamics immediately following exposure, and apply these models to understanding how drug prophylaxis can act to reduce the risk of infection. Because HIV infection following exposure is a relatively rare event, we work with stochastic models which we base on continuous-time branching processes, allowing us to compute the risk of infection under different scenarios. We obtain analytical solutions for viral extinction probabilities, allowing us to avoid extensive computer simulations. We predict in the case of PrEP that reverse transcriptase inhibitors should be somewhat more effective than protease inhibitors and also that single drugs should be nearly as effective as a combination approach. We then model viral dynamics under PEP and find that fast initiation of therapy is essential for risk reduction. However, we predict that a two-week PEP regimen would be nearly as effective as the current recommendation of four weeks of therapy. Our work provides a coherent platform for studying the early dynamics of HIV and indicates possible directions for experimental and theoretical work.