Numerical approaches for the rapid analysis of prophylactic efficacy against HIV with arbitrary drug-dosing schemes

Pre-exposure prophylaxis (PrEP) is an important pillar to prevent HIV transmission. Because of experimental and clinical shortcomings, mathematical models that integrate pharmacological, viral- and host factors are frequently used to quantify clinical efficacy of PrEP. Stochastic simulations of these models provides sample statistics from which the clinical efficacy is approximated. However, many stochastic simulations are needed to reduce the associated sampling error. To remedy the shortcomings of stochastic simulation, we developed three numerical methods that allow predicting the efficacy of arbitrary prophylactic regimen directly from a viral dynamics model, without sampling. We apply the methods to various hypothetical dolutegravir (DTG) prophylaxis scenarios. The approaches are verified against one another, as well as state-of-the-art stochastic simulation. While the methods are more accurate than stochastic simulation, they are superior in terms of computational performance. For example, a continuous 6-month prophylactic profile is computed within a few seconds on a laptop computer. The methods computational performance, therefore, substantially expands the horizon of feasible analysis in the context of PrEP, and possibly other applications. Author summaryPre-exposure prophylaxis (PrEP) is an important tool to prevent HIV transmission. However, experimental identification of parameters that determine prophylactic efficacy is extremely difficult. Clues about these parameters could prove essential for the design of next-generation PrEP compounds. Integrative mathematical models can fill this void: Based on stochastic simulation, a sample statistic can be generated, from which the prophylactic efficacy is estimated. However, for this sample statistic to be accurate, many simulations need to be performed. Here, we introduce three numerical methods to directly compute the prophylactic efficacy from a viral dynamics model, without the need for sampling. Based on several examples with dolutegravir (DTG) -based short- and long-term PrEP, as well as post-exposure prophylaxis we demonstrate the correctness of the new methods and their outstanding computational performance. Due to the methods computational performance, a number of analysis, including formal sensitivity analysis are becoming feasible with the proposed methods.