Mathematical Modeling of Post-Exposure Prophylaxis of SARS-CoV-2

Abstract

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in December 2019, and as of August 29, 2022, this virus was responsible for about 6 million confirmed deaths and about 450 million confirmed cases of COVID-19 globally. In this project, we used mathematical modeling to investigate the impact of post-exposure prophylaxis in preventing the spread of SARS-CoV-2. The disease-free equilibrium of our model is derived, and the basic reproduction number is computed, using the next generation matrix approach. We studied the elasticity indices of the reproduction number with respect to each parameter and identified parameters that are most sensitive in increasing the reproduction number and those that are most sensitive in decreasing the reproduction number. Numerical simulations suggest that an increase in the modification parameter for the transmission rate of breakthrough cases results in more infectiousness for those not on prophylaxis when compared to individuals on prophylaxis. The outcomes of our contour plot suggest the possibility of eradicating the virus from the population under different combinations of the proportion of individuals who recently came in contact with an infectious individual and have been administered an antiviral drug such as REGEN-CoV. Results of numerical simulations and contour plots highlight the importance of post-exposure prophylaxis on the transmission of SARS-CoV-2 in the population.