The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in December 2019 poses devastating effects in public health. Despite widespread availability of COVID-19 vaccines, a number of individuals who have been exposed or who are at high risk of exposure to an individual infected with SARS-CoV-2 are either not fully vaccinated or are fully vaccinated but have immune systems that cannot produce enough antibodies to fight against the virus. In such individuals, post-exposure prophylaxis (PEP) is an important approach in reducing the spread of the virus. In this project, we formulate a mathematical model for PEP against SARS-CoV-2 with multiple exposed and infectious classes, consisting of individuals on prophylaxis and those who are not on prophylaxis. The disease-free equilibrium of our model is derived, and the control reproduction number is computed, using the next generation matrix approach. We established the local stability of the disease-free equilibrium when the reproduction number is below one. The elasticity indices of the reproduction number with respect to each parameter are computed and parameters that are most sensitive in increasing/decreasing the reproduction number are identified. Results of numerical simulations indicate a decrease in the number of breakthrough cases, and contour plots indicate the possibility of eradicating the virus from the population. These results highlight the importance of post-exposure prophylaxis in individuals from the same institutional setting, such as nursing homes, prisons, or healthcare facilities.


Department of Mathematics and Honors Program

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