Stochastic analysis of two‐strain epidemic model with non‐monotone incidence rates: Application to COVID‐19 pandemic

Abstract

This work is devoted to the mathematical analysis of a COVID‐19 two‐strain epidemic model. The COVID‐19 mathematical model described the infection forces of each strain by a nonmonotonic incidence function. First, we establish the well‐posedness of the COVID‐19 stochastic model in terms of existence and uniqueness of the global positive solution. After that, we investigate the results of the stochastic extinction and persistence in mean of the COVID‐19 disease. The findings show that both strains of COVID‐19 pandemic extinct, when the basic reproduction number is less than unity. If the latter is not achieved, then the infection related to the strain with higher stochastic basic reproduction number will persist. Additionally, both strains can persist at the same time, if their related stochastic basic reproduction numbers are both greater than one. Finally, various numerical simulations are carried out in order to validate the theoretical findings concerning the extinction and persistence in mean of the disease. As an application of our work, we have chosen to compare our deterministic and stochastic results with COVID‐19 clinical data.