A Stochastic Analysis of a Siqr Epidemic Model With Short and Long-term Prophylaxis

Abstract This paper aims to incorporate a high order stochastic perturbation into a SIQR epidemic model with transient prophylaxis and lasting prophylaxis. The existence and uniqueness of the global positive solution is proven and a stochastic condition in order to study the extinction of an infectious disease is established. The existence of a stationary distribution for the stochastic epidemic model is investigated as well. Numerical simulations are conducted to support our theoretical results and an example of application with COVID-19 data from Canada is used to estimate the transmission rate and basic reproduction number while constructing a model fitting the data.