A stochastic analysis of a SIQR epidemic model with short and long-term prophylaxis

This paper aims to incorporate a high order diffusion term into a SIQR epidemic model with transient prophylaxis and lasting prophylaxis. The existence and uniqueness of the global positive solution is proven and we find a condition ensuring the extinction of an infectious disease. 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 reproduction number associated with the stochastic model, while constructing a model fitting the data. •A stochastic SIQR epidemic model with higher-order perturbation is investigated.•The existence and uniqueness of the global positive solution are studied.•A stochastic threshold is established for extinction.•COVID-19 data from Canada are used to estimate the transmission rate.