In this talk, I will present a new deterministic SIQR model and its stochastic version, using systems of stochastic differential equations. Properties like extinction with probability one and existence of a unique stationary distribution are studied, leading to improved definitions of reproduction numbers. 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.

This is joint work with Idriss Sekkak, Bouchra R. Nasri, Jude Dzevela Kong, and Mohamed El Fatini.