Containing and Managing an Emerging Disease Outbreak: A Stochastic Modelling Approach.

The aim of this work is to design and analyze a novel stochastic model for an infectious disease transmission dynamics, that captures human responses to information about the disease, policy, and disease progression in the event of an outbreak. We design a behaviour-structured stochastic Susceptible-Infected-Quarantine-Recovered model incorporating a population logistic growth, non pharmaceutical interventions and a general functional response in order to capture respectively the long time growth of a population size, instant measures established by decision makers and human response behaviour. We carry out a thorough analysis to investigate the existence of the global and positive solutions and to explore the extinction and the persistence of the disease regarding the basic reproduction number of the model. Moreover, we use suitable Lyapunov functions and establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the stochastic SIQR model. In addition, we estimate the parameters of the model by fitting it to confirmed COVID-19 cases in Morocco using least squares method.