Quarantine alone or in combination with treatment measures to control COVID-19

Due to its complex nature, Coronavirus has perplexed many researchers worldwide and endangered the lives of people across the globe forcing them to take social distancing and close geographical borders in order to control the spread of the disease. This study, therefore, seeks to develop a new mathematical model which delineates the dynamics of COVID-19. This latter takes into account the common characteristics that typify not only this disease as well as the infectious undetected cases, but also the ones under medical treatment. Thus we maintain that the more infected people are figured out and treated, the better we prevent the spread of Covid-19. In this paper, we study a stochastic epidemic model of Covid-19 with quarantine alone or in combination with treatment measures. Firstly, we establish the existence and uniqueness of the global positive solution to the proposed model. Secondly, we establish conditions for extinction and persistence in mean. Finally, to put on validation of the theorical results we present some numerical simulations.