The role of asymptomatic class, quarantine and isolation in the transmission of COVID-19

We formulate a deterministic epidemic model for the spread of Corona Virus Disease (COVID-19). We have included asymptomatic, quarantine and isolation compartments in the model, as studies have stressed upon the importance of these population groups on the transmission of the disease. We calculate the basic reproduction number (Formula presented.) and show that for (Formula presented.) the disease dies out and for (Formula presented.) the disease is endemic. Using sensitivity analysis we establish that (Formula presented.) is most sensitive to the rate of quarantine and isolation and that a high level of quarantine needs to be maintained as well as isolation to control the disease. Based on this we devise optimal quarantine and isolation strategies, noting that high levels need to be maintained during the early stages of the outbreak. Using data from the Wuhan outbreak, which has nearly run its course we estimate that (Formula presented.) which while in agreement with other estimates in the literature is on the lower side.