Can medication mitigate the need for a strict lock down?: A mathematical study of control strategies for COVID-19 infection

We formulate a deterministic epidemic model to study the effects of medication on the transmission dynamics of Corona Virus Disease (COVID-19). We are especially interested in how the availability of medication could change the necessary quarantine measures for effective control of the disease. We model the transmission by extending the SEIR model to include asymptomatic, quarantined, isolated and medicated population compartments. We calculate the basic reproduction number R₀ and show that for R₀ < 1 the disease dies out and for R₀ > 1 the disease is endemic. Using sensitivity analysis we establish that R₀ is most sensitive to the rates of quarantine and medication. We also study how the effectiveness and the rate of medication along with the quarantine rate affect R₀. We devise optimal quarantine, medication and isolation strategies, noting that availability of medication reduces the duration and severity of the lock-down needed for effective disease control. Our study also reinforces the idea that with the availability of medication, while the severity of the lock downs can be eased over time some social distancing protocols need to be observed, at least till a vaccine is found. We also analyze the COVID-109 outbreak data for four different countries, in two of these, India and Pakistan the curve is still rising, and in he other two, Italy and Spain, the epidemic curve is now falling due to effective quarantine measures. We provide estimates of R₀ and the proportion of asymptomatic individuals in the population for these countries.