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Critical Community Size for COVID-19: A Model Based Approach for Strategic Lockdown Policy

Abstract

Among the U.S. cities hit by the 1918 Spanish flu, social distancing played a pivotal role in flattening the pandemic curve. Similarly, to fight against COVID-19, restrictive mass quarantine or lockdown has been implemented as the most important controlling measure. India has already enforced a lockdown of 10 weeks and is extending the period depending on the current disease scenario. However, the idea that, if the susceptible population drops below certain threshold, the infection would naturally die out in small communities after a fixed time (following the outbreak), unless the disease is reintroduced from outside, was proposed by M. S. Bartlett in 1957. This threshold was termed as Critical Community Size (CCS). We propose an Susceptible-Exposed-Infected-Recovered (SEIR) model that explains COVID-19 disease dynamics. Using our model, we have calculated state-specific Temporary Eradication of Spread Time (TEST) and CCS that would essentially determine the ideal number of lockdown days required and the size of quarantined population. With the given state-wise rates of death, recovery and other parameters, we have identified that, if at a place the total number of susceptible population drops below CCS, infection will cease to exist after a period of expected time to extinction (TTE), unless it is re-introduced from outside. The expected TTE suggests that the disease might take a long time to fade away from the human population in absence of pharmaceutical interventions. But we find that the disease might subside substantially after TEST. This would imply lockdown phases as much as TEST could be sufficient to contain COVID-19.

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