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.
MIDAS Coordination Center
University of Pittsburgh
A737 Public Health
130 DeSoto Street
Pittsburgh PA 15261