Mitigating COVID-19 on a small-world network

Continuous deterministic models have been widely used to guide non-pharmaceutical interventions (NPIs) to combat the spread of the coronavirus disease 2019 (COVID-19). The validity of continuous deterministic models is questionable because they fail to incorporate two important characteristics of human society: high clustering and low degree of separation. A small-world network model is used to study the spread of COVID-19, thus providing more reliable information to provide guidance to mitigate it. Optimal timing of lockdown and reopening society is investigated so that intervention measures to combat COVID-19 can work more efficiently. Several important findings are listed as follows: travel restrictions should be implemented as soon as possible; if 'flattening the curve' is the purpose of the interventions, measures to reduce community transmission need not be very strict so that the lockdown can be sustainable; the fraction of the population that is susceptible, rather than the levels of daily new cases and deaths, is a better criterion to decide when to reopen society; and society can be safely reopened when the susceptible population is still as high as 70%, given that the basic reproduction number is 2.5. Results from small-world network models can be significantly different than those from continuous deterministic models, and the differences are mainly due to a major shortfall intrinsically embedded in the continuous deterministic models. As such, small-world network models provide meaningful improvements over continuous deterministic models and therefore should be used in the mathematical modeling of infection spread to guide the present COVID-19 interventions. For future epidemics, the present framework of mathematical modeling can be a better alternative to continuous deterministic models.