Abstract
Classical epidemiological models assume mass action. However, this assumption is violated when interactions are not random. With the recent COVID-19 pandemic, and resulting shelter in place social distancing directives, mass action models must be modified to account for limited social interactions. In this paper we apply a pairwise network model with moment closure to study the early transmission of COVID-19 in New York and San Francisco and to investigate the factors determining the severity and duration of outbreak in these two cities. In particular, we consider the role of population density, transmission rates and social distancing on the disease dynamics and outcomes. Sensitivity analysis shows that there is a strongly negative correlation between the clustering coefficient in the pairwise model and the basic reproduction number and the effective reproduction number. The shelter in place policy makes the clustering coefficient increase thereby reducing the basic reproduction number and the effective reproduction number. By switching population densities in New York and San Francisco we demonstrate how the outbreak would progress if New York had the same density as San Francisco and vice-versa. The results underscore the crucial role that population density has in the epidemic outcomes. We also show that under the assumption of no further changes in policy or transmission dynamics not lifting the shelter in place policy would have little effect on final outbreak size in New York, but would reduce the final size in San Francisco by 97%.