Two-level modeling of quarantine

Front propagation in a spatial system of weakly interacting networks

We consider the spread of epidemic in a spatial metapopulation system consisting of weakly interacting patches. Each local patch is represented by a network with a certain node degree distribution and individuals can migrate between neighboring patches. Stochastic particle simulations of the SIR model show that after a short transient, the spatial spread of epidemic has a form of a propagating front. A theoretical analysis shows that the speed of front propagation depends on the effective diffusion coefficient and on the local proliferation rate similarly to fronts described by the Fisher-Kolmogorov equation. To determine the speed of front propagation, first, the early-time dynamics in a local patch is computed analytically by employing degree based approximation for the case of a constant disease duration. The resulting delay differential equation is solved for early times to obtain the local growth exponent. Next, the reaction diffusion equation is derived from the effective master equation and the effective diffusion coefficient and the overall proliferation rate are determined. Finally, the fourth order derivative in the reaction diffusion equation is taken into account to obtain the discrete correction to the front propagation speed. The analytical results are in a good agreement with the results of stochastic particle simulations.

When and how do business shutdowns work? Evidence from Italy's first COVID-19 wave

Governments around the world have adopted unprecedented policies to deal with COVID-19. This paper zooms in on business shutdowns and investigates their effectiveness in reducing mortality. We leverage highly granular death registry data for almost 5000 Italian municipalities in a diff-in-diff approach that allows us to mitigate endogeneity concerns credibly. Our results, which are robust to controlling for a host of co-factors, offer strong evidence that business shutdowns effectively curb mortality. We calculate that they may have reduced the death toll from the first wave of COVID-19 in Italy by about 40%. Our findings also highlight that timeliness is key - by acting 1 week earlier, their effectiveness could have been increased by an additional 5%. Finally, shutdowns should be targeted. Closing service activities with a high degree of interpersonal contact saves the most lives. Shutting down production activities, while substantially reducing mobility, only has mild effects on mortality.

Empirical study and model simulation of global stock market dynamics during COVID-19

At the beginning of 2020, COVID-19 swept the world and changed various aspects of human society, such as economy and finance, life and health, migration and population. We first empirically study how the dynamic behaviors of stock markets are affected by COVID-19, and focus on the large volatility dynamics, variation-fluctuation correlation function and epidemic-fluctuation correlation function. Then we generalize the Heston model to simulate the global stock market dynamics, and an epidemic index computed from empirical data is directly taken as the external force in the modelling.