Recent work showed that the initial COVID-19 data from China  followed a subexponential power-law increase in the number of confirmed cases. This was attributed to a combination of effective containment and mitigation measures employed as well as behaviorial changes by the population. In view of this , we performed a Monte Carlo random walk study to better understand proximity-based infectious disease spread, particularly under restrictions. Our model is found to be rather robust and reproduces the observed power-law growth without relying on any external parameters. Three\langle \rangle growth regimes (quadratic,  power-law and exponential)  emerge naturally from our simulations. These\langle \rangle\lesssim \langle \rangle results suggest that the early containment of the disease within China was close to optimal and could not have been significantly improved upon . We show that reasonable agreement with other data can be attained by incorporating small-world-like connections in the simulations. The prescribed model and its generalizations might be useful for future strategies in the midst of the present pandemic .
Recent analysis of COVID-19 data from China showed that the number of confirmed cases followed a subexponential power-law increase , with a growth exponent of around 2.2. The power-law behavior was attributed to a combination of effective containment and mitigation measures employed as well as behavioral changes by the population. In this work, we report a random walk Monte Carlo simulation study of proximity-based infection spread. Social distancing is incorporated in the simulations through a single parameter, the size of each step in the random walk process. The step size l is taken to be a multiple of\langle r\rangle, which is the average separation between individuals. Three temporal growth regimes (quadratic, intermediate power-law and exponential) are shown to emerge naturally from our simulations. For l =\langle r\rangle, we get intermediate power-law growth exponents that are in general agreement with available data from China. On the other hand, we obtain a quadratic growth for smaller step sizes l\lesssim \langle r\rangle/2 , while for large l the growth is found to be exponential. Together with available data, these results suggest that the early containment of the disease within China was close to optimal . We further performed a comparative case study of data from three other countries, India, Brazil and South Africa . We show that reasonable agreement with these data can be obtained by incorporating small-world-like connections in our simulations .
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