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Recent analysis of early COVID-19 data from China showed that the number ofconfirmed cases followed a subexponential power-law increase, with a growthexponent of around 2.2 [B.\,F.~Maier, D.~Brockmann, {\it Science} {\bf 368},742 (2020)]. The power-law behavior was attributed to a combination ofeffective containment and mitigation measures employed as well as behavioralchanges by the population. In this work, we report a random walk Monte Carlosimulation study of proximity-based infection spread. Control interventionssuch as lockdown measures and mobility restrictions are incorporated in thesimulations through a single parameter, the size of each step in the randomwalk process. The step size $l$ is taken to be a multiple of $\langle r\rangle$, which is the average separation between individuals. Three temporalgrowth regimes (quadratic, intermediate power-law and exponential) are shown toemerge naturally from our simulations. For $l = \langle r \rangle$, we getintermediate power-law growth exponents that are in general agreement withavailable data from China. On the other hand, we obtain a quadratic growth forsmaller step sizes $l \lesssim \langle r \rangle/2 $, while for large $l$ thegrowth is found to be exponential. %Together with available data, these resultssuggest that the early containment of the disease within China was close tooptimal. We further performed a comparative case study of early fatality data(under varying levels of lockdown conditions) from three other countries,India, Brazil and South Africa. We show that reasonable agreement with thesedata can be obtained by incorporating small-world-like connections in oursimulations.

A random walk Monte Carlo simulation study of COVID-19-like infection spread