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

Triambak, S.; Mahapatra, D. P.

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.