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

TL;DR

This study uses a random walk Monte Carlo model to simulate COVID-19 spread, revealing different growth regimes depending on control measures and mobility, and compares results with data from multiple countries.

Contribution

It introduces a proximity-based Monte Carlo simulation incorporating control measures and small-world connections to model COVID-19 spread.

Findings

Intermediate power-law growth matches Chinese data.

Quadratic growth occurs with smaller step sizes.

Exponential growth appears with larger step sizes.

Abstract

Recent analysis of early 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 [B.\,F.~Maier, D.~Brockmann, {\it Science} {\bf 368}, 742 (2020)]. 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. Control interventions such as lockdown measures and mobility restrictions are 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 early fatality data (under varying levels of lockdown conditions) 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.