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

Abstract

Recent analysis of early COVID-19 data from China showed that the number of con-firmed cases followed a subexponential power-law increase, with a growth exponentof around 2.2 (Maier and Brockmann, 2020). The power-law behavior was attributed toa combination of effective containment and mitigation measures employed as well asbehavioral changes by the population. In this work, we report a random walk MonteCarlo simulation study of proximity-based infection spread. Control interventions suchas lockdown measures and mobility restrictions are incorporated in the simulationsthrough a single parameter, the size of each step in the random walk process. Thestep sizelis taken to be a multiple of⟨r⟩, which is the average separation betweenindividuals. Three temporal growth regimes (quadratic, intermediate power-law andexponential) are shown to emerge naturally from our simulations. Forl= ⟨r⟩, we getintermediate power-law growth exponents that are in general agreement with availabledata from China. On the other hand, we obtain a quadratic growth for smaller stepsizesl≲⟨r⟩/2, while for largelthe growth is found to be exponential. We furtherperformed a comparative case study of early fatality data (under varying levels oflockdown conditions) from three other countries, India, Brazil and South Africa. Weshow that reasonable agreement with these data can be obtained by incorporatingsmall-world-like connections in our simulations.