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 confirmed cases followed a subexponential power-law increase, with a growth exponent of around 2.2 (Maier and Brockmann, 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 is taken to be a multiple of , 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 , 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 , while for large the growth is found to be exponential. 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.

A new logistic growth model applied to COVID-19 fatality data

“…Such control interventions prevent a homogeneous mixing ( Fofana and Hurford, 2017 ) of the population, which if unchecked would lead to exponential growth, provided there is no depletion of the susceptible population ( Bailey, 1975 ). Our simulations ( Triambak and Mahapatra, 2021 ) further showed that the minimum growth exponent obtained under the most stringent mobility restrictions is quadratic growth . More realistically one would expect growth exponents that are slightly higher than 2, under the most effective containment scenarios ( Maier and Brockmann, 2020 , Triambak and Mahapatra, 2021 ).…”

“…Our simulations ( Triambak and Mahapatra, 2021 ) further showed that the minimum growth exponent obtained under the most stringent mobility restrictions is quadratic growth . More realistically one would expect growth exponents that are slightly higher than 2, under the most effective containment scenarios ( Maier and Brockmann, 2020 , Triambak and Mahapatra, 2021 ). It is reasonable to expect that during the first wave of the pandemic (in 2020) most countries followed similar contaiment strategies at various levels to counter the spread of COVID-19 within their populace.…”

“…( Pell et al, 2018 , Chowell et al, 2019 , Wang et al, 2012 ). Along these lines, our previous work ( Triambak and Mahapatra, 2021 ) also showed that the commonly used generalized LGM ( Richards, 1959 ) works for exponential growth, it may fail to satisfactorily fit epidemic data when there is sub-exponential power-law growth. As a continuation of our engagement with this problem, we present in this work a logistic growth model that describes such data more accurately.…”

“…It is reasonable to expect that during the first wave of the pandemic (in 2020) most countries followed similar contaiment strategies at various levels to counter the spread of COVID-19 within their populace. Therefore their cumulative infection (and fatality) curves are expected to have power-law growth exponents in the range of 2 to 3 ( Triambak and Mahapatra, 2021 ). Below we develop a new LGM that can adequately describe such data, and make reasonably accurate and consistent predictions.…”

“…Other methods involved the use of phenomenological models ( Majumder and Mandl, 2020 , Roosa et al, 2020 ), time-varying and non-linear Markov processes ( Wang et al, 2020a , Gourieroux and Jasiak, 2020 ), superpositions of epidemic waves ( Koltsova et al, 2020 ), hybrid nonparametric models ( Wang et al, 2020b ) and other data-driven approaches ( Salas, 2021 , Schneble et al, 2021 , Altmejd et al, 2020 ), including those based on artificial intelligence ( Chen et al, 2020 ), etc. Along these lines, we recently performed a random walk Monte Carlo study to make temporal growth exponent predictions for COVID-19-like disease spread ( Triambak and Mahapatra, 2021 ), particularly for a spatially constrained, yet stochastically interacting population. In that work, similar to other simulational approaches ( Mollison, 1977 , Filipe and Gibson, 1998 ), the spread of the disease was modeled on the basis of proximity-based interactions.…”