Epidemic via superstatistics and random walk on a torus. Issue 6 (5th October 2020) - Alzeley, Omar
Abstract : The mathematical study of diseases and their dissemination has, at most, been a subject for just over three centuries. Superstatistics is based on the idea of the superposition of at least two parameters. To date, this methodology has not been applied to epidemiology. In this article, we investigate the spread of epidemics of the susceptible‐infected‐removed (SIR) type using superstatistics and random walk on a torus. This article aims to bring together two areas which have recently become active areas of research. We model epidemics on a torus in terms of a "game" between the susceptible and the infected. We also compute the probabilities for all possible transitions between them. Furthermore, we investigate the behavior and structure of our setup model. Finally, we study the superstatistics of stochastic processes and apply their techniques to a well‐known model in the epidemic literature known as SIR. No other work, to the best of our knowledge, has studied SIR via superstatistics to date