Finite-size behavior in phase transitions and scaling in the progress of an epidemic

Abstract

Analytical descriptions of patterns concerning spread and fatality during an epidemic, covering natural as well as restriction periods, are important for reducing damage. We employ a scaling model to investigate this aspect in the real data of COVID-19. It transpires from our study that the statistics of fatality in many geographical regions follow unique behavior, implying the existence of universality. Via Monte Carlo simulations in finite boxes, we also present results on coarsening dynamics in a generic model that is used frequently for the studies of phase transitions in various condensed matter systems. It is shown that the overall growth, in a large set of regions, concerning disease dynamics, and that during phase transitions in a broad class of finite systems are closely related to each other and can be described via a single and compact mathematical function, thereby providing a new angle to the studies of the former. In the case of disease we have demonstrated that the employed scaling model has predictive capability, when used appropriately, even for periods with complex social restrictions. These results are of much general epidemiological relevance.