Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19 - Mello, Isys F. [UNESP]; Squillante, Lucas [UNESP]; Gomes, Gabriel O.; Seridonio, Antonio C. [UNESP]; de Souza, Mariano [UNESP] (Elsevier, 2021)
We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin S = 1/2 Ising-like model and a (logistic) Fermi–Dirac-like function to describe the spread of Covid-19. Our analysis show that: (i) in many cases the epidemic curve can be described by a Gaussian-type function; (ii) the temporal evolution of the accumulative number of infections and fatalities follow a logistic function; (iii) the key role played by the quarantine to block the spread of Covid-19 in terms of an interacting parameter between people. In the frame of elementary percolation theory, we show that: (i) the percolation probability can be associated with the probability of a person being infected with Covid-19; (ii) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing. Yet, we make a connection between epidemiological concepts and well-established concepts in condensed matter Physics.
Keywords: Covid-19; Ising-model; Logistic function; Percolation theory