Epidemics, the Ising-model and percolation theory: a comprehensive review focussed on Covid-19

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 reinforces well-established literature results, namely: emph{i}) that the epidemic curves can be described by a Gaussian-type function; emph{ii}) that the temporal evolution of the accumulative number of infections and fatalities follow a logistic function, which has some resemblance with a distorted Fermi-Dirac-like function; emph{iii}) the key role played by the quarantine to block the spread of Covid-19 in terms of an emph{interacting} parameter, which emulates the contact between infected and non-infected people. Furthermore, in the frame of elementary percolation theory, we show that: emph{i}) the percolation probability can be associated with the probability of a person being infected with Covid-19; emph{ii}) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing, impacting thus in the probability of an infected person to infect other people. Increasing the number of infected people leads to an increase in the number of net connections, giving rise thus to a higher probability of new infections (percolation). We demonstrate the importance of social distancing in preventing the spread of Covid-19 in a pedagogical way. Given the impossibility of making a precise forecast of the disease spread, we highlight the importance of taking into account additional factors, such as climate changes and urbanization, in the mathematical description of epidemics. Yet, we make a connection between the standard mathematical models employed in epidemics and well-established concepts in condensed matter Physics, such as the Fermi gas and the Landau Fermi-liquid picture.