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Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19

Author

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  • Mello, Isys F.
  • Squillante, Lucas
  • Gomes, Gabriel O.
  • Seridonio, Antonio C.
  • de Souza, Mariano

Abstract

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.

Suggested Citation

  • Mello, Isys F. & Squillante, Lucas & Gomes, Gabriel O. & Seridonio, Antonio C. & de Souza, Mariano, 2021. "Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    • Handle: RePEc:eee:phsmap:v:573:y:2021:i:c:s0378437121002351
    DOI: 10.1016/j.physa.2021.125963
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    Citations

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    Cited by:

    1. Yang, Bo & Yu, Zhenhua & Cai, Yuanli, 2022. "The impact of vaccination on the spread of COVID-19: Studying by a mathematical model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    2. Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Pascoal, R. & Rocha, H., 2022. "Population density impact on COVID-19 mortality rate: A multifractal analysis using French data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    4. Yann Lucas Silva & Ariadne Andrade Costa, 2024. "Periodic boundary condition effects in small-world networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(7), pages 1-9, July.

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