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Spreading of Infections on Network Models: Percolation Clusters and Random Trees

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  • Hector Eduardo Roman

    (Dipartimento di Fisica, Università di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy)

  • Fabrizio Croccolo

    (Laboratoire des Fluides Complexes et de leurs Réservoirs (LFCR), UMR 5150, Centre National de la Recherche Scientifique (CNRS), TOTAL, E2S UPPA, Universite de Pau et des Pays de l’Adour, 64600 Anglet, France)

Abstract

We discuss network models as a general and suitable framework for describing the spreading of an infectious disease within a population. We discuss two types of finite random structures as building blocks of the network, one based on percolation concepts and the second one on random tree structures. We study, as is done for the SIR model, the time evolution of the number of susceptible (S), infected (I) and recovered (R) individuals, in the presence of a spreading infectious disease, by incorporating a healing mechanism for infecteds. In addition, we discuss in detail the implementation of lockdowns and how to simulate them. For percolation clusters, we present numerical results based on site percolation on a square lattice, while for random trees we derive new analytical results, which are illustrated in detail with a few examples. It is argued that such hierarchical networks can complement the well-known SIR model in most circumstances. We illustrate these ideas by revisiting USA COVID-19 data.

Suggested Citation

  • Hector Eduardo Roman & Fabrizio Croccolo, 2021. "Spreading of Infections on Network Models: Percolation Clusters and Random Trees," Mathematics, MDPI, vol. 9(23), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3054-:d:689849
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    References listed on IDEAS

    as
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    4. Fernández-Villaverde, Jesús & Jones, Charles I., 2022. "Estimating and simulating a SIRD Model of COVID-19 for many countries, states, and cities," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    5. Shao, Qi & Han, Dun, 2022. "Epidemic spreading in metapopulation networks with heterogeneous mobility rates," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Croccolo, Fabrizio & Roman, H. Eduardo, 2020. "Spreading of infections on random graphs: A percolation-type model for COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. S. P. Lukyanets & I. S. Gandzha & O. V. Kliushnichenko, 2020. "Modeling and Controlling the Spread of Epidemic with Various Social and Economic Scenarios," Papers 2006.08375, arXiv.org, revised Feb 2021.
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