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Mean-field-type equations for spread of epidemics: the ‘small world’ model

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  • Kleczkowski, Adam
  • Grenfell, Bryan T.

Abstract

In the paper we study a cellular automata (CA) model of epidemic dynamics. The effects of local spatial correlations on a temporal (aggregated) spread of single epidemics are studied, as a function of increasing proportion of global contacts (‘small world’ model). We conjecture that even in the presence of high local correlations, the aggregated (mean-field-type) models can be quite successful, if the contact rate is treated as a free parameter. The dependence of the (estimated) contact rate on the mixing parameter can be understood in terms of a simple probabilistic model. The contact rate reflects not only a microscopic and epidemiological situation, but also a complicated social pattern, including short- and long-range contacts as well as a possibly hierarchical structure of human society.

Suggested Citation

  • Kleczkowski, Adam & Grenfell, Bryan T., 1999. "Mean-field-type equations for spread of epidemics: the ‘small world’ model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 355-360.
    • Handle: RePEc:eee:phsmap:v:274:y:1999:i:1:p:355-360
    DOI: 10.1016/S0378-4371(99)00393-3
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    Cited by:

    1. Saoud, Bilal & Moussaoui, Abdelouahab, 2018. "A new hierarchical method to find community structure in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 418-426.
    2. Diego R. Amancio & Osvaldo N. Oliveira jr & Luciano F. Costa, 2015. "Topological-collaborative approach for disambiguating authors’ names in collaborative networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 465-485, January.
    3. Yang, Yang & Sun, Peng Gang & Hu, Xia & Li, Zhou Jun, 2014. "Closed walks for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 129-143.
    4. Xiao, Yao & Yang, Mofeng & Zhu, Zheng & Yang, Hai & Zhang, Lei & Ghader, Sepehr, 2021. "Modeling indoor-level non-pharmaceutical interventions during the COVID-19 pandemic: A pedestrian dynamics-based microscopic simulation approach," Transport Policy, Elsevier, vol. 109(C), pages 12-23.
    5. Schimit, P.H.T. & Monteiro, L.H.A., 2009. "On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata," Ecological Modelling, Elsevier, vol. 220(7), pages 1034-1042.

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