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Critically spanning epidemic outbreak cluster in random geometric networks

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  • Saha, Dipa
  • Mitra, Sayantan
  • Sensharma, Ankur

Abstract

The central quantity of interest in the mathematical modeling of infectious diseases is perhaps the epidemic threshold, which indicates the capability of a pathogen to infect a sizable fraction of a population. Depending on the system and the approach, this threshold can be related to different system parameters. In this study, we employ the stochastic, asynchronous susceptible–infected–recovered (SIR) model in a random geometric graph (RGG), which, by virtue of its definition, is a conspicuously suitable spatial network for analyzing epidemic spreading. We adopt a percolation approach to determine the epidemic criterion in terms of a characteristic length scale, namely, the transmission range of the pathogen. In particular, we numerically calculate the critical transmission range for which the eventual outbreak cluster spans the network. This signals a phase transition whose critical behavior suggests that it belongs to the standard percolation universality class. A direct estimate of the fractal dimension of the outbreak cluster agrees well with that obtained from the critical exponents.

Suggested Citation

  • Saha, Dipa & Mitra, Sayantan & Sensharma, Ankur, 2023. "Critically spanning epidemic outbreak cluster in random geometric networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    • Handle: RePEc:eee:phsmap:v:629:y:2023:i:c:s0378437123007811
    DOI: 10.1016/j.physa.2023.129226
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    References listed on IDEAS

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    1. Jichang Zhao & Daqing Li & Hillel Sanhedrai & Reuven Cohen & Shlomo Havlin, 2016. "Spatio-temporal propagation of cascading overload failures in spatially embedded networks," Nature Communications, Nature, vol. 7(1), pages 1-6, April.
    2. Saha, Dipa & Mitra, Sayantan & Bhowmik, Bishnu & Sensharma, Ankur, 2021. "Isotropic random geometric networks in two dimensions with a penetrable cavity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    3. Sharma, Natasha & Verma, Atul Kumar & Gupta, Arvind Kumar, 2021. "Spatial network based model forecasting transmission and control of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    4. Bustamante-Castañeda, F. & Caputo, J.-G. & Cruz-Pacheco, G. & Knippel, A. & Mouatamide, F., 2021. "Epidemic model on a network: Analysis and applications to COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
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