An Ultrametric Random Walk Model for Disease Spread Taking into Account Social Clustering of the Population
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International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden
2
Centro de Geociencias, Campus UNAM Juriquilla, Universidad Nacional Autonoma de Mexico (UNAM), Blvd. Juriquilla 3001, 76230 Queretaro, Mexico
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(9), 931; https://doi.org/10.3390/e22090931
Received: 5 August 2020
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Revised: 21 August 2020
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Accepted: 21 August 2020
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Published: 25 August 2020
(This article belongs to the Special Issue Entropy and Epidemiology)
We present a mathematical model of disease (say a virus) spread that takes into account the hierarchic structure of social clusters in a population. It describes the dependence of epidemic’s dynamics on the strength of barriers between clusters. These barriers are established by authorities as preventative measures; partially they are based on existing socio-economic conditions. We applied the theory of random walk on the energy landscapes represented by ultrametric spaces (having tree-like geometry). This is a part of statistical physics with applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, a virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy levels composing this barrier. Infection spreads rather easily inside a social cluster (say a working collective), but jumps to other clusters are constrained by social barriers. The model implies the power law,
Keywords:
disease spread; herd immunity; hierarchy of social clusters; ultrametric spaces; trees; social barriers; linear growing barriers; energy landscapes; random walk on trees
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MDPI and ACS Style
Khrennikov, A.; Oleschko, K. An Ultrametric Random Walk Model for Disease Spread Taking into Account Social Clustering of the Population. Entropy 2020, 22, 931. https://doi.org/10.3390/e22090931
AMA Style
Khrennikov A, Oleschko K. An Ultrametric Random Walk Model for Disease Spread Taking into Account Social Clustering of the Population. Entropy. 2020; 22(9):931. https://doi.org/10.3390/e22090931
Chicago/Turabian StyleKhrennikov, Andrei, and Klaudia Oleschko. 2020. "An Ultrametric Random Walk Model for Disease Spread Taking into Account Social Clustering of the Population" Entropy 22, no. 9: 931. https://doi.org/10.3390/e22090931
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