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An Ultrametric Random Walk Model for Disease Spread Taking into Account Social Clustering of the Population
Linnaeus University, Faculty of Technology, Department of Mathematics. (Int Ctr Math Modeling Phys & Cognit Sci)ORCID iD: 0000-0002-9857-0938
Univ Nacl Autonoma Mexico, Mexico.
2020 (English)In: Entropy, E-ISSN 1099-4300, Vol. 22, no 9, p. 1-13, article id 931Article in journal (Refereed) Published
Abstract [en]

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,1-t-a,for approaching herd immunity, where the parameterais proportional to inverse of one-step barrier Delta.We consider linearly increasing barriers (with respect to hierarchy), i.e., them-step barrier Delta m=m Delta.We also introduce a quantity characterizing the process of infection distribution from one level of social hierarchy to the nearest lower levels, spreading entropyE.The parameterais proportional toE.

Place, publisher, year, edition, pages
MDPI, 2020. Vol. 22, no 9, p. 1-13, article id 931
Keywords [en]
disease spread, herd immunity, hierarchy of social clusters, ultrametric spaces, trees, social barriers, linear growing barriers, energy landscapes, random walk on trees
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-98821DOI: 10.3390/e22090931ISI: 000580068400001Scopus ID: 2-s2.0-85090849654OAI: oai:DiVA.org:lnu-98821DiVA, id: diva2:1500261
Available from: 2020-11-11 Created: 2020-11-11 Last updated: 2023-03-28Bibliographically approved

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Khrennikov, Andrei

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