An Ultrametric Random Walk Model for Disease Spread Taking into Account Social Clustering of the Population
Por:
Khrennikov A., Oleschko K.
Publicada:
1 sep 2020
Resumen:
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.
Filiaciones:
Khrennikov A.:
Linnaeus Univ, Int Ctr Math Modeling Phys & Cognit Sci, SE-35195 Vaxjo, Sweden
Oleschko K.:
Univ Nacl Autonoma Mexico, Ctr Geociencias, Campus UNAM Juriquilla,Blvd Juriquilla 3001, Queretaro 76230, Mexico
All Open Access, Gold
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