A computational framework for evaluating the role of mobility on the propagation of epidemics on point processes.
Boolean model
Contact process
Epidemic
Markov process
Moment measures
Motion
Phase diagram
Point process
SIS model
Shot-noise process
Stationary regime
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
20 12 2021
20 12 2021
Historique:
received:
01
10
2020
accepted:
21
10
2021
revised:
15
08
2021
entrez:
20
12
2021
pubmed:
21
12
2021
medline:
28
12
2021
Statut:
epublish
Résumé
This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of the paper is a model where points are also subject to some random motion. Conservation equations for moment measures are leveraged to analyze the stationary regime of the point processes of infected and susceptible individuals. A heuristic factorization of the third moment measure is then proposed to obtain simple polynomial equations allowing one to derive closed form approximations for the fraction of infected individuals in the steady state. These polynomial equations also lead to a phase diagram which tentatively delineates the regions of the space of parameters (population density, infection radius, infection and recovery rate, and motion rate) where the epidemic survives and those where there is extinction. A key take-away from this phase diagram is that the extinction of the epidemic is not always aided by a decrease in the motion rate. These results are substantiated by simulations on large two dimensional tori. These simulations show that the polynomial equations accurately predict the fraction of infected individuals when the epidemic survives. The simulations also show that the proposed phase diagram accurately predicts the parameter regions where the mean survival time of the epidemic increases (resp. decreases) with motion rate.
Identifiants
pubmed: 34928428
doi: 10.1007/s00285-021-01692-1
pii: 10.1007/s00285-021-01692-1
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
4Informations de copyright
© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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