hal-02968842
https://cnrs.hal.science/hal-02968842
https://cnrs.hal.science/hal-02968842/document
https://cnrs.hal.science/hal-02968842/file/arXiv-2010.07731.pdf
arxiv:2010.07731
doi:10.1007/s00161-021-00970-z
[CNRS] CNRS - Centre national de la recherche scientifique
[IJLRDA] Institut Jean Le Rond d'Alembert
[SORBONNE-UNIVERSITE] Sorbonne Université
[SORBONNE-UNIV] Sorbonne Université 01/01/2018
[SU-SCIENCES] Faculté des Sciences de Sorbonne Université
[SU-TI] Sorbonne Université - Texte Intégral
[ALLIANCE-SU] Alliance Sorbonne Université
A markovian random walk model of epidemic spreading
Bestehorn, Michael
Riascos, Alejandro,
Michelitsch, Thomas,
Collet, Bernard,
[PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
[SDV] Life Sciences [q-bio]
[STAT.AP] Statistics [stat]/Applications [stat.AP]
ART
Markovian random walks
ergodic networks
epidemic spreading
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.
2021-01-16
2020-10-16
en
Continuum Mechanics and Thermodynamics
Springer Verlag