%0 Journal Article %T A markovian random walk model of epidemic spreading %+ Brandenburgische Technische Universität Cottbus-Senftenberg (BTU) %+ Universidad Nacional Autónoma de México = National Autonomous University of Mexico (UNAM) %+ Institut Jean Le Rond d'Alembert (DALEMBERT) %A Bestehorn, Michael %A Riascos, Alejandro, P %A Michelitsch, Thomas, M %A Collet, Bernard, A %< avec comité de lecture %@ 0935-1175 %J Continuum Mechanics and Thermodynamics %I Springer Verlag %8 2021-01-16 %D 2021 %Z 2010.07731 %R 10.1007/s00161-021-00970-z %K Markovian random walks %K ergodic networks %K epidemic spreading %Z Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] %Z Life Sciences [q-bio] %Z Statistics [stat]/Applications [stat.AP]Journal articles %X 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. %G English %2 https://cnrs.hal.science/hal-02968842/document %2 https://cnrs.hal.science/hal-02968842/file/arXiv-2010.07731.pdf %L hal-02968842 %U https://cnrs.hal.science/hal-02968842 %~ CNRS %~ IJLRDA %~ SORBONNE-UNIVERSITE %~ SORBONNE-UNIV %~ SU-SCIENCES %~ SU-TI %~ ALLIANCE-SU