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arXiv · 2010.07731

A markovian random walk model of epidemic spreading

Michael Bestehorn·Alejandro P. Riascos·Thomas M. Michelitsch·Bernard A. Collet
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Abstract

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.

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Michael Bestehorn, Alejandro P. Riascos, Thomas M. Michelitsch, Bernard A. Collet. 2020-10-15. A markovian random walk model of epidemic spreading. https://doi.org/10.1007/s00161-021-00970-z

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