A Markovian random walk model of epidemic spreading
Tóm tắt
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.
Tài liệu tham khảo
Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Barabási, A.-L.: Network Science. Cambridge University Press, Cambridge (2016)
Hughes, B.D.: Random Walks and Random Environments: Vol. 1: Random Walks (Oxford University Press, USA, 1996)
Riascos, A.P., Mateos, J.L.: Emergence of encounter networks due to human mobility. Plos One 12(10), e0184532 (2017). https://doi.org/10.1371/journal.pone.0184532
Metzler, R., Klafter, J.: The random Walk’s guide to anomalous diffusion : a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000)
Martcheva, M.: An Introduction to Mathematical Epidemiology. Springer (2015). ISBN 978-1-4899-7612-3
Belik, V., Geisel, T., Brockmann, D.: Recurrent host mobility in spatial epidemics: beyond reaction-diffusion. Eur. Phys. J. B 84, 579–587 (2011). https://doi.org/10.1140/epjb/e2011-20485-2
Feng, L., Zhao, Q., Zhou, C.: Epidemic spreading in heterogeneous networks with recurrent mobility patterns. Phys. Rev. E 102, 022306 (2020). https://doi.org/10.1103/PhysRevE.102.022306
Pastor-Satorras, R.A., Vespignani, A.: Epidemic dynamics and endemic states in complex networks. Phys. Rev. E 63, 066117 (2001)
Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001)
Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87, 925 (2015)
Pastor-Satorras, R., Vespignani, A.: Epidemics and immunization in scale-free networks. In: Bornholdt, S., Schuster, H.G. (eds.) Handbook of graph and networks. Wiley-VCH, Berlin (2003)
Mancastroppa, M., Burioni, R., Colizza, V., Vezzani, A.: Active and inactive quarantine in epidemic spreading on adaptive activity-driven networks. Phys. Rev. E 102, 020301(R) (2020). https://doi.org/10.1103/PhysRevE.63.066117
Moore, C., Newman, M.E.J.: Epidemics and percolation in small-world networks. Phys. Rev. E 61, 5678–5682 (2000)
Newman, M.E.J., Watts, D.J.: Scaling and percolation in the small-world network model. Phys. Rev. E 60, 7332–7342 (1999)
Cacciapaglia, G., Sannino, F.: Second wave COVID-19 pandemics in Europe: a temporal playbook. Sci. Rep. 10, 15514 (2020). https://doi.org/10.1038/s41598-020-72611-5
Website of the European centre for disease prevention and control. https://www.ecdc.europa.eu/en/cases-2019-ncov-eueea
Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. A115, 700–721 (1927)
Anderson, R.M., May, R.M.: Population biology of infectious diseases: Part I. Nature 280, 361–367 (1979)
Riascos, A.P., Sanders, D.P.: Mean encounter times for multiple random walkers on networks, (Submitted), preprint. arXiv:2008.12806
Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012). https://doi.org/10.1016/j.physrep.2012.03.001
Holme, P., Modern, P.: temporal network theory: a colloquium. Eur. Phys. J. B 88(9), 234 (2015). https://doi.org/10.1140/epjb/e2015-60657-4
Riascos, A.P., Michelitsch, T.M.: A. Pizarro-Medina, Non-local biased random walks and fractional transport on directed networks. Phys. Rev. E 102, 022142 (2020). https://doi.org/10.1103/PhysRevE.102.022142
Michelitsch, T., Riascos, A.P., Collet, B.A., Nowakowski, A., Nicolleau, F.: Fractional Dynamics on Networks and Lattices, ISTE-Wiley March 2019, ISBN : 9781786301581
Michelitsch, T.M., Polito, F., Riascos, A.P.: Biased continuous-time random walks with Mittag-Leffler jumps. Fractal Fract. 4(4), 51 (2020). https://doi.org/10.3390/fractalfract4040051