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Intuitively one expects that for any plausible parametric epidemic model, there will be some region in parameter-space where the epidemic affects (with high probability) only a small proportion of a large population, another region where it affects (with high probability) a nonnegligible proportion, with a lower-dimensional “critical” interface. This dichotomy is certainly true in well-studied specific models, but we know of no very general results. A recent result stated for a bond percolation model can be restated as giving weak conditions under which the dichotomy holds for an SI epidemic model on arbitrary finite networks. This result suggests a conjecture for more complex and more realistic SIR epidemic models, and the purpose of this article** is to record the conjecture.
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Tom
Strony
229--234
Opis fizyczny
Bibliogr. 6 poz.
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autor
- U.C. Berkeley, Department of Statistics, 367 Evans Hall # 3860, U.C. Berkeley, CA, 94720, USA
Bibliografia
- [1] D. Aldous, The incipient giant component in bond percolation on general finite weighted graphs, Electron. Commun. Probab. 21 (2016), paper no. 68.
- [2] D. J. Daley and J. Gani, Epidemic Modelling: An Introduction, Cambridge Stud. Math. Biol., Vol. 15, Cambridge University Press, Cambridge 1999.
- [3] L. Danon et al., Networks and the epidemiology of infectious disease, Interdiscip. Perspect. Infect. Dis., Vol. 2011 (2011), article ID 284909.
- [4] O. Diekmann, H. Heesterbeek, and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Princeton Ser. Theor. Comput. Biol., Princeton University Press, Princeton, NJ, 2013.
- [5] R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, Epidemic processes in complex networks, Rev. Modern Phys. 87 (3) (2015), pp. 925-979.
- [6] L. Pellis et al., Eight challenges for network epidemic models, Epidemics 10 (2015), pp. 58-62.
Uwagi
Dedicated to Tomasz in honor of a distinguished career.
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
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Bibliografia
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