The SI and SIR epidemics on general networks

• Autorzy: Aldous D.

Identyfikatory

DOI

10.19195/0208-4147.37.2.2

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

epidemic model; SI epidemic; SIR epidemic

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 2
• Strony: 229--234
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Aldous D.

• 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).