Near-critical SIR epidemic on a random graph with given degrees
| Autor: | Peter Windridge, Malwina J. Luczak, Svante Janson, Thomas House |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
05C80
0102 computer and information sciences 01 natural sciences Article Giant component Combinatorics 010104 statistics & probability SIR epidemic Corollary 60J28 Modelling and Simulation 92D30 Random regular graph FOS: Mathematics Humans Uniform boundedness Quantitative Biology::Populations and Evolution Critical window Biologiska vetenskaper Configuration model 0101 mathematics Epidemics Probability Mathematics Population Density Random graph Discrete mathematics Matematik Conjecture Degree (graph theory) Applied Mathematics Probability (math.PR) Models Theoretical Random graph with given degrees Biological Sciences Agricultural and Biological Sciences (miscellaneous) 3. Good health Vertex (geometry) 010201 computation theory & mathematics Modeling and Simulation 05C80 60F99 60J28 92D30 60F99 Mathematics - Probability |
| Zdroj: | Janson, S, Luczak, M, Windridge, P & House, T 2016, ' Near-critical SIR epidemic on a random graph with given degrees ', Journal of Mathematical Biology, vol. 74, no. 0, pp. 843–886 . https://doi.org/10.1007/s00285-016-1043-z Journal of Mathematical Biology |
| Popis: | Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the basic reproductive ratio is 1. In this paper, we study near-critical behaviour in the context of a susceptible-infective-recovered (SIR) epidemic on a random (multi)graph on $n$ vertices with a given degree sequence. We concentrate on the regime just above the threshold for the emergence of a large epidemic, where the basic reproductive ratio is $1 + \omega (n) n^{-1/3}$, with $\omega (n)$ tending to infinity slowly as the population size, $n$, tends to infinity. We determine the probability that a large epidemic occurs, and the size of a large epidemic. Our results require basic regularity conditions on the degree sequences, and the assumption that the third moment of the degree of a random susceptible vertex stays uniformly bounded as $n \to \infty$. As a corollary, we determine the probability and size of a large near-critical epidemic on a standard binomial random graph in the `sparse' regime, where the average degree is constant. As a further consequence of our method, we obtain an improved result on the size of the giant component in a random graph with given degrees just above the critical window, proving a conjecture by Janson and Luczak. Comment: 38 pages; rewritten introduction; added simulation; one new author |
| Databáze: | OpenAIRE |
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