Modelling the spread of two successive SIR epidemics on a configuration model network Article Swipe

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Frank Ball , Abid Ali Lashari , David Sirl , Pieter Trapman ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2410.20889

We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one. The first epidemic is analysed through a bond percolation model, while the second epidemic is approximated by a three-type branching process in which the types of individuals depend on their position in the percolation clusters used for the first epidemic. This branching process approximation enables us to calculate, in the large population limit and conditional upon a large outbreak in the first epidemic, a threshold parameter and the probability of a large outbreak for the second epidemic. A second branching process approximation enables us to calculate the fraction of the population that are infected by such a second large outbreak. We illustrate our results through some specific cases which have appeared previously in the literature and show that our asymptotic results give good approximations for finite populations.

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Artificial Intelligence

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Epidemic model Computer science Network model Geography Demography Artificial intelligence Sociology Population

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2410.20889
PDF: https://arxiv.org/pdf/2410.20889
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4404314648

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DOI: https://doi.org/10.48550/arxiv.2410.20889

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Title: Modelling the spread of two successive SIR epidemics on a configuration model network

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-10-28

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Authors: Frank Ball, Abid Ali Lashari, David Sirl, Pieter Trapman

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Landing page: https://arxiv.org/abs/2410.20889

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PDF URL: https://arxiv.org/pdf/2410.20889

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Concepts: Epidemic model, Computer science, Network model, Geography, Demography, Artificial intelligence, Sociology, Population

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