Modelling the spread of two successive SIR epidemics on a configuration model network
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914993510809600 |
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| author | Ball, Frank Lashari, Abid Ali Sirl, David Trapman, Pieter |
| author_facet | Ball, Frank Lashari, Abid Ali Sirl, David Trapman, Pieter |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_20889 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modelling the spread of two successive SIR epidemics on a configuration model network Ball, Frank Lashari, Abid Ali Sirl, David Trapman, Pieter Populations and Evolution Probability 05C80, 60J80, 60J85, 60K35, 92D30 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. |
| title | Modelling the spread of two successive SIR epidemics on a configuration model network |
| topic | Populations and Evolution Probability 05C80, 60J80, 60J85, 60K35, 92D30 |
| url | https://arxiv.org/abs/2410.20889 |