SIR epidemics in populations with large sub-communities Article Swipe

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Frank Ball , David Sirl , Pieter Trapman ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2204.06902

We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than between them. Our analysis involves approximation of the epidemic process by a chain of within-community large outbreaks spreading between the communities. We derive law of large numbers and central limit type results for the number of individuals and the number of communities affected and the so-called severity of the outbreak. These results are valid as the size of communities tends to infinity, with the number of communities either fixed or also tending to infinity. The weaker between-community connections lead to randomness even in the law of large numbers type limit. As part of our proofs we also obtain a new result concerning the rate of convergence of the expected fraction infected in a standard SIR epidemic to its large-population limit.

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Randomness

Outbreak (2024 Film)

Signal Transmission

Central Limit Theorem

Mathematical Analysis

Materials Science

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Randomness Limit (mathematics) Outbreak Infinity Population Law of large numbers Epidemic model Transmission (telecommunications) Population size Convergence (economics) Central limit theorem Mathematics Range (aeronautics) Demography Geography Statistics Biology Computer science Economics Virology Sociology Random variable Economic growth Telecommunications Mathematical analysis Materials science Composite material

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2204.06902
PDF: https://arxiv.org/pdf/2204.06902
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DOI: https://doi.org/10.48550/arxiv.2204.06902

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Title: SIR epidemics in populations with large sub-communities

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Language: en

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Publication year: 2022

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Publication date: 2022-04-14

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Authors: Frank Ball, David Sirl, Pieter Trapman

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Landing page: https://arxiv.org/abs/2204.06902

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Concepts: Randomness, Limit (mathematics), Outbreak, Infinity, Population, Law of large numbers, Epidemic model, Transmission (telecommunications), Population size, Convergence (economics), Central limit theorem, Mathematics, Range (aeronautics), Demography, Geography, Statistics, Biology, Computer science, Economics, Virology, Sociology, Random variable, Economic growth, Telecommunications, Mathematical analysis, Materials science, Composite material

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abstract_inverted_index.obtain	130
abstract_inverted_index.proofs	127
abstract_inverted_index.result	133
abstract_inverted_index.weaker	108
abstract_inverted_index.within	29
abstract_inverted_index.between	33, 51
abstract_inverted_index.central	61
abstract_inverted_index.defined	15
abstract_inverted_index.disease	27
abstract_inverted_index.numbers	59, 120
abstract_inverted_index.outcome	3
abstract_inverted_index.process	42
abstract_inverted_index.results	64, 84
abstract_inverted_index.tending	104
abstract_inverted_index.affected	75
abstract_inverted_index.analysis	36
abstract_inverted_index.epidemic	13, 41, 148
abstract_inverted_index.expected	141
abstract_inverted_index.fraction	142
abstract_inverted_index.infected	143
abstract_inverted_index.involves	37
abstract_inverted_index.severity	79
abstract_inverted_index.standard	146
abstract_inverted_index.stronger	26
abstract_inverted_index.infective	10
abstract_inverted_index.infinity,	94
abstract_inverted_index.infinity.	106
abstract_inverted_index.outbreak.	82
abstract_inverted_index.outbreaks	49
abstract_inverted_index.so-called	78
abstract_inverted_index.spreading	50
abstract_inverted_index.concerning	134
abstract_inverted_index.population	18
abstract_inverted_index.properties	4
abstract_inverted_index.randomness	113
abstract_inverted_index.recovered)	12
abstract_inverted_index.communities	31, 74, 91, 99
abstract_inverted_index.connections	110
abstract_inverted_index.convergence	138
abstract_inverted_index.individuals	69
abstract_inverted_index.investigate	1
abstract_inverted_index.(susceptible	8
abstract_inverted_index.communities.	53
abstract_inverted_index.transmission	28
abstract_inverted_index.approximation	38
abstract_inverted_index.sub-communities	21
abstract_inverted_index.large-population	151
abstract_inverted_index.within-community	47
abstract_inverted_index.between-community	109
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
sustainable_development_goals[0].id	https://metadata.un.org/sdg/3
sustainable_development_goals[0].score	0.8500000238418579
sustainable_development_goals[0].display_name	Good health and well-being
citation_normalized_percentile