The impact of household structure on disease-induced herd immunity
Abstract The disease-induced herd immunity level %$h_D%$ is the fraction of the population that must be infected by an epidemic to ensure that a new epidemic among the remaining susceptible population is not supercritical. For a homogeneously mixing population %$h_D%$ equals the classical herd immunity level %$h_C%$, which is the fraction of the population that must be vaccinated in advance of an epidemic so that the epidemic is not supercritical. For most forms of heterogeneous mixing %$h_D<h_C%$, sometimes dramatically so. For an SEIR (susceptible %$\rightarrow %$ exposed %$\rightarrow %$ infective %$\rightarrow %$ recovered) model of an epidemic among a population that is partitioned into households, in which individuals mix uniformly within households and, in addition, uniformly at a much lower rate in the population at large, we show that %$h_D>h_C%$ unless variability in the household size distribution is sufficiently large. Thus, introducing household structure into a model typically has the opposite effect on disease-induced herd immunity than most other forms of population heterogeneity. We reach this conclusion by considering an approximation %${\tilde{h}}_D%$ of %$h_D%$, supported by numerical studies using real-world household size distributions. For %$n=2, 3%$, we prove that %${\tilde{h}}_D>h_C%$ when all households have size n, and conjecture that this inequality holds for any common household size n. We prove results comparing %${\tilde{h}}_D%$ and %$h_C%$ for epidemics which are highly infectious within households, and also for epidemics which are weakly infectious within households..
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2023 |
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| Erschienen: |
2023 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:87 |
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| Enthalten in: |
Journal of mathematical biology - 87(2023), 6 vom: 08. Nov. |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Ball, Frank [VerfasserIn] |
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| Links: |
Volltext [kostenfrei] |
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| Themen: |
Disease-induced herd immunity level |
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| Anmerkungen: |
© The Author(s) 2023 |
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| doi: |
10.1007/s00285-023-02010-7 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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SPR053661419 |
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| 100 | 1 | |a Ball, Frank |e verfasserin |0 (orcid)0000-0002-5599-2903 |4 aut | |
| 245 | 1 | 4 | |a The impact of household structure on disease-induced herd immunity |
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| 520 | |a Abstract The disease-induced herd immunity level %$h_D%$ is the fraction of the population that must be infected by an epidemic to ensure that a new epidemic among the remaining susceptible population is not supercritical. For a homogeneously mixing population %$h_D%$ equals the classical herd immunity level %$h_C%$, which is the fraction of the population that must be vaccinated in advance of an epidemic so that the epidemic is not supercritical. For most forms of heterogeneous mixing %$h_D<h_C%$, sometimes dramatically so. For an SEIR (susceptible %$\rightarrow %$ exposed %$\rightarrow %$ infective %$\rightarrow %$ recovered) model of an epidemic among a population that is partitioned into households, in which individuals mix uniformly within households and, in addition, uniformly at a much lower rate in the population at large, we show that %$h_D>h_C%$ unless variability in the household size distribution is sufficiently large. Thus, introducing household structure into a model typically has the opposite effect on disease-induced herd immunity than most other forms of population heterogeneity. We reach this conclusion by considering an approximation %${\tilde{h}}_D%$ of %$h_D%$, supported by numerical studies using real-world household size distributions. For %$n=2, 3%$, we prove that %${\tilde{h}}_D>h_C%$ when all households have size n, and conjecture that this inequality holds for any common household size n. We prove results comparing %${\tilde{h}}_D%$ and %$h_C%$ for epidemics which are highly infectious within households, and also for epidemics which are weakly infectious within households. | ||
| 650 | 4 | |a Disease-induced herd immunity level |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Household epidemic model |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a SEIR epidemic |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Vaccine-induced herd immunity level |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Critcher, Liam |4 aut | |
| 700 | 1 | |a Neal, Peter |0 (orcid)0000-0003-2257-8535 |4 aut | |
| 700 | 1 | |a Sirl, David |0 (orcid)0000-0002-2639-1666 |4 aut | |
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