Epidemiological impact of waning immunization on a vaccinated population

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Abstract

This is an epidemiological SIRV model based study that is de-
signed to analyze the impact of vaccination in containing infection spread, in
a 4-tiered population compartment comprised of susceptible, infected, recov-
ered and vaccinated agents. While many models assume a lifelong protection
through vaccination, we focus on the impact of waning immunization due to
conversion of vaccinated and recovered agents back to susceptible ones. Two
asymptotic states exist, the \disease-free equilibrium" and the \endemic equi-
librium" and we express the transitions between these states as function of the
vaccination and conversion rates and using the basic reproduction number. We
nd that the vaccination of newborns and adults have dierent consequences
on controlling an epidemic. Also, a decaying disease protection within the re-
covered sub-population is not sucient to trigger an epidemic on the linear
level. We perform simulations for a parameter set modelling a disease with
waning immunization like pertussis. For a diusively coupled population, a
transition to the endemic state can proceed via the propagation of a traveling
infection wave, described successfully within a Fisher-Kolmogorov framework.
Original languageEnglish
Article number267
JournalEuropean Physical Journal B: Condensed Matter and Complex Systems
Volume91
DOIs
Publication statusPublished - 1 Nov 2018

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Immunization
Chlordiazepoxide
infectious diseases
compartments
actuators
propagation
simulation

Bibliographical note

© The Author(s) 2018. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this

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title = "Epidemiological impact of waning immunization on a vaccinated population",
abstract = "This is an epidemiological SIRV model based study that is de-signed to analyze the impact of vaccination in containing infection spread, ina 4-tiered population compartment comprised of susceptible, infected, recov-ered and vaccinated agents. While many models assume a lifelong protectionthrough vaccination, we focus on the impact of waning immunization due toconversion of vaccinated and recovered agents back to susceptible ones. Twoasymptotic states exist, the \disease-free equilibrium{"} and the \endemic equi-librium{"} and we express the transitions between these states as function of thevaccination and conversion rates and using the basic reproduction number. Wend that the vaccination of newborns and adults have dierent consequenceson controlling an epidemic. Also, a decaying disease protection within the re-covered sub-population is not sucient to trigger an epidemic on the linearlevel. We perform simulations for a parameter set modelling a disease withwaning immunization like pertussis. For a diusively coupled population, atransition to the endemic state can proceed via the propagation of a travelinginfection wave, described successfully within a Fisher-Kolmogorov framework.",
author = "Ewa Grela and Michael Stich and Chattopadhyay, {Amit K}",
note = "{\circledC} The Author(s) 2018. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.",
year = "2018",
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AU - Grela, Ewa

AU - Stich, Michael

AU - Chattopadhyay, Amit K

N1 - © The Author(s) 2018. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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N2 - This is an epidemiological SIRV model based study that is de-signed to analyze the impact of vaccination in containing infection spread, ina 4-tiered population compartment comprised of susceptible, infected, recov-ered and vaccinated agents. While many models assume a lifelong protectionthrough vaccination, we focus on the impact of waning immunization due toconversion of vaccinated and recovered agents back to susceptible ones. Twoasymptotic states exist, the \disease-free equilibrium" and the \endemic equi-librium" and we express the transitions between these states as function of thevaccination and conversion rates and using the basic reproduction number. Wend that the vaccination of newborns and adults have dierent consequenceson controlling an epidemic. Also, a decaying disease protection within the re-covered sub-population is not sucient to trigger an epidemic on the linearlevel. We perform simulations for a parameter set modelling a disease withwaning immunization like pertussis. For a diusively coupled population, atransition to the endemic state can proceed via the propagation of a travelinginfection wave, described successfully within a Fisher-Kolmogorov framework.

AB - This is an epidemiological SIRV model based study that is de-signed to analyze the impact of vaccination in containing infection spread, ina 4-tiered population compartment comprised of susceptible, infected, recov-ered and vaccinated agents. While many models assume a lifelong protectionthrough vaccination, we focus on the impact of waning immunization due toconversion of vaccinated and recovered agents back to susceptible ones. Twoasymptotic states exist, the \disease-free equilibrium" and the \endemic equi-librium" and we express the transitions between these states as function of thevaccination and conversion rates and using the basic reproduction number. Wend that the vaccination of newborns and adults have dierent consequenceson controlling an epidemic. Also, a decaying disease protection within the re-covered sub-population is not sucient to trigger an epidemic on the linearlevel. We perform simulations for a parameter set modelling a disease withwaning immunization like pertussis. For a diusively coupled population, atransition to the endemic state can proceed via the propagation of a travelinginfection wave, described successfully within a Fisher-Kolmogorov framework.

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