Estimating the distance to an epidemic threshold
Identifieur interne : 000983 ( Main/Exploration ); précédent : 000982; suivant : 000984Estimating the distance to an epidemic threshold
Auteurs : Eamon B. O'Dea ; Andrew W. Park ; John M. DrakeSource :
- Journal of the Royal Society Interface [ 1742-5689 ] ; 2018.
Descripteurs français
- KwdFr :
- MESH :
English descriptors
- KwdEn :
- MESH :
- epidemiology : Coronavirus Infections, Measles, Zoonoses.
- prevention & control : Coronavirus Infections, Measles, Zoonoses.
- Animals, Epidemics, Humans, Middle East Respiratory Syndrome Coronavirus, Models, Biological.
Abstract
The epidemic threshold of the susceptible–infected–recovered model is a boundary separating parameters that permit epidemics from those that do not. This threshold corresponds to parameters where the system's equilibrium becomes unstable. Consequently, we use the average rate at which deviations from the equilibrium shrink to define a distance to this threshold. However, the vital dynamics of the host population may occur slowly even when transmission is far from threshold levels. Here, we show analytically how such slow dynamics can prevent estimation of the distance to the threshold from fluctuations in the susceptible population. Although these results are exact only in the limit of long-term observation of a large system, simulations show that they still provide useful insight into systems with a range of population sizes, environmental noise and observation schemes. Having established some guidelines about when estimates are accurate, we then illustrate how multiple distance estimates can be used to estimate the rate of approach to the threshold. The estimation approach is general and may be applicable to zoonotic pathogens such as Middle East respiratory syndrome-related coronavirus (MERS-CoV) as well as vaccine-preventable diseases like measles.
Url:
DOI: 10.1098/rsif.2018.0034
PubMed: 29950512
PubMed Central: 6030631
Affiliations:
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O'Dea</name><affiliation><nlm:aff id="af1"><addr-line>Department of Ecology</addr-line>,<addr-line>College of Veterinary Medicine</addr-line>,<addr-line>University of Georgia</addr-line>,<addr-line>Athens</addr-line>,<addr-line>GA</addr-line>,<addr-line>USA</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="af2"><addr-line>Center for the Ecology of Infectious Diseases</addr-line>,<addr-line>College of Veterinary Medicine</addr-line>,<addr-line>University of Georgia</addr-line>,<addr-line>Athens</addr-line>,<addr-line>GA</addr-line>,<addr-line>USA</addr-line></nlm:aff></affiliation></author><author><name sortKey="Park, Andrew W" sort="Park, Andrew W" uniqKey="Park A" first="Andrew W." last="Park">Andrew W. Park</name><affiliation><nlm:aff id="af3"><addr-line>Odum School of Ecology</addr-line>,<addr-line>College of Veterinary Medicine</addr-line>,<addr-line>University of Georgia</addr-line>,<addr-line>Athens</addr-line>,<addr-line>GA</addr-line>,<addr-line>USA</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="af4"><addr-line>Infectious Diseases</addr-line>,<addr-line>College of Veterinary Medicine</addr-line>,<addr-line>University of Georgia</addr-line>,<addr-line>Athens</addr-line>,<addr-line>GA</addr-line>,<addr-line>USA</addr-line></nlm:aff></affiliation></author><author><name sortKey="Drake, John M" sort="Drake, John M" uniqKey="Drake J" first="John M." last="Drake">John M. Drake</name><affiliation><nlm:aff id="af2"><addr-line>Center for the Ecology of Infectious Diseases</addr-line>,<addr-line>College of Veterinary Medicine</addr-line>,<addr-line>University of Georgia</addr-line>,<addr-line>Athens</addr-line>,<addr-line>GA</addr-line>,<addr-line>USA</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="af3"><addr-line>Odum School of Ecology</addr-line>,<addr-line>College of Veterinary Medicine</addr-line>,<addr-line>University of Georgia</addr-line>,<addr-line>Athens</addr-line>,<addr-line>GA</addr-line>,<addr-line>USA</addr-line></nlm:aff></affiliation></author></analytic><series><title level="j">Journal of the Royal Society Interface</title><idno type="ISSN">1742-5689</idno><idno type="eISSN">1742-5662</idno><imprint><date when="2018">2018</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Animals</term><term>Coronavirus Infections (epidemiology)</term><term>Coronavirus Infections (prevention & control)</term><term>Epidemics</term><term>Humans</term><term>Measles (epidemiology)</term><term>Measles (prevention & control)</term><term>Middle East Respiratory Syndrome Coronavirus</term><term>Models, Biological</term><term>Zoonoses (epidemiology)</term><term>Zoonoses (prevention & control)</term></keywords><keywords scheme="KwdFr" xml:lang="fr"><term>Animaux</term><term>Coronavirus du syndrome respiratoire du Moyen-Orient</term><term>Humains</term><term>Infections à coronavirus ()</term><term>Infections à coronavirus (épidémiologie)</term><term>Modèles biologiques</term><term>Rougeole ()</term><term>Rougeole (épidémiologie)</term><term>Zoonoses ()</term><term>Zoonoses (épidémiologie)</term><term>Épidémies</term></keywords><keywords scheme="MESH" qualifier="epidemiology" xml:lang="en"><term>Coronavirus Infections</term><term>Measles</term><term>Zoonoses</term></keywords><keywords scheme="MESH" qualifier="prevention & control" xml:lang="en"><term>Coronavirus Infections</term><term>Measles</term><term>Zoonoses</term></keywords><keywords scheme="MESH" qualifier="épidémiologie" xml:lang="fr"><term>Infections à coronavirus</term><term>Rougeole</term><term>Zoonoses</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Animals</term><term>Epidemics</term><term>Humans</term><term>Middle East Respiratory Syndrome Coronavirus</term><term>Models, Biological</term></keywords><keywords scheme="MESH" xml:lang="fr"><term>Animaux</term><term>Coronavirus du syndrome respiratoire du Moyen-Orient</term><term>Humains</term><term>Infections à coronavirus</term><term>Modèles biologiques</term><term>Rougeole</term><term>Zoonoses</term><term>Épidémies</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>The epidemic threshold of the susceptible–infected–recovered model is a boundary separating parameters that permit epidemics from those that do not. This threshold corresponds to parameters where the system's equilibrium becomes unstable. Consequently, we use the average rate at which deviations from the equilibrium shrink to define a distance to this threshold. However, the vital dynamics of the host population may occur slowly even when transmission is far from threshold levels. Here, we show analytically how such slow dynamics can prevent estimation of the distance to the threshold from fluctuations in the susceptible population. Although these results are exact only in the limit of long-term observation of a large system, simulations show that they still provide useful insight into systems with a range of population sizes, environmental noise and observation schemes. Having established some guidelines about when estimates are accurate, we then illustrate how multiple distance estimates can be used to estimate the rate of approach to the threshold. The estimation approach is general and may be applicable to zoonotic pathogens such as Middle East respiratory syndrome-related coronavirus (MERS-CoV) as well as vaccine-preventable diseases like measles.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Bedford, T" uniqKey="Bedford T">T Bedford</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ferrari, Mj" uniqKey="Ferrari M">MJ Ferrari</name></author><author><name sortKey="Grais, Rf" uniqKey="Grais R">RF Grais</name></author><author><name sortKey="Bharti, N" uniqKey="Bharti N">N Bharti</name></author><author><name sortKey="Conlan, Ajk" uniqKey="Conlan A">AJK Conlan</name></author><author><name sortKey="Bj Rnstad, On" uniqKey="Bj Rnstad O">ON Bjørnstad</name></author><author><name sortKey="Wolfson, Lj" uniqKey="Wolfson L">LJ Wolfson</name></author><author><name sortKey="Guerin, Pj" uniqKey="Guerin P">PJ Guerin</name></author><author><name 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Zachary</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mandelshtam, Va" uniqKey="Mandelshtam V">VA Mandelshtam</name></author><author><name sortKey="Taylor, Hs" uniqKey="Taylor H">HS Taylor</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bobashev, Gv" uniqKey="Bobashev G">GV Bobashev</name></author><author><name sortKey="Ellner, Sp" uniqKey="Ellner S">SP Ellner</name></author><author><name sortKey="Nychka, Dw" uniqKey="Nychka D">DW Nychka</name></author><author><name sortKey="Grenfell, Bt" uniqKey="Grenfell B">BT Grenfell</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Rasmussen, Da" uniqKey="Rasmussen D">DA Rasmussen</name></author><author><name sortKey="Ratmann, O" uniqKey="Ratmann O">O Ratmann</name></author><author><name sortKey="Koelle, K" uniqKey="Koelle K">K Koelle</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="O Dea, Eb" uniqKey="O Dea E">EB O'Dea</name></author></analytic></biblStruct></listBibl></div1></back></TEI><affiliations><list></list><tree><noCountry><name sortKey="Drake, John M" sort="Drake, John M" uniqKey="Drake J" first="John M." last="Drake">John M. Drake</name><name sortKey="O Dea, Eamon B" sort="O Dea, Eamon B" uniqKey="O Dea E" first="Eamon B." last="O'Dea">Eamon B. O'Dea</name><name sortKey="Park, Andrew W" sort="Park, Andrew W" uniqKey="Park A" first="Andrew W." last="Park">Andrew W. Park</name></noCountry></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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