Formation of spatial patterns in an epidemic model with constant removal rate of theinfectives
Identifieur interne : 001784 ( Istex/Curation ); précédent : 001783; suivant : 001785Formation of spatial patterns in an epidemic model with constant removal rate of theinfectives
Auteurs : Quan-Xing Liu [République populaire de Chine] ; Zhen Jin [République populaire de Chine, Niger]Source :
- Journal of Statistical Mechanics: Theory and Experiment [ 1742-5468 ] ; 2007.
English descriptors
- Teeft :
- Asymptotic patterns, Bifurcation, Bifurcation parameter, Bubonic plague, Characteristic equation, Constant removal rate, Contour pictures, Critical value, Eigenvalue, Epidemic model, Fourier modes, Growth rate, Gure, Gures, Infective individuals, Infectives, Initial state, Initial states, Iteration, Jacobian matrix, Labyrinthine patterns, Linear regime, Mech, Nite range, Nonlinear regime, Numerical simulations, Paper addresses, Parameter values, Parameters values, Pattern formation, Perturbation, Phys, Population dynamics, Positive equilibrium, Positive equilibrium point, Positive equilibrium points, Real number, Real parts, Spatial, Spatial epidemic model, Spatial model, Spatial patterns, Spatial spread, Spot patterns, Theoretical analysis, Time evolution, Turing, Turing instabilities, Turing instability, Turing mechanisms, Turing space, Unstable wavenumber.
Abstract
This paper addresses the question of how population diffusion affects the formation of thespatial patterns in the spatial epidemic model by Turing mechanisms. In particular, wepresent a theoretical analysis of results of the numerical simulations in two dimensions.Moreover, there is a critical value for the system within the linear regime. Below the criticalvalue the spatial patterns are impermanent, whereas above it stationary spot and stripepatterns can coexist over time. We have observed the striking formation of spatial patternsduring the evolution, but the isolated ordered spot patterns do not emerge in the space.
Url:
DOI: 10.1088/1742-5468/2007/05/P05002
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: Pour aller vers cette notice dans l'étape Curation :001784
Links to Exploration step
ISTEX:3CD736D73B1B174FD0020CA01D9B4A9D1AB68194Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Formation of spatial patterns in an epidemic model with constant removal rate of theinfectives</title>
<author><name sortKey="Liu, Quan Xing" sort="Liu, Quan Xing" uniqKey="Liu Q" first="Quan-Xing" last="Liu">Quan-Xing Liu</name>
<affiliation wicri:level="1"><mods:affiliation>National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, Shanxi 030051, Peoples Republic of China</mods:affiliation>
<country xml:lang="fr">République populaire de Chine</country>
<wicri:regionArea>National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, Shanxi 030051</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, Peoples Republic of China</mods:affiliation>
<country xml:lang="fr">République populaire de Chine</country>
<wicri:regionArea>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051</wicri:regionArea>
</affiliation>
<affiliation><mods:affiliation>E-mail: liuqx315@sina.com</mods:affiliation>
<wicri:noCountry code="no comma">E-mail: liuqx315@sina.com</wicri:noCountry>
</affiliation>
</author>
<author><name sortKey="Jin, Zhen" sort="Jin, Zhen" uniqKey="Jin Z" first="Zhen" last="Jin">Zhen Jin</name>
<affiliation wicri:level="1"><mods:affiliation>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, Peoples Republic of China</mods:affiliation>
<country xml:lang="fr">République populaire de Chine</country>
<wicri:regionArea>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>E-mail: jinzhn@263.net</mods:affiliation>
<country wicri:rule="url">Niger</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:3CD736D73B1B174FD0020CA01D9B4A9D1AB68194</idno>
<date when="2007" year="2007">2007</date>
<idno type="doi">10.1088/1742-5468/2007/05/P05002</idno>
<idno type="url">https://api.istex.fr/ark:/67375/0T8-CW028FQX-8/fulltext.pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001784</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001784</idno>
<idno type="wicri:Area/Istex/Curation">001784</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Formation of spatial patterns in an epidemic model with constant removal rate of theinfectives</title>
<author><name sortKey="Liu, Quan Xing" sort="Liu, Quan Xing" uniqKey="Liu Q" first="Quan-Xing" last="Liu">Quan-Xing Liu</name>
<affiliation wicri:level="1"><mods:affiliation>National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, Shanxi 030051, Peoples Republic of China</mods:affiliation>
<country xml:lang="fr">République populaire de Chine</country>
<wicri:regionArea>National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, Shanxi 030051</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, Peoples Republic of China</mods:affiliation>
<country xml:lang="fr">République populaire de Chine</country>
<wicri:regionArea>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051</wicri:regionArea>
</affiliation>
<affiliation><mods:affiliation>E-mail: liuqx315@sina.com</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Jin, Zhen" sort="Jin, Zhen" uniqKey="Jin Z" first="Zhen" last="Jin">Zhen Jin</name>
<affiliation wicri:level="1"><mods:affiliation>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, Peoples Republic of China</mods:affiliation>
<country xml:lang="fr">République populaire de Chine</country>
<wicri:regionArea>Department of Mathematics, North University of China, Taiyuan, Shanxi 030051</wicri:regionArea>
</affiliation>
<affiliation wicri:level="1"><mods:affiliation>E-mail: jinzhn@263.net</mods:affiliation>
<country wicri:rule="url">Niger</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Journal of Statistical Mechanics: Theory and Experiment</title>
<title level="j" type="abbrev">J. Stat. Mech.</title>
<idno type="ISSN">1742-5468</idno>
<idno type="eISSN">1742-5468</idno>
<imprint><publisher>Institute of Physics Publishing</publisher>
<date type="published" when="2007">2007</date>
<biblScope unit="issue">5</biblScope>
<biblScope unit="page" from="P05002">P05002</biblScope>
<biblScope unit="page" to="P05002">P05002</biblScope>
<biblScope unit="production">Printed in the UK</biblScope>
</imprint>
<idno type="ISSN">1742-5468</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1742-5468</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Asymptotic patterns</term>
<term>Bifurcation</term>
<term>Bifurcation parameter</term>
<term>Bubonic plague</term>
<term>Characteristic equation</term>
<term>Constant removal rate</term>
<term>Contour pictures</term>
<term>Critical value</term>
<term>Eigenvalue</term>
<term>Epidemic model</term>
<term>Fourier modes</term>
<term>Growth rate</term>
<term>Gure</term>
<term>Gures</term>
<term>Infective individuals</term>
<term>Infectives</term>
<term>Initial state</term>
<term>Initial states</term>
<term>Iteration</term>
<term>Jacobian matrix</term>
<term>Labyrinthine patterns</term>
<term>Linear regime</term>
<term>Mech</term>
<term>Nite range</term>
<term>Nonlinear regime</term>
<term>Numerical simulations</term>
<term>Paper addresses</term>
<term>Parameter values</term>
<term>Parameters values</term>
<term>Pattern formation</term>
<term>Perturbation</term>
<term>Phys</term>
<term>Population dynamics</term>
<term>Positive equilibrium</term>
<term>Positive equilibrium point</term>
<term>Positive equilibrium points</term>
<term>Real number</term>
<term>Real parts</term>
<term>Spatial</term>
<term>Spatial epidemic model</term>
<term>Spatial model</term>
<term>Spatial patterns</term>
<term>Spatial spread</term>
<term>Spot patterns</term>
<term>Theoretical analysis</term>
<term>Time evolution</term>
<term>Turing</term>
<term>Turing instabilities</term>
<term>Turing instability</term>
<term>Turing mechanisms</term>
<term>Turing space</term>
<term>Unstable wavenumber</term>
</keywords>
</textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract">This paper addresses the question of how population diffusion affects the formation of thespatial patterns in the spatial epidemic model by Turing mechanisms. In particular, wepresent a theoretical analysis of results of the numerical simulations in two dimensions.Moreover, there is a critical value for the system within the linear regime. Below the criticalvalue the spatial patterns are impermanent, whereas above it stationary spot and stripepatterns can coexist over time. We have observed the striking formation of spatial patternsduring the evolution, but the isolated ordered spot patterns do not emerge in the space.</div>
</front>
</TEI>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Sante/explor/SrasV1/Data/Istex/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001784 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Curation/biblio.hfd -nk 001784 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Sante |area= SrasV1 |flux= Istex |étape= Curation |type= RBID |clé= ISTEX:3CD736D73B1B174FD0020CA01D9B4A9D1AB68194 |texte= Formation of spatial patterns in an epidemic model with constant removal rate of theinfectives }}
This area was generated with Dilib version V0.6.33. |