Persistence, extinction and spatio-temporal synchronization of SIRS spatial models
Identifieur interne : 002D32 ( Main/Exploration ); précédent : 002D31; suivant : 002D33Persistence, extinction and spatio-temporal synchronization of SIRS spatial models
Auteurs : Quan-Xing Liu [République populaire de Chine, Pays-Bas] ; Rong-Hua Wang [République populaire de Chine] ; Zhen Jin [République populaire de Chine, Niger]Source :
- Journal of Statistical Mechanics: Theory and Experiment [ 1742-5468 ] ; 2009.
English descriptors
- Teeft :
- Automaton, Average time, Basic reproduction number, Biol, Cellular, Cellular automata, Cellular automata method, Cellular automata model, Cellular automata simulations, Certain value, Classical expression, Community size, Computer code, Critical community size, Critical value, Cyclic competition, Dengue fever, Disease persistence, Disease spread, Dispersal, Dynamics, Ecol, Ecological, Ecological systems, Epidemic, Epidemic model, Epidemic models, Epidemic persistence, Evolutionary dynamics, Explicit model, Explicit models, Extensive computer simulations, Extinction, Extinction domain, Extinction phase, Extinction probability pext, Extinction time, Extinction times, Focus expansion, Former parameters, Gillespie algorithm, Global disease spread, Grenfell, Grid size, Gure, High mobility, Higher mobility, Important implications, Infection, Infection period, Infection rate, Infectious diseases, Infective individuals, Intrinsic noise, Large scale, Lattice, Lattice models, Lattice simulation, Lattice simulations, Lett, Local populations, Localized disease outbreaks, Long term, Measles, Measles epidemics, Mech, Metapopulation, Metapopulation system, Mobility, Mobility processes, Mobility rate, Mobility rates, Models figure, Nearest neighbors, Nonvanishing infection rate, Opposite combination, Oscillatory behavior, Outbreak, Parameter, Parameter region, Parameter space, Parasite evolution, Pattern formation, Persistence, Phase space, Phase synchronization, Phase transition, Phase transitions, Phys, Plant disease, Population outbreaks, Power laws, Present paper, Previous studies, Proc, Rare events, Rate equations, Reaction scheme, Recurrent epidemics, Resistant period, Results show, Similar results, Simulation, Simulation results, Single patch, Sirs model, Smart preys, Spatial, Spatial distribution, Spatial dynamics, Spatial epidemic model, Spatial epidemics, Spatial hierarchies, Spatial model, Spatial pattern, Spatial patterns, Spatial spread, Spatial structure, Spatial synchrony, Spiral waves, Square lattice, Stable spiral waves, Stat, Static dispersal, Stochastic, Susceptible individuals, Susceptibles, Synchronization, Synchronous dynamics, Synchrony, System size, Temporal evolution, Theor, Time series, Time step, Time units, Total number, Trends ecol, Turbulent waves, Typical snapshots, Whooping cough, Wide range.
Abstract
Spatially explicit models are widely used in todays mathematical ecology and epidemiologyto study persistence and extinction of populations as well as their spatial patterns. Here weextend the earlier work on static dispersal between neighboring individuals to the mobilityof individuals as well as multi-patch environments. As is commonly found, the basicreproductive ratio is maximized for the evolutionarily stable strategy for disease persistencein mean field theory. This has important implications, as it implies that for a wide range ofparameters the infection rate tends to a maximum. This is opposite to the present resultobtained from spatially explicit models, which is that the infection rate is limited by anupper bound. We observe the emergence of trade-offs of extinction and persistence for theparameters of the infection period and infection rate, and show the extinctiontime as having a linear relationship with respect to system size. We further findthat higher mobility can pronouncedly promote the persistence of the spreadof epidemics, i.e., a phase transition occurs from the extinction domain to thepersistence domain, and the wavelength of the spirals increases with the mobility ratioenhancement and will ultimately saturate at a certain value. Furthermore, for themulti-patch case, we find that lower coupling strength leads to anti-phase oscillationof the infected fraction, while higher coupling strength corresponds to in-phaseoscillation.
Url:
DOI: 10.1088/1742-5468/2009/07/P07007
Affiliations:
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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="2009">2009</date><biblScope unit="issue">7</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="23">23</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>Automaton</term><term>Average time</term><term>Basic reproduction number</term><term>Biol</term><term>Cellular</term><term>Cellular automata</term><term>Cellular automata method</term><term>Cellular automata model</term><term>Cellular automata simulations</term><term>Certain value</term><term>Classical expression</term><term>Community size</term><term>Computer code</term><term>Critical community size</term><term>Critical value</term><term>Cyclic competition</term><term>Dengue fever</term><term>Disease persistence</term><term>Disease spread</term><term>Dispersal</term><term>Dynamics</term><term>Ecol</term><term>Ecological</term><term>Ecological systems</term><term>Epidemic</term><term>Epidemic model</term><term>Epidemic models</term><term>Epidemic persistence</term><term>Evolutionary dynamics</term><term>Explicit model</term><term>Explicit models</term><term>Extensive computer simulations</term><term>Extinction</term><term>Extinction domain</term><term>Extinction phase</term><term>Extinction probability pext</term><term>Extinction time</term><term>Extinction times</term><term>Focus expansion</term><term>Former parameters</term><term>Gillespie algorithm</term><term>Global disease spread</term><term>Grenfell</term><term>Grid size</term><term>Gure</term><term>High mobility</term><term>Higher mobility</term><term>Important implications</term><term>Infection</term><term>Infection period</term><term>Infection rate</term><term>Infectious diseases</term><term>Infective individuals</term><term>Intrinsic noise</term><term>Large scale</term><term>Lattice</term><term>Lattice models</term><term>Lattice simulation</term><term>Lattice simulations</term><term>Lett</term><term>Local populations</term><term>Localized disease outbreaks</term><term>Long term</term><term>Measles</term><term>Measles epidemics</term><term>Mech</term><term>Metapopulation</term><term>Metapopulation system</term><term>Mobility</term><term>Mobility processes</term><term>Mobility rate</term><term>Mobility rates</term><term>Models figure</term><term>Nearest neighbors</term><term>Nonvanishing infection rate</term><term>Opposite combination</term><term>Oscillatory behavior</term><term>Outbreak</term><term>Parameter</term><term>Parameter region</term><term>Parameter space</term><term>Parasite evolution</term><term>Pattern formation</term><term>Persistence</term><term>Phase space</term><term>Phase synchronization</term><term>Phase transition</term><term>Phase transitions</term><term>Phys</term><term>Plant disease</term><term>Population outbreaks</term><term>Power laws</term><term>Present paper</term><term>Previous studies</term><term>Proc</term><term>Rare events</term><term>Rate equations</term><term>Reaction scheme</term><term>Recurrent epidemics</term><term>Resistant period</term><term>Results show</term><term>Similar results</term><term>Simulation</term><term>Simulation results</term><term>Single patch</term><term>Sirs model</term><term>Smart preys</term><term>Spatial</term><term>Spatial distribution</term><term>Spatial dynamics</term><term>Spatial epidemic model</term><term>Spatial epidemics</term><term>Spatial hierarchies</term><term>Spatial model</term><term>Spatial pattern</term><term>Spatial patterns</term><term>Spatial spread</term><term>Spatial structure</term><term>Spatial synchrony</term><term>Spiral waves</term><term>Square lattice</term><term>Stable spiral waves</term><term>Stat</term><term>Static dispersal</term><term>Stochastic</term><term>Susceptible individuals</term><term>Susceptibles</term><term>Synchronization</term><term>Synchronous dynamics</term><term>Synchrony</term><term>System size</term><term>Temporal evolution</term><term>Theor</term><term>Time series</term><term>Time step</term><term>Time units</term><term>Total number</term><term>Trends ecol</term><term>Turbulent waves</term><term>Typical snapshots</term><term>Whooping cough</term><term>Wide range</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">Spatially explicit models are widely used in todays mathematical ecology and epidemiologyto study persistence and extinction of populations as well as their spatial patterns. Here weextend the earlier work on static dispersal between neighboring individuals to the mobilityof individuals as well as multi-patch environments. As is commonly found, the basicreproductive ratio is maximized for the evolutionarily stable strategy for disease persistencein mean field theory. This has important implications, as it implies that for a wide range ofparameters the infection rate tends to a maximum. This is opposite to the present resultobtained from spatially explicit models, which is that the infection rate is limited by anupper bound. We observe the emergence of trade-offs of extinction and persistence for theparameters of the infection period and infection rate, and show the extinctiontime as having a linear relationship with respect to system size. We further findthat higher mobility can pronouncedly promote the persistence of the spreadof epidemics, i.e., a phase transition occurs from the extinction domain to thepersistence domain, and the wavelength of the spirals increases with the mobility ratioenhancement and will ultimately saturate at a certain value. Furthermore, for themulti-patch case, we find that lower coupling strength leads to anti-phase oscillationof the infected fraction, while higher coupling strength corresponds to in-phaseoscillation.</div></front></TEI><affiliations><list><country><li>Niger</li><li>Pays-Bas</li><li>République populaire de Chine</li></country></list><tree><country name="République populaire de Chine"><noRegion><name sortKey="Liu, Quan Xing" sort="Liu, Quan Xing" uniqKey="Liu Q" first="Quan-Xing" last="Liu">Quan-Xing Liu</name></noRegion><name sortKey="Jin, Zhen" sort="Jin, Zhen" uniqKey="Jin Z" first="Zhen" last="Jin">Zhen Jin</name><name sortKey="Wang, Rong Hua" sort="Wang, Rong Hua" uniqKey="Wang R" first="Rong-Hua" last="Wang">Rong-Hua Wang</name></country><country name="Pays-Bas"><noRegion><name sortKey="Liu, Quan Xing" sort="Liu, Quan Xing" uniqKey="Liu Q" first="Quan-Xing" last="Liu">Quan-Xing Liu</name></noRegion></country><country name="Niger"><noRegion><name sortKey="Jin, Zhen" sort="Jin, Zhen" uniqKey="Jin Z" first="Zhen" last="Jin">Zhen Jin</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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