摘要
Spatiallyexplicitmodelshavebecomewidelyusedintoday'smathematicalecologyandepidemiologytostudythepersistenceofpopulations.Forsimplicity,populationdynamicsisoftenanalysedbyusingordinarydifferentialequations(ODEs)orpartialdifferentialequations(PDEs)intheone-dimensional(1D)space.Animportantquestionistopredictspeciesextinctionorpersistenceratebymeanofcomputersimulationbasedonthespatialmodel.Recently,ithasbeenreportedthatstableturbulentandregularwavesarepersistentbasedonthespatialsusceptible-infected-resistant-susceptible(SIRS)modelbyusingthecellularautomata(CA)methodinthetwo-dimensional(2D)space[Proc.Natl.Acad.Sci.USA101,18246(2004)].Inthispaper,weaddressotherimportantissuesrelevanttophasetransitionsofepidemicpersistence.Weareinterestedinassessingthesignificanceoftheriskofextinctionin1Dspace.Ourresultsshowthatthe2Dspacecanconsiderablyincreasethepossibilityofpersistenceofspreadofepidemicswhenthedegreedistributionoftheindividualsisuniform,i.e.thepatternof2Dspatialpersistencecorrespondingtoextinctionina1Dsystemwiththesameparameters.Thetrade-offsofextinctionandpersistencebetweentheinfectionperiodandinfectionrateareobservedinthe1Dcase.Moreover,nearthetrade-off(phasetransition)line,anindependentestimationofthedynamicexponentcanbeperformed,anditisinexcellentagreementwiththeresultobtainedbyusingtheconjecturedrelationshipofdirectedpercolation.Wefindthattheintroductionofashort-rangediffusionandalong-rangediffusionamongtheneighbourhoodscanenhancethepersistenceandglobaldiseasespreadinthespace.
出版日期
2009年02月12日（中国Betway体育网页登陆平台首次上网日期，不代表论文的发表时间）
