空間擴(kuò)散的傳染病動力系統(tǒng)行波解研究.pdf

1、中北大學(xué)碩士學(xué)位論文空間擴(kuò)散的傳染病動力系統(tǒng)行波解研究姓名：霍罡申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：靳禎20090510中北大學(xué)學(xué)位論文ThestudiesoftravellingwavesolutionsinepidemicdynamicssystemwithdiffusionABSTRACTInthispaper，weproposethreetypesSIepidemicmodelswithdifferentcapacityt

2、odiffuseinaccordancewiththesymptomsofdifferenttypediseasebasedondiseasesspreadprocessthatspreadfrompathogenstothesurroundingenvironmentatconstantvelocityThen，weinvestigatetheconditionoftheexistenceoftravellingwavesolutio

3、nsofepidemicmodels，andforecasttheminimuminvasionspeedoftheinfectiousdiseasesForadiseasesatisfyingsuchepidemicmodels，aslongaspeopletakevariousmethodstocontroltheinvasionspeedofinfectiousdiseases，andmadeitsmallerthanthemin

4、imuminvasionspeedoftheepidemic，theepidemicwilldieout；orifwemakethediffusionspeedofthesusceptibleisgreaterthantheminimuminvasionspeedofepidemic，wealsocancontroltheinfectiousdiseasesItissurethatourresearchhaveacertainsigni

5、ficanceforthepreventionandcontrolofinfectiousdiseasesInchapter2，weconsiderthissituationthatthesusceptibleandtheinfectioushavedifferentbirthrate，andthediseasehasanonlinearincidencerate，andwealsoassumeonlytheinfectioushave

6、thecapacitytodiffuseThen，webuildaspatiallyextendedSIepidemicmodelByusingtheShootingargument，constructWset，LyapunovfunctionandWazewskitheorem，LaSalle’SInvarianceprinciple，westudytheexistenceofaheteroclinicorbitconnectingt

7、woequilibriumpointsinR3whichcorrespondstoatravellingwaveSOlutionconnectingthediseasefreeandendemicequilibriaforthereactiondiffusionsystemandobtaintheexpressionoftheminimuminvasionspeedofdiseasesCAtthesametime，numericalsi