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1、分类号：翅茫喊fe-1博:位论女随
2、SK和HIV-fDynamicStudiesof施^]Sto、雜..叙Wfe.y；.-•':.�:.'•零M她敏分方程：爲:.，、‘響管春、#U：德:独创性声明本人郑甫茚明：听提交的学位论文是本人在汙师指汙K独立进行研究工作所取得的成果.据我所知，除了特别朋以际注和致谢的地方外，论文中不包含其他人已经发表或撰写过的研究成果.对本人的研究做出重耍贡献的个人和集体，均已在文中作了明确的^•明.本声明的法律结果由本人承担.学位论文作者签名日期:>/上尤学位论文版权使用授权书本学位论文作者完全
3、了解东北师范大学有关保留.使用学位论文的规定，即:东北师范大学有权保留并向国家有关部门或扎构送交学位论文的茇印件和电子版，允许论文被査阅和借阅.本人授权东北师范大学可以将学位论文的全部或部分内容编入有关数据库进行检索，可以采闬彩印、缩印或其它复制手段保存.汇编本学位论文.(保密的学位论文在解密后适用本授权书）学位论文作者茶名:指异教I]巾nR期h)�H期:处/上上2>学位论文作者毕、11:后去向：工作单位:电活通讯地址:邮编::10200::O29:10200200910212SISHIV-1DynamicStudies
4、oftheStochasticSISandHIV-1Models20153,.,..,,,,.,,.,:,,,.,SISSIS,.,,Rs<1,1,Rs>1,,00,.,.,SIS..,;,,,.,T(CTLs)HIV-1,,;,,E0,E1E2,;,..I:;Itˆo;;;;;;;IIAbstractDynamiesofepidemiologyisthestudyofthespreadanddevelopmentofdis-easeswiththepurposetotracefactorsthatarecontribu
5、tetotheiroccurrenee.Inrecentdecades,epidemiologymodelingbymathematicalresearchhasbeenreceivedagreatattentionwithintheacademia.Inthispaper,sincestochasticdifferentialequationscanreflecttherealitymoreaccurately,weextendedsomeclassicaldeter-ministicmodelfortheepidemic
6、sbyinducingrandomperturbationsinthemodels.Usingthequalitativetheoryofstochasticdifferentialequation,westudytheirdy-namicbehaviorsforthestochasticepidemicmodels,suchasthepersistenceofthesystem,thestabilityoftheequilibrium.Moreover,theparameters’influenceonthedynamic
7、albehaviorsisalsoexploredhere.And,bymeansofnumericalsimu-lations,wediscussthetrendoftheepidemiology.Tobespecific,ourresearchisasfollows:InChapter1,abriefintroductionisgivenforthebackgroundofmathematicalmodelingoninfectiousdiseases,includingsomebasiccompartmentalmo
8、dels,somedefinitionsandprerninarytheoremswhichwillbeusedinthispaperareintroducedexhaustively.Moreover,asurveyoftheresultsinthisthesisisalsopresented.InChapter2,weinvestigateastochasticSISmodelwithsaturatedincidencerateandastochasticSISmodelwithnonlinearincidencera
9、te,respectively.weanalyzethedynamicbehaviorsofthetwostochasticSISmodels.First,showthetwomodelsbothexittheuniqueglobalpositivesolution.Second,weinvestigatetheas
