帶時(shí)滯的病毒動(dòng)力學(xué)模型、傳染病模型后向分支的研究.pdf

1、西南大學(xué)碩士學(xué)位論文帶時(shí)滯的病毒動(dòng)力學(xué)模型、傳染病模型后向分支的研究姓名：王戰(zhàn)偉申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王穩(wěn)地20070501AnalysisofvirusdynamicsmodelincludingdelayandepidemicmodelwithbackwardbifurcationAbstractMajorlAppliedrnnme，n8“∞昂蒯坶tBiologicogma&ema拄。嘶喇5DrlWangWend

2、iAn&orlWangzhamoei(s20040sos)Inthispaper，thevirusdynamicsmodelsincludingdelayandepidemicmodelswithbackwardbifurcationarestudiedInthefirstpartofthispaper，theimmuneresponseofHIV1withdelayisstudiedWegivecompletelyqualitativ

3、eanalysistothismodelByusingadiscretedelaytomodeltheintracellulardelayitisshownthatthesufhcientconditiontoe∞ttrethestabilityoftheinfectedequilibriumdoesnotchangewouldbeenlargedbYSturmsequenceNumericalsimulationsarepresent

4、edtoillustratetheresultsInthesecondpart，themodelofcelltocellspreadofHIV1withtwodistributeddelaysarestudiedWeconsiderthelagbetweenthetimeanewcellisreproducedandwhenitbecomesmatureandthelagbetweenthetimeacellisinfectedandw

5、henitbeaustoinfectothercells，andmodelthetwophasesbygammadistributionsIfthesusceptiblecellsproliferatelogisticallywecanobtainconditionsinwhichthemodelundergoestheHopfbifurcation，andconditionsinwhichthepositiveequilibriumi

6、salwaysunstable，andconditionsinwhichthepositiveequilibriumisalwaysasymptoticallystable，andconditionsinwhichstabilitychangesfromstabletounstabletostable，byusingtwoaveragetimedelaysa8bifurcationparametersThen，numericalsimu

7、lationsarepresentedtoillustratetheseresultsInthethirdpartasimpleSISmodelwithtreatmenteisstudiedWbusethetreatmentratewhichisproportionaltothenumberoftheinfectiveswhenthecapacityoftreatmentisnotreachedandotherwise，takesthe