SI害虫控制模型的分析及策略

南京师范大学硕士学位论文SI害虫控制模型的分析及策略姓名：汤珠峰申请学位级别：硕士专业：数学；应用数学指导教师：崔景安2009-05-051980GohSI..GohLogistic...HollingII.....SI.:Logistic;;;;iiiAbstract1980,GoHproposedaSImodelaboutpestcontrol.Inhispaper,hegavesomepoliciesonpestcontrolindynamicsaspect.Notonlythemodelhasbeenusedextensivelybutalsobasingonhismodelmanypeopleamendthemodeltogetsomemoreconsummatepestcontroldynamicsmodel.BasingonGoH’smodelinthispaperweconsiderthatsusceptiblepestobeyLogisticincreaselawandboththesusceptiblepestandinfectiouspestconsumetheresourceoftheenvironment,thenestablishtwopestcontroldynamicsmod-els.Inthepaperwehaveanalyzedtheexistenceandthestabilityofthepositiveequilibriumandboundaryequilibrium.Andthenaccordingtheresultofnumer-icalsimulation,weprovideseveralstrategiesonthepestcontrol.Concerningthesecondmodel,givensatisfyingHollingIIpredacityfunctionbetweenpestandcrop,weestablishadynamicssystemofthreevariableinbaseofappendingcropintothefirstmodel.Invirtueofcomplexityofthismodel,vianumericalsim-ulation,wegainsomequalitativeofthemodel.Inaddition,comparedaformermodel(notconsideringbirthofsusceptiblepest),wegetholdofsomenewpointdifferentfromformer.Last,inordertoemphasizethatthequestionofpestcontrolisradicallyamatterofecologyandeffectivecontrolmusthaveaecologyforesight,herewegivetheconceptofecologicindexinpestcontrol.Furthermore,wefindthemath-ematicalmethodtoobtaintheecologicindexinthefirstmodel.Consequently,wecanjudgeaSIpestcontrolmodelisvalidornotfromtwoaspectsofeconomicandecologic.ivvKeywords:Logisticincrease;Constantcontrol;Economicinjurylevel;Eco-nomicthreshold;Ecologicindex:123451250015009503001750-18801870-1890189619011899-1909192119281939DDT194219441946DDTDDT195919601962¢1972DDT112[32]....IPMintergratedpestmanagement..)............SanyiTang[31]...IPM13......[11-15]..[11,16-19][20-30].1980Goh[5].SI....2x2.11980Goh[5]8:_S=¡rSI;_I=rSI¡!I+¹;(2.1)S(t)I(t)t!r¹.[33]SI.8:_S=S(¡r1¡®I+kµy);_I=®SI¡¯I+¹;_y=y(r2¡µS¡!y);(2.2)y(t)Logisticy(r2¡!y).kµyS.2.1.2.12.2..Logistic.[3]8:_S=S(1¡S)¡rSI2;_I=rSI2¡!I+¹;(2.3)425(2.3)(i)1(ii)rSI2..8:_S=aS(1¡S+IK)¡rSI;_I=rSI¡!I+¹;(2.4)aK.r.Logistic.HollingII.8:_S=aS(1¡S+IK)¡rSI+kµyS1+bS;_I=rSI¡!I+¹;_y=y(®¡µS1+bS¡¯y);(2.5)x2.22.42.1S(t)I(t)(2.4)S(0);I(0)¸0..VV(t)=S(t)+I(t):dVdtj(2:4)=aS(1¡S+IK)¡!I+¹·a(K¡S¡I)¡!I+¹26·a(K¡V)+¹V(t)·aK+¹a+[S(0)+I(0)¡aK+¹a]e¡at:tS(t)aK+¹a+0;I(t)aK+¹a+0:(0).¤2.2¹¹aK!a+rK(2.4)E0=(0;¹!)E1(S1;I1);¹aK!a+rK,(2.4)E0=(0;¹!)..(2.4)E0=(0;¹!):(2.4)a(1¡S+IK)¡rI=0;(2:6)rSI¡!I+¹=0:(2:7)(2.6)(2.7)S=¡(1+rKa)I+K;(2:8)S=!r¡¹rI:(2:9)I¡S(2.8)(2.9)1.1(2.4)aKa+rK¹!;27.1S=¡(1+rKa)I+KS=!r¡¹rI.E1(S1;I1).¹aK!a+rK,¹0:¹¸aK!a+rK;(2.4).(2.4)..(2.4)E0JE0=0@a¡(aK+r)¹!0r¹!¡!1A:¸1;¸2¸1+¸2=a¡(aK+r)¹!¡!;28¸1¸2=¡![a¡(aK+r)¹!]:¹aK!a+rKE0.(2.4)E1(S1;I1)JE1=0@a¡2aS1K¡(aK+r)I1¡aS1K¡rS1rI1rS1¡!1A:0S1!r;aK¡a!ra+rKI1aKa+rK:a¡2aS1K¡(aK+r)I1=a¡2a[¡(1+rKa)I1+K]K¡(aK+r)I1=¡a+(aK+r)I1¡a+(aK+r)aKa+rK¡a+a=0:E1(S1;I1)JE1=0@¡¡+¡1A:E1(S1;I1)..¤2.3(2.4)..DulacB(S;I)=1SI:29D=@(PB)@S+@(QB)@I=¡aKI¡¹SI20;8:P=aS(1¡S+IK)¡rSIQ=rSI¡!I+¹:BendixsonDulacD0=f(S;I)jS0;I0g;(2.4).(2.4)..¤3....(2.4)(2.8)(2.9)I1S1I1=K¡!r+q(!r¡K)2+4¹r(1+rKa)2+2rKa;S1=K+!r¡q(!r¡K)2+4¹r(1+rKa)2:(3:1)(3.1)S1¹S1=f(¹):f(¹)¹.f(¹).f¹=f¡1(S1):¹S1=K+!r¡q(!r¡K)2+4¹r(1+rKa)2:x3.1EIL.10311.22S(0)=10;I(0)=0;a=0:002;r=0:003;K=50;!=0:04;¹=0:001....2f(¹)·L:(L!r)¹¸f¡1(L),¹1:x3.2.economicthresholdcontrolactionthreshold312..33S(0)=10;I(0)=0;a=0:002;r=0:003;K=50;!=0:04;¹=0:01.3.3.S(t)¹S(0)S(0),¹¹¹S(0)¹.EIL.3131010.110.210.310.410.5s020406080100t2020.0520.120.1520.220.2520.320.35s01020304050t28.52929.530s01020304050t39.239.439.639.840s051015202530t.4a=0:002;r=0:003;K=50;!=0:04;¹=0:01S(0)10203040.EIL.x3.32.52.5.5.314246810s02468q0.81.21.62y.5..6(0.6)..1.5.3...31500.20.40.60.811.21.4s1020304050t0246810i1020304050t00.511.522.53y1020304050t0.511.522.53s051015202530t05101520i51015202530t2345678y051015202530t.6.r1=0:2;®=0:8;k=0:9;µ=5;¯=0:5;r2=3;!=0:2..41962RachelCarsonSilentSpring.1966FAOIOBCIPC1972CEQIPCIPMintergratedpestmanagement.....SI.x4.1I1=K¡!r+q(!r¡K)2+4¹r(1+rKa)2+2rKa,g(¹):I1=K¡!r+q(!r¡K)2+4¹r(1+rKa)2+2rKa·EEg(¹)·E:16417¹·ra(a+rK)E2¡(K¡!r)rE,¹¤:¹1¹¹0¹·¹¤(0;t0)¹¹00¹·¹¤(0;t0).¹1¡¹¤=0LEaa+rK(L¡K+!r2)2¡a+rKa[E¡12aa+rK(K¡!r)]2=a!r(a+rK):L-E7LE.7¹1¡¹¤·0SILE¹1¡¹¤0418.SI.x4.2L.EE·K.810L·K+!r2¡q!r+(K¡(!r)24E1.E=KPPmin.Pmin·P·1..88FK+!r2¡q!r+(K¡!r)240E(K+!r2¡p!,a(K¡!r)2(a+rK))D(0,12a(K¡!r)pr+apr(K+!r¡a!)(a+rK)pr).(L;E).1E2E419.P0P¸P0EE.SI.2L¸K+!r2¡q!r+(K¡(!r)24EPPmaxE=KPminPmin·P·Pmax1.10L·K+!r2¡q!r+(K¡(!r)24P=P0E0E·E0P¸P0.E0P0.2E0.1E0.E·LP1.ELE=KP.L1P0E0(E0·L).LP0E0.SIL.[1]Anderson,R.M.,1978.Regulationandstabilityofhost-parasitepopulationinteractions.I.RegulatoryProcesses.J.Anim.Ecol.47,219-247.[2]Burges,H.D.,Hussey,N.W.,1971.MicrobialControlofInsectsandMites.AcademicPress,NewYork.[3]Zhang,H.,Jiao,J.J.,Chen,L.S.,2006.Pestmanagementthroughcontinuousandimpulsivecontrolstrategies.[4]Tanada,Y.,1964.Epizootiologyofinsectdisease.In:DeBach,P.(Ed.),Bilogi-calControlofInsectPestsandWeeds.ChapmanandHall,London.[5]Goh,B.S.,1980.ManagementandAnalysisofBiologicalPopulations.Els