SARS疫情的实证分析和预测

SARS,(,,100871)[]SARS;SIR;;[]SIR,SARS,,SIRSARSEmpiricalanalysisandforecastingforSARSepidemicsituationWANGDuo,ZHAOXiaofei(DepartmentoffinancialMathematics,LMAM,SchoolofMathematicalScience,PekingUniversity,Beijing100871,China)KEYWORDSSARS;SIRmodel;Curvefitting,EmpiricalanalysisSUMMARYBasedontheSIRepidemicmodel,theempiricalanalysisfortheSARSepidemicsituationispresented.TheresultsshowthattheSIRmodelsapplicableapprosimatelyfordescribingtheSARSepidemicsituation.TheforecastingforSARSepidemicsituationisalsogiven.1SIRKermack[1]1927(SIR)(19051906),SIR()[2]SARS,SIRSARS,I(t),S(t),R(t),()t:(1),3N;(2)();(3)KermackMcKendrick[1](SIR):dSdt=-rSIdIdt=rSI-IdRdt=I(1)r,[1]:dRdtAsech2(t-)(2)sech(x)=2ex+e-x,A,,,:A=322r2S0,=12,=tanh-1(rS0-1)S0,tanh(x)=ex-e-xex+e-x,=[(rS0-1)2+2r2S0(N-S0)2]1/2SARS(,),,SARS:(10271007),supportedbyNatureScienceFoundationofChina(10271007)andRFDPCorrespondingauthoremail,[e-mail]27()JOURNALOFPEKINGUNIVERSITY(HEALTHSCIENCES)Vol.35SupplementMay2003©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,SIR:(4),,SIRSARS2,2003422,dR/dt,Matlab(2),A,,,(2)2.1SARS423515,dR/dt,(2)y=155[sech(0.0787t-0.650)]2(3)(3)11Table1Comparisonofdailynumbersofnewpatientscomputedbyformula(3)andrealnumbersfornationalSARSepidemicsituation(HongKong,TaiwanandMacaoarenotincluded)04-2304-2404-2504-2604-2704-2804-2904-3005-0105-0205-0305-0405-0505-0605-0705-0805-0905-1005-1105-1205-1305-1405-15113.8122.9131.4139.0145.4150.4153.7155.1154.6152.3148.1142.4135.4127.3118.5109.399.990.681.673.064.957.450.51101011421461391671451451591481481451411051391301097864697550490.030.220.070.050.040.100.060.070.030.030.000.020.040.210.140.160.080.160.270.060.130.150.03(3):522(,)19.0(20);5278.9(10);5314.8(5);6150.5()615()47222.2SARS423515,,(2)y=95.6[sech(0.0651t-0.366)]2(4)(4)22Table2Comparisonofdailynumbersofnewpatientscomputedbyformula(4)andrealnumbersforBeijingSARSepidemicsituation04-2304-2404-2504-2604-2704-2804-2904-3005-0105-0205-0305-0405-0505-0605-0705-0805-0905-1005-1105-1205-1305-1405-1587.590.592.994.695.595.694.593.591.288.384.480.976.672.167.362.657.853.148.644.340.236.332.7787286106106761028310281946189568594455038434436250.120.260.080.100.090.250.070.120.110.090.090.320.130.280.210.330.280.060.280.030.080.010.31(4)SARS:5221417;5269.1(10);5314.8(5);6180.47()6172634()517+,,517SARS1968,SARS()37()JOURNALOFPEKINGUNIVERSITY(HEALTHSCIENCES)Vol.35SupplementMay2003©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.3,SIRSARS,,,SARS,61518SARS(),,SARS,(1/5),,,SARS,,4262753,,5917,2,35610,,5,6SARS,SIR,SARS1KermackWO,McKendrickAG,Acontributiontothemathemati2caltheoryofepidemics[J].ProcRoyalSoc(SeriesA),1927,115:70027212,,1[A].:,1[M].:,200214302453(2003205221)(:),,,,:(1)(1992)(,1992);(2)(,1987),,,,,,,,()47()JOURNALOFPEKINGUNIVERSITY(HEALTHSCIENCES)Vol.35SupplementMay2003©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.