2006数学建模B题(含附件)

2006高教社杯全国大学生数学建模竞赛题目（请先阅读“对论文格式的统一要求”）B题: 艾滋病疗法的评价及疗效的预测艾滋病是当前人类社会最严重的瘟疫之一，从1981年发现以来的20多年间，它已经吞噬了近3000万人的生命。艾滋病的医学全名为“获得性免疫缺损综合症”，英文简称AIDS，它是由艾滋病毒（医学全名为“人体免疫缺损病毒”, 英文简称HIV）引起的。这种病毒破坏人的免疫系统，使人体丧失抵抗各种疾病的能力，从而严重危害人的生命。人类免疫系统的CD4细胞在抵御HIV的入侵中起着重要作用，当CD4被HIV感染而裂解时，其数量会急剧减少，HIV将迅速增加，导致AIDS发作。 艾滋病治疗的目的，是尽量减少人体内HIV的数量，同时产生更多的CD4，至少要有效地降低CD4减少的速度，以提高人体免疫能力。迄今为止人类还没有找到能根治AIDS的疗法，目前的一些AIDS疗法不仅对人体有副作用，而且成本也很高。许多国家和医疗组织都在积极试验、寻找更好的AIDS疗法。现在得到了美国艾滋病医疗试验机构ACTG公布的两组数据。 ACTG320（见附件1）是同时服用zidovudine（齐多夫定），lamivudine（拉美夫定）和indinavir（茚地那韦）3种药物的300多名病人每隔几周测试的CD4和HIV的浓度（每毫升血液里的数量）。193A（见附件2）是将1300多名病人随机地分为4组，每组按下述4种疗法中的一种服药，大约每隔8周测试的CD4浓度（这组数据缺HIV浓度，它的测试成本很高）。4种疗法的日用药分别为：600mg zidovudine或400mg didanosine（去羟基苷），这两种药按月轮换使用；600 mg zidovudine加2.25 mg zalcitabine（扎西他滨）；600 mg zidovudine加400 mg didanosine；600 mg zidovudine加400 mg didanosine，再加400 mg nevirapine（奈韦拉平）。请你完成以下问题：（1）利用附件1的数据，预测继续治疗的效果，或者确定最佳治疗终止时间（继续治疗指在测试终止后继续服药，如果认为继续服药效果不好，则可选择提前终止治疗）。（2）利用附件2的数据，评价4种疗法的优劣（仅以CD4为标准），并对较优的疗法预测继续治疗的效果，或者确定最佳治疗终止时间。(3) 艾滋病药品的主要供给商对不发达国家提供的药品价格如下：600mg zidovudine 1.60美元，400mg didanosine 0.85美元，2.25 mg zalcitabine 1.85美元，400 mg nevirapine 1.20美元。如果病人需要考虑4种疗法的费用，对（2）中的评价和预测（或者提前终止）有什么改变。附件1 ACTG320数据同时服用3种药物（zidovudine, lamivudine,indinavir）的300多名病人每隔几周测试的CD4和HIV的浓度。第1列是病人编号，第2列是测试CD4的时刻（周），第3列是测得的CD4（乘以0.2个/ul），第4列是测试HIV的时刻（周），第5列是测得的HIV（单位不详）。PtIDCD4DateCD4CountRNADateVLoad23424017805.523424422843.923424812684.723424251712542342440994052342501405.32342546242.423425911093.72342523122232.6234254032023426010104.523426415141.723426811581.72342626149262.82342646120463.423426541412342701005.32342741142.72342773072.62342724137242234274022523428016105.523428322032.523428831681.92342824645241.72342840451401.7234290705.52342962664.3234291240124234292764272.72342944111444.323429511092343007805.623430414042.123430724571.82343024201241.72343039220391.72343104205.223431310032.523431710172.32343124154241.723431391402343206305.723432538953.523432918092.62343224264241.92343240334401.72343341045.42343398292.6234331288122.8234332857284.12343344692343401705.92343442146.12343472475234343929395.42343502505.223435410244.523435813283.92343524186242.32343602405.423436410642.523436811982.52343624203241.723437014705.323437421442.623437824382.22343725204161.923438015905.623438418643.623438733572.82343902404.82343955653.92343993693.42343925133251.7234394212023440010905.323440421643.823440915494.6234402617626523441013905.323441428944.323441820984.62344124238244.92344139196395.123442014004.923442318933.323442732472.42344223252234.42344240305404.72344305305.223443418741.823443928581.92344322200221.72344338248383.22344402105.323444515952.123444919791.72344425197251.72344441180411.7234450109052344541214323445819482.62344524135241.72344539185391.72344601404.52344643542.32344684782.4234462747275.12344640454052344650542344703305.12344746243.72344788782.32344724128243.12344740168403.62344804105.723448411044.723448818284.7234482187215.32344839197394.82344902305.823449417742.723449818682.42344925155251.72344940169401.723450012052345045642.42345087781.72345025137251.72345042122421.72345109605.72345147943.82345199292.52345123257233.42345142137424.6234520990523452417343.523452726572.82345223232231.72345239235391.7234530005.62345342442.82345383582.22345324201242.22345340255402.22345403904.72345442244.42345483184.5234542212224.4234543920394.823455012303.623455415541.923455818981.72345524226241.72345539203391.923455540234561015.62345652753.6234568984234562443243.723456407740423457010004.32345749342.623457810382.32345724145241.7234574013323458018405.123458427743.523458828682.923458232662345908705.323459414643.623459818482.72345924187241.82345933183333.72346008405.62346048244.523460812783.62346025137251.7234604081402.4234610305.7234614945.52346181085.5234612465244.82346140104404.723462013903.823462512352.223462913291.72346225133251.72346240189401.723463013104.123463417942.2234638248223463102082346325191251.72346341207411.7234634921423464024705.423464528153.423464935192.62346424356242.52346440382402.42346504004.52346557152.32346585381.7234652484234653971391.72346602105.42346658653.623466814983.42346624117244.12346646127373.9234670004.623467532532346771771.82346723246231.72346739211391.82346747023468020104.623468519651.823468928291.72346826192261.7234690505.6234694743.3234698118523469248245.923469334234694229423.3234700804.22347033433.92347086782.2234702445242.9234704088403.323470489923471015104.923471319932.723471730071.72347123277231.72347139397391.7234721615.1234725555.22347284084.9234722574254.3234724113415.3234724682347302005.623473415543.423473817282.62347324160241.72347340142403.82347401340523474317832.123474711971.92347423305231.72347439305391.72347501004.923475494323475930922347525130252.32347539137391.92347604904.923476473432347688084.62347624137243.42347640187401.72347702405.82347747743.323477812583.42347724226243.323477341062347745160454.3234780805.52347843342.92347884882.123478155123478247245.4234784202347904305.12347949641.723479710073.92347923159231.72347941692348009005.723480424343.523480815482.62348024266241.92348040348402.223481020403.92348142304223481816981.72348124294241.72348140473401.7234820405.823482440422348287281.8234821102348303304.72348344444.42348386384.92348324102244.62348339176393.923484031052348448544.82348485084.92348425209251.723485017304.723485418741.723485931194.32348526217261.72348539230391.72348601304.62348645342.32348688781.7234862394231.7234864060401.723487015004.223487521751.823487916394.22348725185254.42348740185403.523488015004.223488421042.323488924991.72348825320251.72348840399401.7234890304.92348933632.12348985582.3234892486242.12348940146401.723490015104.623490523653.1234909214922349026150261.723490421772349109904.423491413042.423491814081.92349125282252.22349209404.823492312232.923492714372.32349222212221.723493010905.72349342124423493822483.52349323228232.12349401904.92349442045.12349482685234942215225.12349513715.923495649234951178114.22349528223283.62349544223444.12349605705.323496420243.92349692.62349629236292.72349639260393.523497015804.723497321432.723497823682.22349724340241.72349740497401.7234980505.6234984745.62349880234990705.823499418442349972573.2234992489244.9234994657465.52350001105.92350041645.823500810182.22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