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ControllingtheEradicationofPolioRyanHernandezMay1,2003

1IntroductionPoliomyelitisischaracterizedbyfever,motorparalysis,andatrophyofskeletalmuscles(acuteflaccidparalysis,AFP).Thecripplingvirushasdisablednearly20millionpeoplelivingtoday[11].Soon,however,thisviruswillnolongerhurtourchildren.Sinceitscreationin1988,theGlobalPolioEradicationInitiativehashelpedcuttheglobaltollofpolioparalysisfromanestimated350,000tofewerthan500in2001[11].Afterbeingdeemederadicated,poliowillbecomethesecondvirustohavebeeneradicatedfromtheworld(thefirstbeingsmallpoxin1980[10]).Thegoalofpolioeradicationhasbeenmetinmostpartsoftheworld(WHOdeemedtheAmericasPolio-freein1994[11]andthe51countriesrepresentingtheEUROregionwerecertifiedpolio-freeinJune2002[1]),andeachcountrythathascitizenssufferingfromthediseasehasbeengivenaplanofactionforeradication[1].Therearetwomainvaccinesthatareusedtobuildthehumanimmunesystem:oralpoliovirusvaccineandinactivatedpoliovirusvaccine.OPV,asitsnamesuggestscanbeadministeredorally,eitherasadropintothemouth,oronasugarpill.Thebenefitsofthisvaccinearethatitdoesnotrequireatrainedmedicalstafffortheimmunizationofpeople,nordoesitrequiresterileinjectionequipment.Themaincostofusingthisvaccinationisthatitisastrainof“live”virus,hencethosegiventhisvaccineenteraninfectiousstage,andthereisariskofsufferingtheconsequencesofcontractingpoliowhenusingit.IPVisa“dead”formofthevirus,hencethereisnoriskofcontractingpoliofromthevaccine,however,itisnotcompletelyeective.Onlyafractionofthosewhoreceivethisvaccinebecomecompletelyimmune,whereasothersenterastageofreducedsusceptibility(hencecanstillcontractthewild-strainofpoliovirus).Thisvaccinecanonlybeadministeredthroughaninjection.Thiscreatestheneedfortrainedmedicalstaffandtheuseoflargeamountsofsterileinjectionequipment(whichisbynomeansinexpensive)[11].Themainmethodbywhichdevelopingcountriesvaccinatethepopulationisbyorganizingnationalimmunizationdays(NIDs).Thesedaysareorganizedbymanygroupsinternational

1organizations(onecouldseethescheduleofnationalimmunizationdaysforeachcountrybyvisiting).Generally,theseprogramstargetaspecificagegroup(mostlychildren),andonecouldbevaccinatedmultipletimes.Thegoalofmathematicallymodelingpolioistopredictthetransmissionofpolio.Modelsincludingvaccinationdynamicsgenerallyseektofindsomeminimumvaccinationlevelsuchthattheviruswillbeeradicated.Thegoalhereistodetermineanoptimalpolioeradicationstrategyforagivencountrybysubjectingasystemofdierentialequationtothetheoryofoptimalcontrol.

2MathematicalModelsofPoliomyelitisOneofthemorerecentdeterministicmodelsofpoliotransmissionandvaccinationprovidesasystemofdierentialequationsforeachvaccineseparately[4].Variousothermodelshaveaddressedvariousaspectsofthetransmissionofpoliovirus.Forexample,Cvjetanovic,et.al.consideredanagestructuredmodel[2].Thiswouldbekeyforlookingattheeectsofanationalimmunizationdaywhereonlythosefromacertainagebracketarebeingvaccinated.

2.1TheOPVModelTheOPVmodelofEichnerandHadeler[4]considers4sub-populations:thefractionofthepopulationcurrentlysusceptible(s);thefractionofthepopulationthathasbeenvaccinated,butarestillintheinfectivestage(v);thefractionofthepopulationthathasbeeninfectedbywildpoliovirus(w);andthefractionofthepopulationthathasbecomeimmune(r).Inthismodel,theauthorsassumeaconstantpopulation,andhencethebirthrate=deathrate=µ.Themodelisasfollows:

˙s=(1−p)µ−wsw−vsv−µs(1)˙v=pµ+vsv−vv−µv(2)

˙w=wsw−ww−µw(3)

˙r=ww+vv−µr(4)

wherepistheconstantfractionofnewbirthsthatarevaccinated(theauthorsassumevaccinationatbirth),µisboththebirthanddeathrateofthepopulation,βvandwaretheinfectionratesthatsomeoneinpopulationvandw(resp.)contactsandinfectsasusceptibleindividual,andvandwaretherecoveryratesofpopulationvandw(resp.).Itisofinteresttonotethatsincewehaveaconstantpopulationwehavethefollowingrelationship:s+v+w+r=1,henceweneedonlyconsiderthe3dimensionalsystemof(s,v,w).

2FollowingtheanalysisofEichnerandHadeleronthismodel,wecanfindthebasicreproductivenumbers,RvandRw,ofthevandwpopulations(resp.).Thebasicreproductivenumberdeterminesthenumberofpeoplethatwillbeinfectedbyanaverageinfectedperson.IfRw≥1,thevirusisendemic.Inthiscasewehave

Rv=vv+µ(5)

Rw=ww+µ.(6)

Ingeneral,RwandRvaregreaterthanone,thusthediseaseisendemicandhenceitisrequiredthatweusevaccinationstoforcethesystemintoavirus-freeequilibrium(orunin-fected).Theuninfectedequilibriumcanbyfoundbysettingw=0andsolvingfor¯sand¯vbysetting˙s=0and˙v=0.Fromthiswefind

¯s=Rv+12Rv−12Rv{(Rv−1)2+4pRv}1/2(7)¯v=µ(1−¯s)µ+v.(8)However,sinceweassumethatwearenotyetonanuninfectedequilibriumtrajectory,wesolvethe(s,v,w)systemforequilibriumandfind

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高三英语(陕西专版人教版)一轮综合能力训练卷 1

高三英语(陕西专版人教版)一轮综合能力训练卷 1

综合能力训练卷(一)第一部分英语知识运用(共四节，满分55分)第一节语音知识(共5小题；每小题1分，满分5分)从每小题的A、B、C、D四个选项中，找出其划线部分与所给单词的划线部分读音相同的选项。

1．cookA.food B．root C．bamboo D．foot2．operateA.natural B．nationC．plastic D．lack3．wantedA.judged B．woundedC．worked D．stopped4．uniteA.equipmentB.oppositeC.tightly D．spirit5．smoothA．feather B.toothC．thief D．warmth第二节情景对话(共5小题；每小题1分，满分5分)根据对话情景和内容，从对话后所给的选项中选出能填入每一空白处的最佳选项。

选项中有两个为多余选项。

W: Welcome! What can I do for you?M: I’m looking for a necklace for my wife. __6__W: That is so sweet! I’ll help you to find one that she’ll love.M: Really? Thanks!W: Sure. __7__M: I think a crystal necklace would be better because it stands for purity, and my wife likes crystals very much.W: OK. __8__M: Hmmm. Let me take a look. It’s very pretty, but why is it special?W: You see, normally a crystal pendant(吊坠) is on a gold or silver chain, but this one is on a fabric string. __9__M: Yeah, I see what you mean. I think I’ll take it.__10__W: No problem. The wrapping will take a little while. Please wait a moment.A．Can you wrap it for me with purple wrapping paper?B．I think this heart-shaped one is special.C．The crystal one is much more expensive.D．So which would you like, a gold or crystal necklace?E．How would you like to pay for it?F．Tomorrow’s our wedding anniversary.G．This makes the necklace special, so it will stand out from the crowd.第三节语法和词汇知识(共15小题；每小题1分，满分15分)从每题所给的A、B、C、D四个选项中，选出可以填入空白处的最佳选项。

浙江省宁波市2022-2023学年高二上学期期末九校联考英语试题

浙江省宁波市2022-2023学年高二上学期期末九校联考英语试题

宁波市一2022学年第学期期末九校联考 高二英语试题（答案在最后） 本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）。

满分150分，考试时间120分钟。

注意事项：1．答第Ⅰ卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

2．选出每小题答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

不能答在本试卷上，否则无效。

第Ⅰ卷第一部分：听力（共两节，满分30分）第一节：（共5小题；每小题1. 5分，满分7. 5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A 、B 、C 三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What time was the woman supposed to arrive?A. At 9: 15B. At 9: 30.C. At 9: 45.2. What is Rachel going to do this Wednesday?A. Go to a wedding.B. Have a birthday party.C. Go to a graduation party.3. What is the man?A. A poet.B. A teacher.C. A reporter.4. What match is the man watching now?A. Diving.B. Swimming.C. Table tennis.5. Where does the conversation probably take place?A. At a hotel.B. In a restaurant.C. At the airport.第二节：（共15小题；每小题1. 5分，满分22. 5分）听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A 、B 、C 三个选项中选出最佳选项。

2013年高考真题解析——新课标全国卷I(英语)纯word版

2013年高考真题解析——新课标全国卷I(英语)纯word版

2013·新课标全国卷Ⅰ第二部分英语知识运用(共两节，满分45分)第一节单项填空(共15小题；每小题1分，满分15分)从A、B、C、D四个选项中，选出可以填入空白处的最佳选项。

例：We________ last night, but we went to the concert instead.A．must have studied B. might studyC. should have studiedD. would study答案是C。

21．—Why, this is nothing but common vegetable soup!—________，madam. It's our soup of the day.A. Let me seeB. So it isC. Don't mention itD. Neither do I21．B 本题考查交际用语。

let me see 让我想一想；so it is 它的确是；don't mention it 不客气；neither do I 我也不。

上下句中的soup提示，双方都在说同一个汤，显然答话人认同对方的说法，故选B。

句意：——啊，这只不过是普通的蔬菜汤！——夫人，的确是。

这是我们今天的特色汤。

22．] They might just have a place ________on the writing course—why don't you give it a try?A. leaveB. leftC. leavingD. to leave22．B 本题考查非谓语动词的用法。

此处left作定语修饰a place。

句意：他们可能还有个预留的学习写作课的机会，你为什么不试一试呢？23．Try not to cough more than you can ________ since it may cause problems to your lungs.A. checkB. allowC. stopD. help23．D 本题考查动词词义辨析。

大学英语(2-1)专升本 复习题及答案

大学英语(2-1)专升本 复习题及答案

山东科技大学继续教育学院本科大学英语1 复习题Unit1P8一．1.The group elects one of its members to be their spokesperson.2.Wage increases are being kept to a (n) minimum in many companies because of the economic depression.3.The engineering profession now has many distinct branches.4.Now that you’re13,you should have more sense of responsibility.5.Students usually pursue one or more of the subjects which they have studied at “A” level,such as Art,Drama,English,Music,etc.6.We need to make sure that we exploit our resources fully as possible.7.Congress is considering measures to restrict the sale of cigarettes.8.College courses should be designed to equip students with knowledge and skills to help them survive modern society.9.The local government granted $1.1million so that the old teacher could be taken down and rebuilt.10.For his achievement in the medical field, the Mayor awarded him a medal of merit. 三．1大家都赞成建造一所新校舍的计划Everybody approves of the plans for a new school building2.演员需要学会对贬斥性评论一笑置之。