本文關(guān)鍵詞： 動(dòng)力學(xué) 模型 時(shí)間序列 流行性 疫苗　出處：《山東大學(xué)》2009年碩士論文　論文類型：學(xué)位論文

【摘要】： 艾滋病全名為獲得性免疫缺陷綜合征(Acquired Immune DeficiencySyndrome),縮寫為AIDS,它蔓延迅速,死亡率高,至今為止人類對(duì)艾滋病仍然束手無策,而且艾滋病在全球的傳播趨勢越來越猛烈。根據(jù)聯(lián)合國艾滋病防止署2008年的報(bào)告,共有新增300萬人感染艾滋病毒。從2001年到2007年,世界范圍內(nèi)HIV病毒攜帶者繼續(xù)增長。已從3000萬增長到3300萬。2007年,有2百萬人死于艾滋病;從1981年發(fā)現(xiàn)第一例艾滋病患者至今,約有總計(jì)2900萬人死于艾滋病,這遠(yuǎn)遠(yuǎn)高于20世紀(jì)所有死于戰(zhàn)爭的人口數(shù)。 流行性傳染病傳播的研究,特別是艾滋病的研究,一直是專家學(xué)者重點(diǎn)關(guān)注的對(duì)象。對(duì)于HIV傳播的研究,最初只是局限于采用一些簡單的觀察數(shù)據(jù)和統(tǒng)計(jì)數(shù)據(jù)做出分析和推斷。這不能有效的反映其傳播本質(zhì)。 事實(shí)上,數(shù)學(xué)模型,可作為預(yù)測和制定政策的工具。許多學(xué)者提出了一些有價(jià)值的研究。Hethcote[1,2]提出了一類存封閉的人口系統(tǒng)中或是在流入流出平衡的系統(tǒng)中簡化的傳染性疾病模型。Gonzalez-Guzman通過分析未考慮具體細(xì)菌平衡的從易感人群到環(huán)境的細(xì)菌流動(dòng)的直接傳播和間接傳播作用,研究了一類傷寒病傳播的SIS模型。Blower S.[3,4]通過一系列數(shù)學(xué)模型討論了疫苗在治療傳染病中的作用,在這一領(lǐng)域做出了巨大貢獻(xiàn)。法國學(xué)者B.Cazelles[5]和N.P.Chau[5]曾利用Kalman Filter模型來獲得HIV傳播的改變,但他們最后采用了復(fù)雜的泛函分析方法。Wang La-di[6]和Li Jian-quan[6]共同討論了一類非線性發(fā)病率模型。Apiradee Lim[10]采用了統(tǒng)計(jì)方法來預(yù)測人口統(tǒng)計(jì)學(xué)時(shí)間序列,并把它應(yīng)用到對(duì)泰國南部HIV/AIDS和其他傳染病死亡率的估計(jì)上。現(xiàn)在有許多方法來研究傳染病的傳播,如傳統(tǒng)的SIR模型,指數(shù)模型,微分方程,動(dòng)力系統(tǒng),時(shí)間序列等模型。 然而,一些國內(nèi)學(xué)者只是將HIV/AIDS傳播當(dāng)作其他常見傳染病那樣研究而忽視了艾滋病的一些具體特點(diǎn)。而另外一些學(xué)者忽略了諸如ARV藥物治療和預(yù)防疫苗的干預(yù)作用。與此同時(shí),一些國際學(xué)者提出了一些有趣的想法,但其中大多數(shù)是側(cè)重于定性分析模型理論,我們很少能看到一些模型通過一些實(shí)例,特別是某些具體國家的實(shí)例來給我們清晰直觀,鮮明有力的解釋。 為了進(jìn)行更為量化的和科學(xué)系統(tǒng)的分析,在這篇論文里,我們建立了一系列的時(shí)間序列模型,最優(yōu)化模型,灰色模型,動(dòng)力系統(tǒng)模型來共同預(yù)測某些國家2008年至2050年感染艾滋病病毒的人口數(shù)目,并在不同的情況下對(duì)比四類模型。 在灰色模型中,我們首先對(duì)其,特別是GM(1,1)模型做了簡要介紹,然后用它估計(jì)了海地感染艾滋病的人口數(shù)目。在最優(yōu)化模型中,我們發(fā)現(xiàn)應(yīng)該將有限的資金優(yōu)先用在注射疫苗上,余下的錢再來做藥物治療。 我們更加重點(diǎn)的討論了時(shí)間序列模型和動(dòng)力系統(tǒng)模型。在時(shí)間序列模型中,我們運(yùn)用足夠多的數(shù)據(jù)以及ARIMA(p,d,q)模型來模擬俄羅斯,中國以及其他國家的艾滋病傳播趨勢。我們得到結(jié)論在艾滋病藥物的積極作用下,諸如俄羅斯,德國,法國等一些發(fā)達(dá)國家的每年新增艾滋病人數(shù)正在逐年減少。而政府如果不采取一些積極的措施的話,中國等一些發(fā)展中國家將在未來幾年面臨艾滋病的爆發(fā)。 在動(dòng)力系統(tǒng)模型中,我們考慮了以下四種情況:(1)沒有任何附加措施;(2)提供ARV藥物治療;(3)潛在的預(yù)防艾滋病病毒的疫苗;(4)同時(shí)使用藥物和疫苗;最后,我們的結(jié)論是疫苗在減少艾滋病傳播以及最終消滅艾滋病方面發(fā)揮了巨大貢獻(xiàn)。與ARV藥物治療相比,有諸多明顯的優(yōu)勢。因此,我們應(yīng)積極致力于提高疫苗的研發(fā)經(jīng)費(fèi)并促進(jìn)疫苗的早日問世。另一方面,我們不應(yīng)忽視藥物治療的重要性,藥物的治療在新疫苗尚未出現(xiàn)之前仍是必不可少的方法,并且對(duì)于已患病的人來說,這是他們唯一的希望。所以,我們應(yīng)先把有限的資金投入到藥物治療,在2008年至2010年繼續(xù)保持這種疾病的傳播處于低水平,然后我們艾滋病病毒的預(yù)防疫苗上大力投入。
[Abstract]:The AIDS pandemic is known as Acquired Immune Deficiency Syndrome ( AIDS ) , which has spread rapidly and has a high mortality rate . Since 2001 , there are more than 3 million people living with HIV . From 2001 to 2007 , there were a total of 3 million people living with HIV . From 2001 to 2007 , there were more than 3 million people who died of AIDS . From 2001 to 2007 , about 29 million people died of AIDS , much higher than all those killed in war in the 20th century . Research on the spread of epidemic infectious diseases , especially AIDS research , has been the focus of experts and scholars . For the research of HIV transmission , it is only limited to the analysis and extrapolation of some simple observation data and statistical data , which cannot effectively reflect its transmission nature . In fact , the mathematical model can be used as a tool for forecasting and developing policies . Many scholars have proposed some valuable research . However , some domestic scholars simply ignore some of the specific features of AIDS by studying the spread of HIV / AIDS as other common infectious diseases , while others neglect the intervention of AIDS . At the same time , some international scholars have put forward some interesting ideas , but most of them focus on qualitative analysis model theory , and we rarely see some models that give us a clear and powerful interpretation through some examples , especially in some specific countries . In order to carry out more quantitative and scientific analysis , we have set up a series of time series models , optimization models , grey models and power system models to jointly predict the number of people infected with HIV in some countries from 2008 to 2050 and to compare four types of models in different situations . In the grey model , we first introduced the model , especially the GM ( 1,1 ) model , and then used it to estimate the number of people infected with AIDS in Haiti . In the optimization model , we found that a limited amount of money should be used as a priority on the vaccine , and the rest of the money should be used for drug therapy . We have focused more on the time series model and the power system model . In the time series model , we use enough data and a model to simulate the spread of AIDS in Russia , China and other countries . We have concluded that , under the active role of AIDS drugs , the annual increase in AIDS among some developed countries , such as Russia , Germany and France , is declining year by year , and some developing countries , such as Russia , Germany and France , will face the outbreak of AIDS in the next few years . In the power system model , we consider the following four situations : ( 1 ) there is no additional measure ; ( 2 ) there is no additional measure ; ( 3 ) potential HIV vaccine ; ( 4 ) concurrent use of drugs and vaccines ; and , on the other hand , we should not lose sight of the importance of drug therapy . Therefore , we should not lose sight of the importance of drug therapy . Therefore , we should not lose sight of the importance of drug therapy . Therefore , we should first put limited funds into drug therapy , continue to maintain the spread of this disease at a low level between 2008 and 2010 , and then invest heavily in the vaccine against AIDS .

【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2009
【分類號(hào)】：R181.3

【共引文獻(xiàn)】

相關(guān)期刊論文 前3條

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2 徐翠翠;赫孝良;;一類具有潛伏期和隔離項(xiàng)的SEIQR流行病模型[J];商丘師范學(xué)院學(xué)報(bào);2010年06期

3 李建全;婁潔;婁梅枝;;Some discrete SI and SIS epidemic models[J];Applied Mathematics and Mechanics(English Edition);2008年01期

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本文編號(hào)：1520738