考虑疫苗和药物影响下的多样化全球艾滋病传播模型

发布时间：2018-02-21 02:29

本文关键词： 动力学模型时间序列流行性疫苗　出处：《山东大学》2009年硕士论文　论文类型：学位论文

【摘要】： 艾滋病全名为获得性免疫缺陷综合征(Acquired Immune DeficiencySyndrome),缩写为AIDS,它蔓延迅速,死亡率高,至今为止人类对艾滋病仍然束手无策,而且艾滋病在全球的传播趋势越来越猛烈。根据联合国艾滋病防止署2008年的报告,共有新增300万人感染艾滋病毒。从2001年到2007年,世界范围内HIV病毒携带者继续增长。已从3000万增长到3300万。2007年,有2百万人死于艾滋病;从1981年发现第一例艾滋病患者至今,约有总计2900万人死于艾滋病,这远远高于20世纪所有死于战争的人口数。流行性传染病传播的研究,特别是艾滋病的研究,一直是专家学者重点关注的对象。对于HIV传播的研究,最初只是局限于采用一些简单的观察数据和统计数据做出分析和推断。这不能有效的反映其传播本质。事实上,数学模型,可作为预测和制定政策的工具。许多学者提出了一些有价值的研究。Hethcote[1,2]提出了一类存封闭的人口系统中或是在流入流出平衡的系统中简化的传染性疾病模型。Gonzalez-Guzman通过分析未考虑具体细菌平衡的从易感人群到环境的细菌流动的直接传播和间接传播作用,研究了一类伤寒病传播的SIS模型。Blower S.[3,4]通过一系列数学模型讨论了疫苗在治疗传染病中的作用,在这一领域做出了巨大贡献。法国学者B.Cazelles[5]和N.P.Chau[5]曾利用Kalman Filter模型来获得HIV传播的改变,但他们最后采用了复杂的泛函分析方法。Wang La-di[6]和Li Jian-quan[6]共同讨论了一类非线性发病率模型。Apiradee Lim[10]采用了统计方法来预测人口统计学时间序列,并把它应用到对泰国南部HIV/AIDS和其他传染病死亡率的估计上。现在有许多方法来研究传染病的传播,如传统的SIR模型,指数模型,微分方程,动力系统,时间序列等模型。然而,一些国内学者只是将HIV/AIDS传播当作其他常见传染病那样研究而忽视了艾滋病的一些具体特点。而另外一些学者忽略了诸如ARV药物治疗和预防疫苗的干预作用。与此同时,一些国际学者提出了一些有趣的想法,但其中大多数是侧重于定性分析模型理论,我们很少能看到一些模型通过一些实例,特别是某些具体国家的实例来给我们清晰直观,鲜明有力的解释。为了进行更为量化的和科学系统的分析,在这篇论文里,我们建立了一系列的时间序列模型,最优化模型,灰色模型,动力系统模型来共同预测某些国家2008年至2050年感染艾滋病病毒的人口数目,并在不同的情况下对比四类模型。在灰色模型中,我们首先对其,特别是GM(1,1)模型做了简要介绍,然后用它估计了海地感染艾滋病的人口数目。在最优化模型中,我们发现应该将有限的资金优先用在注射疫苗上,余下的钱再来做药物治疗。我们更加重点的讨论了时间序列模型和动力系统模型。在时间序列模型中,我们运用足够多的数据以及ARIMA(p,d,q)模型来模拟俄罗斯,中国以及其他国家的艾滋病传播趋势。我们得到结论在艾滋病药物的积极作用下,诸如俄罗斯,德国,法国等一些发达国家的每年新增艾滋病人数正在逐年减少。而政府如果不采取一些积极的措施的话,中国等一些发展中国家将在未来几年面临艾滋病的爆发。在动力系统模型中,我们考虑了以下四种情况:(1)没有任何附加措施;(2)提供ARV药物治疗;(3)潜在的预防艾滋病病毒的疫苗;(4)同时使用药物和疫苗;最后,我们的结论是疫苗在减少艾滋病传播以及最终消灭艾滋病方面发挥了巨大贡献。与ARV药物治疗相比,有诸多明显的优势。因此,我们应积极致力于提高疫苗的研发经费并促进疫苗的早日问世。另一方面,我们不应忽视药物治疗的重要性,药物的治疗在新疫苗尚未出现之前仍是必不可少的方法,并且对于已患病的人来说,这是他们唯一的希望。所以,我们应先把有限的资金投入到药物治疗,在2008年至2010年继续保持这种疾病的传播处于低水平,然后我们艾滋病病毒的预防疫苗上大力投入。
[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 .

【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：R181.3

【共引文献】