几类受媒体影响的流行病模型的研究

发布时间：2017-12-27 18:13

本文关键词：几类受媒体影响的流行病模型的研究　出处：《华中师范大学》2016年博士论文　论文类型：学位论文

【摘要】：伴随着全球化趋势,人类在地球上居住方式的变化致使与新出现和重新出现的传染病相关联的疫情正以历史上前所未有的数量发生,如HIV/AIDS、SARS、 H1N1、H7N9、EVD、MERS,寨卡病毒等。对某些疾病其疫苗成本高昂且提供的免疫保护短暂,而对某些疾病我们甚至还没有疫苗或有效的药物。毋庸置疑,以上事实对人类的生存发展、经济和社会稳定构成了巨大威胁。但是近些年的研究表明,新媒体时代的到来给我们提供了一个有效的疾病预防控制措施。在疾病暴发期间,公共卫生部门和机构广泛使用大众媒体,让公众及时获知与疫情相关的信息,促使人们改变行为方式,疾病暴发的严重程度会得以显著削弱。本文的主题是探究如何在传染病模型中反映媒体影响的内在特征,并探究这些模型的动力学行为,从而加深我们对疾病预防与控制的了解。本文由六章组成。在第一章中,我们介绍了媒体报道对传染病动力学模型的影响的研究背景与研究现状,并给出一些预备知识。第二章讨论了最优的流感控制措施和几种措施最有效的联合方案。我们构建了一类具有媒体报道、不完全接种和抗病毒治疗的SVEIAR模型,获得其阈值动力学性质。通过对控制再生数和地方病平衡点进行灵敏性分析,我们评估了流感控制措施的有效性,并提出一个含有以上三种措施的最优控制问题以设计最优控制方案。最后,通过成本效益分析得出,在所考虑的各方案中联合以上三种措施是最有成本效益的方案。数值模拟显示,媒体报道在抑制流感传播中起到了主导作用。第三章给出了一类具有媒体影响和潜伏与复发两个时滞的SEIR传染病模型。该模型中,我们将人群中的接触率模拟为依赖于感染病例数的单调递减的饱和函数。通过构造合适的Lyapunov泛函,我们研究了模型的持久性和全局稳定性。数值结果表明,媒体报道与个体在疫情中的及时反应对疾病控制起到了关键作用。在第四章中,我们建立了一类含有媒体影响、不完全接种和一般潜伏期分布的SVEIR传染病模型。我们的主要结果揭示,接种再生数完全决定了疾病绝灭与否。我们也讨论了两类停留在潜伏期的特殊形式的概率分布,当概率为负指数分布时,我们给出了一个有效证明对应的常微分SVEIR模型地方病平衡点全局稳定性的方法,该方法改进了已有的方法；当概率为分段函数时,我们利用所导出的时滞微分系统较好地拟合了中国2012-2015年流行性腮腺炎的数据。本章也详细讨论了接种的影响。在第五章中,我们考虑了一类具有媒体预警和logistic增长的SIS传染病模型。一般而言,媒体预警只有感染病例数达到某一临界值才会发出。在该模型中,我们用一个非光滑连续的传染率函数来反映媒体影响及其阈值策略。对该模型的分析显示,及早的媒体预警和较强的媒体报道对于减少在地方病平衡点处的感染病例是更为可取的。更重要的是,我们发现存在一个预警临界值的阈值区间,在该区间内模型有三个地方病平衡点,而且双稳态可能会发生。否则,模型只有唯一全局渐近稳定的地方病平衡点。最后,我们在第六章中概括了全文,并对受媒体影响的传染病动力学模型作了研究展望。
[Abstract]:With the trend of globalization, the changes in the way of human living on the earth have led to the unprecedented number of outbreaks associated with new and emerging infectious diseases, such as HIV/AIDS, SARS, H1N1, H7N9, EVD, MERS, and Chaga virus. The high cost of vaccines for certain diseases and the provision of immune protection are short, and we have no even vaccines or effective drugs for certain diseases. There is no doubt that the above facts pose a great threat to the survival, development, economic and social stability of human beings. But recent studies have shown that the arrival of the new media era has provided us with an effective prevention and control measure of disease. During the outbreak of disease, mass media is widely used in public health departments and institutions, so that the public can get information related to epidemic in time, prompting people to change their behavior patterns, and the severity of disease outbreaks will be significantly weakened. The theme of this paper is to explore how to reflect the intrinsic characteristics of media influence in infectious disease models, and explore the dynamic behaviors of these models, so as to deepen our understanding of disease prevention and control. This article is composed of six chapters. In the first chapter, we introduce the research background and research status of the impact of media coverage on the dynamic model of infectious diseases, and give some preparatory knowledge. The second chapter discusses the optimal influenza control measures and the most effective joint schemes for several measures. We have constructed a SVEIAR model with media coverage, incomplete inoculation and antiviral therapy to obtain its threshold dynamic properties. Through sensitivity analysis of control regeneration number and endemic equilibrium, we evaluated the effectiveness of influenza control measures, and proposed an optimal control problem with three measures to design the optimal control scheme. Finally, through the cost-benefit analysis, the combination of the above three measures is the most cost-effective scheme in the various schemes considered. Numerical simulations show that media coverage plays a leading role in inhibiting the spread of influenza. In the third chapter, a class of SEIR infectious disease models with media influence and two delay of latency and recurrence are given. In this model, the contact rate in the population is simulated as a monotonous decreasing saturation function dependent on the number of infected cases. By constructing a suitable Lyapunov functional, we have studied the persistence and global stability of the model. The numerical results show that media reporting and the timely response of individuals to the epidemic have played a key role in disease control. In the fourth chapter, we have established a SVEIR epidemic model with media impact, incomplete inoculation and the distribution of the general latent period. Our main results reveal that the number of inoculation determines whether the disease is extinct or not. We also discuss the probability distribution of stay in the special form of latency of the two class, when the probability of negative exponential distribution, we give a method to prove effective corresponding differential SVEIR model the global stability of the endemic equilibrium, the method improves the existing method; when the probability is a piecewise function, we use the delay differential systems fit well Chinese 2012-2015 mumps data. The impact of inoculation is also discussed in detail in this chapter. In the fifth chapter, we consider a class of SIS infectious disease models with media early warning and logistic growth. In general, media early-warning is only issued when the number of infected cases reaches a certain threshold. In this model, we use a nonsmooth continuous contagion rate function to reflect the media impact and the threshold strategy. The analysis of the model shows that early media early-warning and strong media coverage are more desirable to reduce the incidence of infection at the endemic equilibrium. More importantly, we found that there is a threshold interval for the early warning threshold. There are three endemic equilibrium points in the model, and the bistable state may occur. Otherwise, the model has only the only global asymptotically stable endemic equilibrium point. Finally, we summarize the full text in the sixth chapter and make a research prospect on the dynamic model of communicable diseases affected by the media.
【学位授予单位】：华中师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O175

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