公共卫生教育影响下传染病模型的动力学分析

发布时间：2018-12-20 07:53

【摘要】：近些年来,传染病尤其是突发传染病层出不穷,如何遏制传染病的暴发,缓解传染病的流行,是当今世界所面临的迫在眉睫的重大问题.由于突发传染病猝不及防的发生,对此公众缺乏必要的心理准备,往往被惊慌,疑虑所笼罩,因此在处理这类突发事件时,可以针对广大群众开展公共卫生教育活动,直接面向公众传播疾病相关知识和防护措施,其在传染病控制过程中起着引导社会舆论方向,传播正确知识信息,抚慰公众情绪的重要作用.公共卫生教育的方式包括大众传播和人际传播.到目前为止,考虑大众传播对传染病预防与控制影响的研究已有不少成果,但公共卫生教育中的人际传播方式对传染病防控的影响程度在一定程度上仍是一个未知数,迄今还没有明确的结论来刻画说明人际传播对传染病预防与控制的影响.本文在经典仓室模型的研究基础上,基于公共卫生教育两种方式的影响,将易感者S进一步分为不了解传染病的易感者S1和了解传染病的易感者S2,并结合实际假设S1的疾病感染率大于S2的感染率,建立并分析了几类不同类型的传染病模型.首先,针对某些具有终生免疫的传染病分析了公共卫生教育对其产生的影响,通过分析得到决定疾病暴发与否的两个阈值条件R1,R2,同时系统至多存在一个正平衡点,且只要存在则一定局部渐近稳定.进一步排除了周期解的存在性,从而得出当系统存在惟一局部稳定的平衡点时,它一定是全局渐近稳定的.另外,讨论了增加公共卫生教育投入量对系统正平衡点存在性的影响,结果显示增加公共卫生教育投入量会导致正平衡点的存在区域缩小,且人际传播比大众传播对系统正平衡点的存在区域的影响更大.其次,研究了具有暂时性免疫的传染病模型在公共卫生教育影响下的传播动力学,系统的正平衡点有且仅有一个,且一旦存在就是全局渐近稳定的.通过分析发现,当R21R1时,随着公共卫生教育参数值的增大,系统的正平衡点会退化成无病平衡点,此时意味着疾病不会在人群中暴发;当1R2R1时,虽然正平衡点E*一直存在,但是染病者I的数量会随着公共卫生教育活动的增加而减少,这同样意味着公共卫生教育会减缓疾病的流行状态.最后,建立了两个斑块间考虑单方向迁移的斑块模型,利用微分方程定性及稳定性理论分析模型可得,系统至多存在一个正平衡点.并利用Hurwitz判据判断平衡点的局部性态,发现系统正平衡点只要存在则一定局部渐近稳定.若要想疾病得到有效控制,就需要结合实际情况采取相应的防范措施使得系统正平衡点存在的条件不成立.这也为现实生活中控制疾病的蔓延提供了理论依据.
[Abstract]:In recent years, infectious diseases, especially sudden infectious diseases, emerge in endlessly. How to curb the outbreak of infectious diseases and ease the epidemic of infectious diseases is an urgent and important problem facing the world today. Because of the sudden outbreak of infectious diseases and the lack of necessary psychological preparation for this, the public is often shrouded in panic and doubt. Therefore, when dealing with such emergencies, public health education activities can be carried out for the general public. Direct transmission of disease-related knowledge and protective measures to the public plays an important role in guiding the direction of public opinion, disseminating correct knowledge and information, and soothing the public mood in the process of infectious disease control. Public health education includes mass communication and interpersonal communication. Up to now, many achievements have been made in considering the influence of mass communication on the prevention and control of infectious diseases, but the influence of interpersonal transmission in public health education on the prevention and control of infectious diseases remains unknown to some extent. There are no clear conclusions on the impact of interpersonal transmission on the prevention and control of infectious diseases. Based on the study of classical storeroom model and the influence of public health education, the susceptible person S is further divided into susceptible persons who do not understand infectious diseases S1 and susceptible persons who understand infectious diseases. Combined with the actual assumption that the disease infection rate of S1 is greater than that of S2, several kinds of infectious disease models are established and analyzed. First of all, the impact of public health education on certain infectious diseases with lifetime immunity is analyzed. Two threshold conditions, R1 and R2, which determine the outbreak or not of the disease, are obtained, and there is at most one positive equilibrium point in the system. And if it exists, it will be locally asymptotically stable. Furthermore, the existence of periodic solution is excluded, and it is obtained that the system must be globally asymptotically stable when there is a unique locally stable equilibrium point. In addition, the influence of increasing the input of public health education on the existence of the positive equilibrium point of the system is discussed. The results show that increasing the input of public health education will lead to the reduction of the existence area of the positive equilibrium point. And interpersonal communication has a greater impact on the existence of positive equilibrium than mass communication. Secondly, the transmission dynamics of infectious disease model with temporary immunity under the influence of public health education is studied. The positive equilibrium of the system has only one and is globally asymptotically stable if it exists. It is found that the positive equilibrium point of the system will degenerate into disease-free equilibrium point with the increase of public health education parameters when R21R1, which means that the disease will not break out in the population. When 1R2R1, although the positive balance point E * has always existed, the number of infected people I will decrease with the increase of public health education activities, which also means that public health education will slow down the prevalence of the disease. Finally, a patch model considering unidirectional migration between two patches is established. The model can be obtained by qualitative analysis of differential equations and stability theory. At most, there exists a positive equilibrium point in the system. The Hurwitz criterion is used to judge the local behavior of the equilibrium point, and it is found that the positive equilibrium point of the system is locally asymptotically stable if it exists. If the disease is to be effectively controlled, it is necessary to take corresponding preventive measures according to the actual situation so that the condition of the existence of the positive equilibrium point of the system is not valid. This also provides a theoretical basis for controlling the spread of disease in real life.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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