公共衛(wèi)生教育影響下傳染病模型的動力學(xué)分析
發(fā)布時間：2018-12-20 07:53
【摘要】：近些年來,傳染病尤其是突發(fā)傳染病層出不窮,如何遏制傳染病的暴發(fā),緩解傳染病的流行,是當今世界所面臨的迫在眉睫的重大問題.由于突發(fā)傳染病猝不及防的發(fā)生,對此公眾缺乏必要的心理準備,往往被驚慌,疑慮所籠罩,因此在處理這類突發(fā)事件時,可以針對廣大群眾開展公共衛(wèi)生教育活動,直接面向公眾傳播疾病相關(guān)知識和防護措施,其在傳染病控制過程中起著引導(dǎo)社會輿論方向,傳播正確知識信息,撫慰公眾情緒的重要作用.公共衛(wèi)生教育的方式包括大眾傳播和人際傳播.到目前為止,考慮大眾傳播對傳染病預(yù)防與控制影響的研究已有不少成果,但公共衛(wèi)生教育中的人際傳播方式對傳染病防控的影響程度在一定程度上仍是一個未知數(shù),迄今還沒有明確的結(jié)論來刻畫說明人際傳播對傳染病預(yù)防與控制的影響.本文在經(jīng)典倉室模型的研究基礎(chǔ)上,基于公共衛(wèi)生教育兩種方式的影響,將易感者S進一步分為不了解傳染病的易感者S1和了解傳染病的易感者S2,并結(jié)合實際假設(shè)S1的疾病感染率大于S2的感染率,建立并分析了幾類不同類型的傳染病模型.首先,針對某些具有終生免疫的傳染病分析了公共衛(wèi)生教育對其產(chǎn)生的影響,通過分析得到?jīng)Q定疾病暴發(fā)與否的兩個閾值條件R1,R2,同時系統(tǒng)至多存在一個正平衡點,且只要存在則一定局部漸近穩(wěn)定.進一步排除了周期解的存在性,從而得出當系統(tǒng)存在惟一局部穩(wěn)定的平衡點時,它一定是全局漸近穩(wěn)定的.另外,討論了增加公共衛(wèi)生教育投入量對系統(tǒng)正平衡點存在性的影響,結(jié)果顯示增加公共衛(wèi)生教育投入量會導(dǎo)致正平衡點的存在區(qū)域縮小,且人際傳播比大眾傳播對系統(tǒng)正平衡點的存在區(qū)域的影響更大.其次,研究了具有暫時性免疫的傳染病模型在公共衛(wèi)生教育影響下的傳播動力學(xué),系統(tǒng)的正平衡點有且僅有一個,且一旦存在就是全局漸近穩(wěn)定的.通過分析發(fā)現(xiàn),當R21R1時,隨著公共衛(wèi)生教育參數(shù)值的增大,系統(tǒng)的正平衡點會退化成無病平衡點,此時意味著疾病不會在人群中暴發(fā);當1R2R1時,雖然正平衡點E*一直存在,但是染病者I的數(shù)量會隨著公共衛(wèi)生教育活動的增加而減少,這同樣意味著公共衛(wèi)生教育會減緩疾病的流行狀態(tài).最后,建立了兩個斑塊間考慮單方向遷移的斑塊模型,利用微分方程定性及穩(wěn)定性理論分析模型可得,系統(tǒng)至多存在一個正平衡點.并利用Hurwitz判據(jù)判斷平衡點的局部性態(tài),發(fā)現(xiàn)系統(tǒng)正平衡點只要存在則一定局部漸近穩(wěn)定.若要想疾病得到有效控制,就需要結(jié)合實際情況采取相應(yīng)的防范措施使得系統(tǒng)正平衡點存在的條件不成立.這也為現(xiàn)實生活中控制疾病的蔓延提供了理論依據(jù).
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175
本文編號：2387679
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175
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