本文關鍵詞：幾類受媒體影響的流行病模型的研究　出處：《華中師范大學》2016年博士論文　論文類型：學位論文

  更多相關文章： 媒體報道與預警 不完全接種 Lyapunov泛函 全局穩(wěn)定性 無限分布時滯 卡方檢驗 擬合優(yōu)度

【摘要】：伴隨著全球化趨勢,人類在地球上居住方式的變化致使與新出現和重新出現的傳染病相關聯的疫情正以歷史上前所未有的數量發(fā)生,如HIV/AIDS、SARS、 H1N1、H7N9、EVD、MERS,寨卡病毒等。對某些疾病其疫苗成本高昂且提供的免疫保護短暫,而對某些疾病我們甚至還沒有疫苗或有效的藥物。毋庸置疑,以上事實對人類的生存發(fā)展、經濟和社會穩(wěn)定構成了巨大威脅。但是近些年的研究表明,新媒體時代的到來給我們提供了一個有效的疾病預防控制措施。在疾病暴發(fā)期間,公共衛(wèi)生部門和機構廣泛使用大眾媒體,讓公眾及時獲知與疫情相關的信息,促使人們改變行為方式,疾病暴發(fā)的嚴重程度會得以顯著削弱。本文的主題是探究如何在傳染病模型中反映媒體影響的內在特征,并探究這些模型的動力學行為,從而加深我們對疾病預防與控制的了解。本文由六章組成。在第一章中,我們介紹了媒體報道對傳染病動力學模型的影響的研究背景與研究現狀,并給出一些預備知識。第二章討論了最優(yōu)的流感控制措施和幾種措施最有效的聯合方案。我們構建了一類具有媒體報道、不完全接種和抗病毒治療的SVEIAR模型,獲得其閾值動力學性質。通過對控制再生數和地方病平衡點進行靈敏性分析,我們評估了流感控制措施的有效性,并提出一個含有以上三種措施的最優(yōu)控制問題以設計最優(yōu)控制方案。最后,通過成本效益分析得出,在所考慮的各方案中聯合以上三種措施是最有成本效益的方案。數值模擬顯示,媒體報道在抑制流感傳播中起到了主導作用。第三章給出了一類具有媒體影響和潛伏與復發(fā)兩個時滯的SEIR傳染病模型。該模型中,我們將人群中的接觸率模擬為依賴于感染病例數的單調遞減的飽和函數。通過構造合適的Lyapunov泛函,我們研究了模型的持久性和全局穩(wěn)定性。數值結果表明,媒體報道與個體在疫情中的及時反應對疾病控制起到了關鍵作用。在第四章中,我們建立了一類含有媒體影響、不完全接種和一般潛伏期分布的SVEIR傳染病模型。我們的主要結果揭示,接種再生數完全決定了疾病絕滅與否。我們也討論了兩類停留在潛伏期的特殊形式的概率分布,當概率為負指數分布時,我們給出了一個有效證明對應的常微分SVEIR模型地方病平衡點全局穩(wěn)定性的方法,該方法改進了已有的方法；當概率為分段函數時,我們利用所導出的時滯微分系統(tǒng)較好地擬合了中國2012-2015年流行性腮腺炎的數據。本章也詳細討論了接種的影響。在第五章中,我們考慮了一類具有媒體預警和logistic增長的SIS傳染病模型。一般而言,媒體預警只有感染病例數達到某一臨界值才會發(fā)出。在該模型中,我們用一個非光滑連續(xù)的傳染率函數來反映媒體影響及其閾值策略。對該模型的分析顯示,及早的媒體預警和較強的媒體報道對于減少在地方病平衡點處的感染病例是更為可取的。更重要的是,我們發(fā)現存在一個預警臨界值的閾值區(qū)間,在該區(qū)間內模型有三個地方病平衡點,而且雙穩(wěn)態(tài)可能會發(fā)生。否則,模型只有唯一全局漸近穩(wěn)定的地方病平衡點。最后,我們在第六章中概括了全文,并對受媒體影響的傳染病動力學模型作了研究展望。
[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.
【學位授予單位】：華中師范大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O175

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