【摘要】：媒體報(bào)道是指媒體通過(guò)一系列可靠渠道獲得有關(guān)信息,然后通過(guò)網(wǎng)絡(luò)、電視、報(bào)刊等形式將信息告知公眾的一種信息傳遞方式。因此當(dāng)疾病在社會(huì)生活中出現(xiàn)時(shí),媒體會(huì)在第一時(shí)間將更可能多的信息告知公眾。這使得公眾對(duì)疾病有一定的了解,并促使其做出相應(yīng)的行為反應(yīng)以減少自身及家人被疾病感染的幾率,這在一定程度上減小了疾病的傳染率。在這樣的認(rèn)識(shí)基礎(chǔ)上本文建立了一類(lèi)有關(guān)媒體報(bào)道的媒介傳染病模型,其中為刻畫(huà)媒體報(bào)道的具體影響形式,文章用一個(gè)單調(diào)遞減的函數(shù)h(x)來(lái)描述媒體報(bào)道在疾病傳播過(guò)程中的影響。這里的函數(shù)h(x)稱(chēng)為媒體函數(shù),其單調(diào)遞減特性的依據(jù)是:當(dāng)疾病爆發(fā)時(shí),媒體會(huì)將疾病的爆發(fā)程度以及預(yù)防措施告知公眾,而公眾在獲得相關(guān)信息后會(huì)做出相應(yīng)的個(gè)體行為以減少感染幾率,這使得傳染率在一定基礎(chǔ)上呈減少趨勢(shì)。而在文章的理論分析部分,主要討論了平衡點(diǎn)存在唯一性及其穩(wěn)定性。在討論地方病平衡點(diǎn)的局部穩(wěn)定性中計(jì)算得到Hop f分支產(chǎn)生的條件,通過(guò)構(gòu)造Lyapunov函數(shù)證明了無(wú)病平衡點(diǎn)的全局穩(wěn)定性。由于在模型中我們引入了一類(lèi)一般函數(shù),所以在應(yīng)用Lyapunov函數(shù)證明地方病平衡點(diǎn)的全局穩(wěn)定性時(shí)需要添加一個(gè)條件。最后我們對(duì)一般的媒體函數(shù)取具體形式,一方面對(duì)文章的理論證明部分進(jìn)行具體實(shí)例的應(yīng)用,另一方面選取一類(lèi)分段光滑函數(shù)考察與媒體報(bào)道直接相關(guān)的參數(shù)。前者我們找到了系統(tǒng)產(chǎn)生Hopf分支的條件,并進(jìn)行仿真得到震蕩圖。后者我們通過(guò)運(yùn)用朗伯W函數(shù)將系統(tǒng)轉(zhuǎn)換成一個(gè)開(kāi)關(guān)系統(tǒng),并得到開(kāi)關(guān)曲面及證明了其兩個(gè)子系統(tǒng)平衡存在的問(wèn)題。
[Abstract]:Media report refers to a kind of information transmission method in which the media obtain the relevant information through a series of reliable channels, and then communicate the information to the public through the form of network, television, newspaper and so on. As a result, when disease occurs in social life, the media will be more likely to inform the public in the first place. This enables the public to have a certain understanding of the disease and urge them to make corresponding behavioral responses to reduce the risk of infection of their own and family members, which to a certain extent reduce the infection rate of the disease. On the basis of this understanding, this paper sets up a kind of media infectious disease model about the media report, which describes the concrete influence form of the media report. In this paper, a monotone decreasing function h (x) is used to describe the influence of media coverage on the spread of disease. The function h (x) here is called the media function, and its monotone decline is based on the fact that when an outbreak occurs, the media will inform the public about the extent of the outbreak and the precautions taken to prevent it. After obtaining the relevant information, the public will make the corresponding individual behavior to reduce the probability of infection, which makes the infection rate show a decreasing trend on a certain basis. In the part of theoretical analysis, the existence and uniqueness of equilibrium point and its stability are discussed. In the discussion of local stability of endemic equilibrium point, the condition of generating Hop f bifurcation is obtained, and the global stability of disease free equilibrium point is proved by constructing Lyapunov function. Because we introduce a class of general functions in the model, we need to add a condition when applying the Lyapunov function to prove the global stability of the endemic equilibrium point. Finally, we take the concrete form of the general media function. On the one hand, we apply the theoretical proof part of the paper to a concrete example, on the other hand, we select a class of piecewise smooth functions to investigate the parameters directly related to the media report. In the former, we find the conditions under which the system produces Hopf bifurcation, and simulate it to get the oscillation diagram. In the latter, we transform the system into a switching system by using Lambert W function, and obtain the switching surface and prove the problem of the balance between the two subsystems.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 謝英超;程燕;賀天宇;;一類(lèi)具有非線性發(fā)生率的時(shí)滯傳染病模型的全局穩(wěn)定性[J];應(yīng)用數(shù)學(xué)和力學(xué);2015年10期

2 劉玉英;肖燕妮;;一類(lèi)受媒體影響的傳染病模型的研究[J];應(yīng)用數(shù)學(xué)和力學(xué);2013年04期

3 藤洋洋;趙維銳;朱華平;;具有時(shí)滯和標(biāo)準(zhǔn)發(fā)生率的SIR流行病模型全局穩(wěn)定性分析[J];湖北民族學(xué)院學(xué)報(bào)(自然科學(xué)版);2012年03期

，

本文編號(hào)：2447478