本文選題：傳染病模型 + 飽和接觸率��； 參考：《昆明理工大學(xué)》2009年碩士論文

【摘要】：根據(jù)世界衛(wèi)生組織最新的研究報(bào)告,傳染病仍是危害人類生命和健康的第一殺手,人類依然面臨著各種傳染病長期而嚴(yán)竣的威脅。我們對傳染病發(fā)病機(jī)理、流行規(guī)律、趨勢預(yù)測的研究往往通過理論分析、模擬仿真等方法來進(jìn)行。傳染病動(dòng)力學(xué)模型就是一種對傳染病研究的重要方法。根據(jù)傳染病的傳播途徑,這些模型通常被分為SI,SIR, SIS。SIRS,SEI,SEIR以及其他模式。 以上的一些模式都沒有考慮接種疫苗的情況,然而在實(shí)際生活中,接種疫苗是控制疾病的常用方法,例如乙型肝炎,麻疹和流行性感冒等等。因此在本文第二章研究了一類具有標(biāo)準(zhǔn)接觸率的SEIV傳染病模型：此模型存在兩個(gè)平衡點(diǎn),分別為無病平衡點(diǎn)和地方病平衡點(diǎn)。當(dāng)基本再生數(shù)σ1時(shí),無病平衡點(diǎn)是全局漸近穩(wěn)定的,在這種情況下,地方病平衡點(diǎn)是不存在的。另一種情況下,當(dāng)基本再生數(shù)σ1時(shí),系統(tǒng)存在唯一的地方病平衡點(diǎn),疾病一直持續(xù)存在,在一定的情況下,地方病平衡點(diǎn)是全局漸近穩(wěn)定的。 疾病的發(fā)生率是指每個(gè)單位時(shí)間內(nèi)新增加的病例數(shù)目,疾病的接觸率在關(guān)于傳染病的數(shù)學(xué)模型的研究中起著非常重要的作用。蒂梅和卡斯蒂-查韋斯提出發(fā)生率的一般形式應(yīng)該寫成λ0C(N)S/NI,S和I分別表示在t時(shí)刻易感染者和患病者的數(shù)目,λ0表示當(dāng)兩個(gè)個(gè)體接觸時(shí)在單位時(shí)間內(nèi)疾病傳播的可能性,C(N)是指單位時(shí)間內(nèi)一個(gè)患者與他人接觸的次數(shù),第三章在第二章的基礎(chǔ)上研究了帶有飽和接觸率的SEIV模型：此模型也存在兩個(gè)平衡點(diǎn),分別為無病平衡點(diǎn)和地方病平衡點(diǎn)。當(dāng)基本再生數(shù)σ1時(shí),無病平衡點(diǎn)是全局漸近穩(wěn)定的,在這種情況下,地方病平衡點(diǎn)是不存在的。另一種情況下,當(dāng)基本再生數(shù)σ1時(shí),系統(tǒng)存在唯一的地方病平衡點(diǎn),地方病平衡點(diǎn)是局部漸近穩(wěn)定的。當(dāng)沒有發(fā)生因病死亡時(shí),地方病平衡點(diǎn)是全局漸近穩(wěn)定的。
[Abstract]:According to the latest research report of the World Health Organization, infectious diseases are still the first killer of human life and health, and human beings still face a long-term and serious threat of various infectious diseases. Our research on the pathogenesis, epidemic law and trend prediction of infectious diseases is often carried out by theoretical analysis, simulation and simulation. The kinetic model of infectious diseases is an important method for the study of infectious diseases. According to the route of transmission of infectious diseases, these models are usually classified as SISIRS, SIS.SIRSSEISEIR and other models. None of the above models take into account vaccinations, but in real life vaccination is a common method of disease control, such as hepatitis B, measles and influenza. In the second chapter of this paper, we study a class of SEIV infectious disease models with standard contact rate. There are two equilibrium points in this model, one is disease-free equilibrium point and the other is endemic equilibrium point. When the basic reproduction number 蟽 1, the disease-free equilibrium is globally asymptotically stable. In this case, the endemic equilibrium does not exist. In another case, when the basic reproduction number 蟽 1, the system has a unique endemic equilibrium, and the disease has been persistent. Under certain conditions, the endemic equilibrium is globally asymptotically stable. The incidence of disease refers to the number of new cases per unit of time, and the rate of disease exposure plays a very important role in the study of mathematical models of infectious diseases. Tiemer and Castil-Chavez suggested that the general form of incidence should be written as 位 0C / NS / NIS / NIS and I respectively to indicate the number of susceptible and infected persons at t time, and 位 0 to indicate the possibility of disease transmission per unit time when two individuals are in contact with each other. Sex is the number of times a patient is in contact with another person per unit of time. In chapter 3, based on the second chapter, we study the SEIV model with saturated contact rate. There are two equilibrium points in this model, one is disease-free equilibrium and the other is endemic equilibrium point. When the basic reproduction number 蟽 1, the disease-free equilibrium is globally asymptotically stable. In this case, the endemic equilibrium does not exist. In another case, when the basic reproducing number 蟽 1, the system has a unique endemic equilibrium, and the endemic equilibrium is locally asymptotically stable. When there is no death due to illness, the endemic equilibrium is globally asymptotically stable.
【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2009
【分類號(hào)】：R186;O242.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 王拉娣;李建全;;一類帶有非線性傳染率的SEIS傳染病模型的定性分析[J];應(yīng)用數(shù)學(xué)和力學(xué);2006年05期

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本文編號(hào)：1898290