本文選題：病毒 + 地方病平衡點��； 參考：《新疆大學(xué)》2015年碩士論文

【摘要】：傳染病的防制是關(guān)系到人類健康的國計民生的重大問題,對疾病流行規(guī)律的定量研究是防制工作的重要依據(jù),長期以來,人類與各種傳染病進(jìn)行了不屈不撓的斗爭,使得天花被消滅,麻風(fēng)病,脊髓灰質(zhì)炎被徹底消滅也指日可待,多種抗生素的問世,如1922年英格蘭細(xì)菌學(xué)家亞歷山大.弗萊明(Alexander.Fleming,1881-1955)發(fā)現(xiàn)了青霉素拯救了成千上萬的人生命,然而,世界衛(wèi)生組織(WHO)發(fā)表的世界衛(wèi)生報告表明傳染病依然是人類的第一殺手.本文的第一部分是引言,介紹了一些具有健康帶菌者的傳染病模型及研究背景,目的和意義.第二部分是預(yù)備知識,包括一些基本定理和論文要用的定理,引理,準(zhǔn)則等,第三部分通過不同的三類數(shù)學(xué)模型來說明健康帶菌者對傳染病模型的穩(wěn)定性影響,模型的主要內(nèi)容概述如下首先研究具有Bedding-De Angelis發(fā)生率的健康帶菌者模型,引入第二加性復(fù)合矩陣,利用求譜半徑的方法得到系統(tǒng)的基本再生數(shù),證明了解的正性和地方平衡點的存在,并說明了若基本再生數(shù)小于1,無病平衡點全局穩(wěn)定的;若基本再生數(shù)大于1,則疾病是不穩(wěn)定的,我們利用Bendixson判據(jù)方法分析持續(xù)帶毒平衡點的全局穩(wěn)定性,其次考慮帶一個時滯模擬傳染病,我們分離特征方程的實部與虛部,利用反證法來論斷特征根實部的符號,在討論平衡點的全局穩(wěn)定性時構(gòu)造了一個無限大正定的Liapunov泛函,得到相應(yīng)平衡點在所討論的區(qū)域內(nèi)全局漸近穩(wěn)定的,建立合適的閾值R0,得到當(dāng)R01時,系統(tǒng)的無病平衡點是全局漸近穩(wěn)定的,當(dāng)R01時,得出地方病平衡點是全局漸近穩(wěn)定的,最后考慮帶兩個時滯模擬傳染病的潛伏期,患者對疾病的感染期,首先我們分離特征方程的實部與虛部,利用反證法來論斷特征根實部的符號,在討論平衡點的全局穩(wěn)定性時構(gòu)造了一個無限大正定的Liapunov泛函,得到相應(yīng)平衡點在所討論的區(qū)域內(nèi)全局漸近穩(wěn)定的,最后對兩個時滯對模型的影響作了數(shù)值模擬,驗證了結(jié)論的正確性.
[Abstract]:The prevention and control of infectious diseases is an important issue related to the national economy and the people's livelihood of human health. The quantitative study on the law of disease prevalence is an important basis for the prevention and control work. For a long time, human beings have been engaged in an indomitable struggle against various infectious diseases. The eradication of smallpox, leprosy and poliomyelitis is imminent, and many antibiotics, such as the English bacteriologist Alexander, came out in 1922. Alexander.Flemingn (1881-1955) found penicillin has saved thousands of lives. However, the World Health report published by the World Health Organization (WHO) shows that infectious diseases are still the number one killer of human beings. The first part of this paper is an introduction, which introduces some infectious disease models with healthy carriers and their research background, purpose and significance. The second part is the preparatory knowledge, including some basic theorems and the theorems, Lemma and criteria to be used in the paper. The third part explains the influence of healthy carriers on the stability of infectious disease models through three different mathematical models. The main contents of the model are summarized as follows: firstly, the healthy carrier model with the incidence of Bedding-De Angelis is studied, and the second additive compound matrix is introduced, and the basic regeneration number of the system is obtained by the method of calculating the spectral radius. The existence of positive solutions and local equilibrium points is proved, and it is shown that the disease-free equilibrium points are globally stable if the number of fundamental reproductions is less than 1, and if the number of basic regenerations is greater than 1, the disease is unstable. We use the Bendixson criterion method to analyze the global stability of the persistent poison equilibrium point, and then consider the simulated infectious disease with a delay. We separate the real part from the imaginary part of the characteristic equation, and use the counter-proof method to judge the symbol of the real part of the characteristic root. In this paper, we construct an infinite positive definite Liapunov functional when we discuss the global stability of the equilibrium point. We obtain the globally asymptotically stable equilibrium point in the region under discussion. The disease-free equilibrium of the system is globally asymptotically stable. When R01, the endemic equilibrium is globally asymptotically stable. Finally, the incubation period of the simulated infectious disease with two delays and the infection period of the patient to the disease are considered. First of all, we separate the real part and the imaginary part of the characteristic equation, use the counter-proof method to judge the sign of the real part of the characteristic root, and construct an infinite positive definite Liapunov functional when we discuss the global stability of the equilibrium point. The globally asymptotically stable equilibrium points are obtained. Finally, the effects of two delays on the model are numerically simulated, and the correctness of the conclusions is verified.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175
，

本文編號：1989683