具有非線性傳染率和時(shí)滯的傳染病模型的穩(wěn)定性分析
發(fā)布時(shí)間：2018-11-25 10:28
【摘要】：近年來,許多學(xué)者利用時(shí)滯微分方程的理論研究傳染病模型,并得到了一些重要的結(jié)論。本文在前人研究的基礎(chǔ)上,研究幾類具有非線性傳染率和時(shí)滯的傳染病模型的穩(wěn)定性。主要內(nèi)容如下:第一部分,建立一類具有單時(shí)滯,傳染率為βS~n的SIR傳染病模型;然后借助基本再生數(shù)R_0,利用微分方程線性化理論、Hurwitz判斷,LaSalle不變原理,給出模型局部漸近穩(wěn)定和全局漸近穩(wěn)定的一些充分條件。第二部分,建立一類具有單時(shí)滯,傳染率為的SIRS傳染病模型;然后借助基本再生數(shù)R_1,利用線性化矩陣、Hurwitz判斷,迭代技巧,比較原理,獲得模型局部漸近穩(wěn)定和全局漸近穩(wěn)定的一些充分條件。第三部分,在第二部分的基礎(chǔ)上,我們建立了一類具有非線線性傳染和雙時(shí)滯的SIRS模型,利用第二部分的研究方法,分析了模型的穩(wěn)定性。
[Abstract]:In recent years, many scholars have made use of the theory of delay differential equation to study the infectious disease model, and got some important conclusions. On the basis of previous studies, this paper studies the stability of several infectious disease models with nonlinear infection rate and time delay. The main contents are as follows: in the first part, a class of SIR infectious disease model with single delay and infection rate of 尾 -Sn is established. Then some sufficient conditions for the local asymptotic stability and global asymptotic stability of the model are given by means of the basic reproducing number R _ 0, using the linearization theory of differential equations, the Hurwitz judgment and the LaSalle invariant principle. In the second part, a class of SIRS infectious disease model with single time delay and infection rate is established. Then some sufficient conditions for the local asymptotic stability and global asymptotic stability of the model are obtained by means of the basic reproducing number R _ 1, using linearization matrix, Hurwitz judgment, iterative technique and comparison principle. In the third part, on the basis of the second part, we establish a class of SIRS model with nonlinear linear contagion and double delay. The stability of the model is analyzed by using the method of the second part.
【學(xué)位授予單位】：重慶師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175
[Abstract]:In recent years, many scholars have made use of the theory of delay differential equation to study the infectious disease model, and got some important conclusions. On the basis of previous studies, this paper studies the stability of several infectious disease models with nonlinear infection rate and time delay. The main contents are as follows: in the first part, a class of SIR infectious disease model with single delay and infection rate of 尾 -Sn is established. Then some sufficient conditions for the local asymptotic stability and global asymptotic stability of the model are given by means of the basic reproducing number R _ 0, using the linearization theory of differential equations, the Hurwitz judgment and the LaSalle invariant principle. In the second part, a class of SIRS infectious disease model with single time delay and infection rate is established. Then some sufficient conditions for the local asymptotic stability and global asymptotic stability of the model are obtained by means of the basic reproducing number R _ 1, using linearization matrix, Hurwitz judgment, iterative technique and comparison principle. In the third part, on the basis of the second part, we establish a class of SIRS model with nonlinear linear contagion and double delay. The stability of the model is analyzed by using the method of the second part.
【學(xué)位授予單位】：重慶師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175
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1 王佳穎;竇霽虹;童姍姍;;具有非線性傳染率的病毒動(dòng)力學(xué)模型的穩(wěn)定性分析[J];陜西科技大學(xué)學(xué)報(bào)(自然科學(xué)版);2011年05期
2 林乾金;董霖;葉星e，
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