幾類具有狀態(tài)依賴脈沖控制的傳染病模型研究
發(fā)布時(shí)間：2019-04-10 17:33
【摘要】：近年來(lái),脈沖微分方程的研究熱點(diǎn)正逐步由固定時(shí)刻脈沖控制系統(tǒng)轉(zhuǎn)向狀態(tài)依賴脈沖控制系統(tǒng).在此背景下,本文詳細(xì)討論了狀態(tài)依賴脈沖控制對(duì)具有種群總數(shù)變化傳染病模型動(dòng)力學(xué)的影響,主要研究?jī)?nèi)容如下:1.第一部分(對(duì)應(yīng)第2節(jié)),主要討論了兩類具有人口總數(shù)變化,連續(xù)接種和狀態(tài)依賴脈沖接種SIS傳染病模型的動(dòng)力學(xué).在第一個(gè)控制模型中,我們以染病者在人口總數(shù)中所占的比例作為檢測(cè)閾值,通過(guò)Poincare映射,類Poincare準(zhǔn)則和定性分析方法,得到了該控制模型正的階-1周期解的存在性和軌道漸近穩(wěn)定性.其次,將易感者在人口總數(shù)中所占的比例作為檢測(cè)閾值,提出了第二個(gè)控制模型,建立了該控制模型無(wú)病周期解存在和全局軌道漸近穩(wěn)定性的判別準(zhǔn)則.最后,通過(guò)數(shù)值模擬驗(yàn)證了主要的理論結(jié)果和狀態(tài)依賴脈沖控制措施的可行性.2.第二部分(對(duì)應(yīng)第3節(jié)),為了探索布魯士菌病在反芻動(dòng)物之間的傳播動(dòng)力學(xué),建立了兩類具有狀態(tài)依賴脈沖控制和種群總數(shù)變化的SIRS傳播模型.討論狀態(tài)依賴脈沖控制策略對(duì)疾病消除和控制的影響.首先,以染病者在種群中所占比例作為檢測(cè)閾值提出具有醫(yī)療資源有限的狀態(tài)依賴脈沖接種的SIRS傳染病模型.通過(guò)定性分析,比較原理等方法,得到了該控制模型正的階-1或階-2周期解存在和軌道漸近穩(wěn)定的充分條件.進(jìn)一步,將易感者在種群中所占的比例作為檢測(cè)閾值建立了另一個(gè)具有狀態(tài)依賴脈沖控制策略的SIRS傳染病模型,討論了該控制模型正的階-1周期解和無(wú)病周期解的存在性和軌道漸近穩(wěn)定性.數(shù)值模擬驗(yàn)證了理論結(jié)果的正確性和狀態(tài)依賴脈沖控制策略的可行性.3.第三部分(對(duì)應(yīng)第4節(jié)),考慮到當(dāng)前有限的醫(yī)療資源,本節(jié)提出了一類具有狀態(tài)依賴脈沖控制和因病死亡的SIR傳染病模型,通過(guò)Poincare映射,類Poincare準(zhǔn)則和定性分析的方法,建立了該模型正的階-1或階-2周期解存在和軌道漸近穩(wěn)定的判別準(zhǔn)則.最后,通過(guò)數(shù)值模擬驗(yàn)證了理論結(jié)果的正確性.
[Abstract]:In recent years, the research focus of impulsive differential equations is gradually changing from fixed-time impulsive control system to state-dependent impulsive control system. Under this background, the effects of state-dependent impulse control on the dynamics of infectious disease models with population change are discussed in detail. The main contents are as follows: 1. In the first part (corresponding to Section 2), the dynamics of two kinds of SIS epidemic models with population change, continuous inoculation and state-dependent pulse vaccination are discussed. In the first control model, we use the proportion of the infected person in the total population as the detection threshold, and use Poincare mapping, Poincare-like criterion and qualitative analysis method. The existence of positive order-1 periodic solution and the asymptotic stability of orbit for the control model are obtained. Secondly, taking the proportion of susceptible persons in the total population as the detection threshold, a second control model is proposed, and the criteria for the existence of disease-free periodic solutions and the asymptotic stability of the global orbit are established. Finally, the main theoretical results and feasibility of state-dependent pulse control are verified by numerical simulation. 2. In the second part (corresponding to Section 3), in order to explore the transmission dynamics of brucellosis among ruminants, two kinds of SIRS propagation models with state-dependent pulse control and population total variation were established. The effects of state-dependent pulse control strategy on disease elimination and control were discussed. Firstly, a SIRS epidemic model with limited medical resources and state-dependent pulse vaccination was proposed based on the proportion of infected persons in the population as the detection threshold. By means of qualitative analysis and comparison principle, the sufficient conditions for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of the orbit of the control model are obtained. Furthermore, another SIRS epidemic model with state-dependent impulse control strategy is established by using the proportion of susceptible persons in the population as the detection threshold. The existence and orbit asymptotic stability of positive order-1 periodic solutions and disease-free periodic solutions for the control model are discussed. Numerical simulation verifies the correctness of the theoretical results and the feasibility of the state-dependent pulse control strategy. 3. In the third part (corresponding to Section 4), considering the current limited medical resources, this section proposes a kind of SIR epidemic model with state-dependent pulse control and disease-related death. It adopts Poincare mapping, Poincare-like criterion and qualitative analysis method. The criteria for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of orbits for the model are established. Finally, the correctness of the theoretical results is verified by numerical simulation.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175;O231
，
本文編號(hào)：2455992
[Abstract]:In recent years, the research focus of impulsive differential equations is gradually changing from fixed-time impulsive control system to state-dependent impulsive control system. Under this background, the effects of state-dependent impulse control on the dynamics of infectious disease models with population change are discussed in detail. The main contents are as follows: 1. In the first part (corresponding to Section 2), the dynamics of two kinds of SIS epidemic models with population change, continuous inoculation and state-dependent pulse vaccination are discussed. In the first control model, we use the proportion of the infected person in the total population as the detection threshold, and use Poincare mapping, Poincare-like criterion and qualitative analysis method. The existence of positive order-1 periodic solution and the asymptotic stability of orbit for the control model are obtained. Secondly, taking the proportion of susceptible persons in the total population as the detection threshold, a second control model is proposed, and the criteria for the existence of disease-free periodic solutions and the asymptotic stability of the global orbit are established. Finally, the main theoretical results and feasibility of state-dependent pulse control are verified by numerical simulation. 2. In the second part (corresponding to Section 3), in order to explore the transmission dynamics of brucellosis among ruminants, two kinds of SIRS propagation models with state-dependent pulse control and population total variation were established. The effects of state-dependent pulse control strategy on disease elimination and control were discussed. Firstly, a SIRS epidemic model with limited medical resources and state-dependent pulse vaccination was proposed based on the proportion of infected persons in the population as the detection threshold. By means of qualitative analysis and comparison principle, the sufficient conditions for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of the orbit of the control model are obtained. Furthermore, another SIRS epidemic model with state-dependent impulse control strategy is established by using the proportion of susceptible persons in the population as the detection threshold. The existence and orbit asymptotic stability of positive order-1 periodic solutions and disease-free periodic solutions for the control model are discussed. Numerical simulation verifies the correctness of the theoretical results and the feasibility of the state-dependent pulse control strategy. 3. In the third part (corresponding to Section 4), considering the current limited medical resources, this section proposes a kind of SIR epidemic model with state-dependent pulse control and disease-related death. It adopts Poincare mapping, Poincare-like criterion and qualitative analysis method. The criteria for the existence of positive order-1 or order-2 periodic solutions and the asymptotic stability of orbits for the model are established. Finally, the correctness of the theoretical results is verified by numerical simulation.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175;O231
，
本文編號(hào)：2455992
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