【摘要】：傳染病動(dòng)力學(xué)是利用動(dòng)力學(xué)方法去研究疾病的發(fā)展過(guò)程,預(yù)測(cè)其流行規(guī)律和發(fā)展趨勢(shì),分析疾病流行的原因和關(guān)鍵因素,尋求對(duì)其進(jìn)行預(yù)防和控制的最優(yōu)策略.基于此,本文將研究具有一般非線性發(fā)生率和多個(gè)并行感染階段的時(shí)滯SIR模型的穩(wěn)定性以及具有部分指數(shù)非擬單調(diào)性的時(shí)滯反應(yīng)擴(kuò)散系統(tǒng)行波解的存在性問(wèn)題.對(duì)于具有一般非線性發(fā)生率和多個(gè)并行感染階段的時(shí)滯SIR模型,首先得到了模型的平衡點(diǎn)和基本再生數(shù)?0,然后通過(guò)構(gòu)造適當(dāng)?shù)腖yapunov函數(shù),研究了平衡點(diǎn)的全局穩(wěn)定性.當(dāng)?0≤1時(shí),無(wú)病平衡點(diǎn)是全局漸近穩(wěn)定的;當(dāng)?01時(shí),地方病平衡點(diǎn)是全局漸近穩(wěn)定的.對(duì)于具有部分指數(shù)非擬單調(diào)性的時(shí)滯反應(yīng)擴(kuò)散系統(tǒng),通過(guò)建立一系列的引理,并利用Schauders不動(dòng)點(diǎn)定理建立了系統(tǒng)行波解的存在性定理.通過(guò)一致持續(xù)生存理論的方法來(lái)確定模型的一致持續(xù)性和所有平衡態(tài)的穩(wěn)定性準(zhǔn)則,得到長(zhǎng)時(shí)間的疾病傳播的閾值動(dòng)力學(xué),并將此方法應(yīng)用到更多的傳染病傳播模型,無(wú)論在穩(wěn)定性理論還是在疾病的控制預(yù)防方面,都是有意義的工作.
[Abstract]:The dynamics of infectious diseases is to study the process of disease development, predict the epidemic law and development trend, analyze the causes and key factors of disease prevalence, and seek the best strategy to prevent and control the disease. Based on this, this paper will study the stability of delay SIR model with general nonlinear incidence and multiple parallel infection stages and the existence of traveling wave solutions for delayed reaction-diffusion systems with partial exponential nonmonotonicity. For the delayed SIR model with general nonlinear incidence and multiple parallel infection stages, the equilibrium point and the basic reproduction number of the model are first obtained. Then, the global stability of the equilibrium point is studied by constructing appropriate Lyapunov functions. When 0 鈮，

本文編號(hào)：2163958