【摘要】：根據(jù)細(xì)菌污染環(huán)境在人群中傳播特點(diǎn),本文建立和分析了兩類具有類年齡結(jié)構(gòu)的細(xì)菌感染動力學(xué)模型.一類是考慮帶有免疫年齡結(jié)構(gòu)的細(xì)菌感染動力學(xué)模型,另一類考慮帶有接種年齡結(jié)構(gòu)的細(xì)菌感染動力學(xué)模型.運(yùn)用微分方程動力學(xué)性質(zhì)理論和知識我們?nèi)址治隽怂Ｐ偷膭恿W(xué)性質(zhì).通過系統(tǒng)地分析,得到了模型基本再生數(shù),以及系統(tǒng)中呈現(xiàn)出的無病平衡態(tài)和地方病平衡態(tài)的存在性,唯一性；運(yùn)用特征線理論和方法,我們分析了模型平衡態(tài)局部穩(wěn)定性,得到了當(dāng)基本再生數(shù)R0≤1時,無病平衡態(tài)E0局部漸近穩(wěn)定；當(dāng)R01時,無病平衡態(tài)E0局部不穩(wěn)定地方性疾病平衡態(tài)E*局部穩(wěn)定；通過運(yùn)用無窮維動力系統(tǒng)持續(xù)生存理論,我們分析了系統(tǒng)的持續(xù)生存性.得到了當(dāng)R01時,系統(tǒng)中疾病持續(xù)生存；最后,我們通過構(gòu)造一類Lyapunov函數(shù),對模型平衡態(tài)的全局穩(wěn)定性進(jìn)行分析.當(dāng)基本再生數(shù)R0≤1時,無病平衡態(tài)E0全局漸近穩(wěn)定；當(dāng)Ro1時,地方性疾病平衡態(tài)E*全局漸近穩(wěn)定.
[Abstract]:According to the characteristics of bacterial contamination in the population, two kinds of bacterial infection dynamics models with similar age structure were established and analyzed in this paper. One is to consider the bacterial infection kinetic model with immune age structure, the other is to consider the bacterial infection kinetic model with inoculation age structure. By using the theory of dynamical properties of differential equations and knowledge, the dynamical properties of the model are analyzed globally. Through systematic analysis, the basic regenerative number of the model and the existence and uniqueness of disease-free equilibrium and endemic equilibrium are obtained. Using the characteristic line theory and method, we analyze the local stability of the equilibrium state of the model, and obtain the local asymptotic stability of the disease-free equilibrium state E _ 0 when the basic regenerative number R _ 0 鈮，

本文編號：2419026