【摘要】：本文研究了一類易感者有常數(shù)輸入,潛伏期和染病期均具有傳染力,且傳染率是一 般傳染率的SEI傳染病模型,利用Liapunov函數(shù)、LaSalle不變集原理證明了無病平衡點 的全局穩(wěn)定性,利用Hurwitz判別準(zhǔn)則證明了地方病平衡點的局部穩(wěn)定性,利用Poincare`? Bendixson性質(zhì)證明了地方病平衡點的全局穩(wěn)定性. 另外,還研究了一類易感者有常 數(shù)輸入,潛伏期、染病期均和恢復(fù)期均具有傳染力,且傳染率是雙線性傳染率的SEIR傳 染病模型, 利用Liapunov函數(shù)、LaSalle不變集原理證明了潛伏期、染病期和恢復(fù)期均 具有傳染力的流行病模型的等價系統(tǒng)的無病平衡點的全局穩(wěn)定性, 利用Hurwitz判別準(zhǔn) 則證明了地方病平衡點的局部穩(wěn)定性,進(jìn)一步利用Poincare`? Bendixson 性質(zhì)證明了 當(dāng)α10 = α20 = 0 時若初始值存在則地方病平衡點是全局穩(wěn)定性的.
[Abstract]:In this paper, we study a class of SEI infectious disease models with constant input, latent period and infection period, and the infection rate is a kind of infectious rate. The global stability of disease-free equilibrium is proved by using the principle of LaSalle invariant set of Liapunov function, the local stability of endemic equilibrium is proved by Hurwitz criterion, and the local stability of endemic equilibrium is proved by Poincare'? The global stability of endemic equilibrium is proved by Bendixson property. In addition, we also studied that a class of susceptible people have constant input, latent period, infection stage and convalescence stage. The transmission rate is a bilinear transmission model of SEIR infection. The latent period is proved by using the Liapunov function LaSalle invariant set principle. The global stability of the disease-free equilibrium point of the equivalent system of epidemic model with infectious force and convalescence is determined by Hurwitz. Then the local stability of endemic equilibrium is proved. Make further use of Poincare'? Bendixson property proves that the endemic equilibrium is globally stable when 偽 10 = 偽 20 = 0 if the initial value exists.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2005
【分類號】：R181.3

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前3條

1 葉星e，

本文編號：2148997