【摘要】：本文簡要介紹了一些關(guān)于流行病模型的基本概念和建立SIS流行病模型的基本方法。對不同的人口統(tǒng)計學(xué)假設(shè)與流行病學(xué)假設(shè)，建立了兩個有遷移的SIS傳染病模型。并運用極限系統(tǒng)理論，Liapunov函數(shù)法，Dulac判據(jù)等對模型進(jìn)行了研究和分析。 文中第一個模型，假設(shè)出生率是Logistic函數(shù)，自然死亡率是常數(shù)，染病的個體不遷移，也不生育下一代，疾病發(fā)生率是雙線性的。我們研究了該模型的無病平衡點與地方病平衡點全局穩(wěn)定性的條件，證明了系統(tǒng)是一致持續(xù)的。得到了這類模型的基本再生數(shù)R_0。并把我們所得到的理論性的結(jié)論用于數(shù)值計算，數(shù)值計算的結(jié)果表明了遷移率的改變，會使得閾值R_0從小于1變化到大于1，而如果R_0＞1，則在適當(dāng)?shù)臈l件下，傳染病會持續(xù)存在。這說明，即使對染病的個體給以嚴(yán)格的限制，，遷移率的改變也會造成疾病的流行。對第二個模型，假設(shè)染病個體可以遷移，其新生兒不被傳染，疾病發(fā)生率為標(biāo)準(zhǔn)型，我們給出了系統(tǒng)的無病平衡點與地方病平衡點全局穩(wěn)定的充分條件。
[Abstract]:This paper briefly introduces some basic concepts of epidemic model and the basic methods of establishing SIS epidemic model. Based on different demographic and epidemiological assumptions, two models of SIS infectious diseases with migration were established. The limit system theory, Liapunov function method and Dulac criterion are used to study and analyze the model. In the first model, assuming that the birth rate is Logistic function, the natural mortality rate is constant, the infected individuals do not migrate, and the next generation is not fertile. The incidence of disease is bilinear. We study the conditions for the global stability of the disease-free equilibrium point and the endemic equilibrium point of the model, and prove that the system is uniformly persistent. The basic regeneration number R 鈮

本文編號：2480997