一类传染病动力学模型的理论研究与计算机仿真
发布时间：2018-07-27 20:08
【摘要】：本文研究了一类易感者有常数输入,潜伏期和染病期均具有传染力,且传染率是一 般传染率的SEI传染病模型,利用Liapunov函数、LaSalle不变集原理证明了无病平衡点 的全局稳定性,利用Hurwitz判别准则证明了地方病平衡点的局部稳定性,利用Poincare`? Bendixson性质证明了地方病平衡点的全局稳定性. 另外,还研究了一类易感者有常 数输入,潜伏期、染病期均和恢复期均具有传染力,且传染率是双线性传染率的SEIR传 染病模型, 利用Liapunov函数、LaSalle不变集原理证明了潜伏期、染病期和恢复期均 具有传染力的流行病模型的等价系统的无病平衡点的全局稳定性, 利用Hurwitz判别准 则证明了地方病平衡点的局部稳定性,进一步利用Poincare`? Bendixson 性质证明了 当α10 = α20 = 0 时若初始值存在则地方病平衡点是全局稳定性的.
[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 伪 10 = 伪 20 = 0 if the initial value exists.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2005
【分类号】：R181.3
[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 伪 10 = 伪 20 = 0 if the initial value exists.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2005
【分类号】：R181.3
【引证文献】
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