两种感染途径和接种的出血热模型稳定性分析

Stability Analysis of Hemorrhagic Fever Model with Two Infection Routes and Vaccination

建立了一类具有两种感染途径和接种的出血热模型,确定了模型的基本再生数R_(0),利用Routh-Hurwitz判据和LaSalle不变集原理,讨论了模型平衡点的局部稳定性.结果表明:当R_(0)<1时,模型仅存在唯一的无病平衡点,且无病平衡点是局部渐近稳定的;当R_(0)>1时,无病平衡点不稳定,模型还存在地方病平衡点,且地方病平衡点局部渐近稳定,最后证明了疾病存在的持久性.

Due to the transmission of hemorrhagic fever,a hemorrhagic fever model with two infecton routes and vaccination was established.The basic reproduction number R_(0) was obtained,and local stability of the equilibria was discussed by using the Routh-Hurwitz criterion and LaSalle invariant set principle.Our results show that if R_(0)<1,there is only a disease-free equilibrium,which is locally asymptotically stable,and if R_(0)>1,the disease-free equilibrium is unstable,there also exists a unique endemic equilibrium,which is locally asymptotically stable.Finally,the persistence of the disease was proved.