• 研究、探讨 •

### Stability and Hopf bifurcation of SI model with time delays

WANG Lie，CHEN Siyang

1. College of Mathematic and Information Science，Shaanxi Normal University，Xi’an 710062，China
• Received:1900-01-01 Revised:1900-01-01 Online:2011-12-21 Published:2011-12-21

### 多时滞SI模型的稳定性和Hopf分支

1. 陕西师范大学 数学与信息科学学院，西安 710062

Abstract: An SI model with epidemic in the time delays predator and prey is proposed.Using the method of latent root the equilibrium points are obtained.Through analysis，the result is achieved that the predator and the prey with epidemic will be extinct when the infection percentage of susceptible is smaller than a threshold.The predator will be extinct when the infection percentage of the susceptible prey is larger than a threshold and the conversion coefficient of the susceptible predator is smaller than a threshold.The boundary equilibrium is locally asymptotically stable when the time delay of prey is suitable small，while a loss of stability by a Hopf bifurcation can occur as the delay increases.The time delay of predator has no influence on the stability of the equilibrium.