具有时滞和阶段结构的生态-流行病模型的稳定性及Hopf分支

本文研究一类具有时滞和阶段结构的生态-流行病模型的稳定性及其Hopf分支．给出了边界平衡点和正平衡点存在的充分条件；通过分析特征方程，运用Hurwitz判定定理，讨论了边界平衡点和正平衡点的局部稳定性，并得到了正平衡点附近存在Hopf分支的充分条件；通过构造适当的Lyapunov泛函，运用LaSall不变集原理，讨论了边界平衡点和正平衡点的全局稳定性，从而得到了该生态模型永久持续生存与灭绝的充分条件．

Stability and Hopf Bifurcation of an Eco-epidemiological Predator-prey Model with Stage-structure and Time Delay

In this paper, the stability and Hopf bifurcation of an eco-epidemiological model with a time delay and a stage structure is investigated. By analyzing the characteristic equations and applying Hurwitz criterion, the local stability of the boundary equilibria and the positive equilibrium are discussed, respectively. Moreover, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By using Lyapunov functions and LaSalle's invariance principle, the global stability of the boundary equilibria and the positive equilibrium is addressed, respectively. Therefore, the sufficient conditions are given for the permanence and extinction of the model.