具有多时滞捕食-被捕食流行病模型的稳定性

The stability of a multi-delay predator-prey systems with epidemic disease

考虑传染病对捕食-被捕食者都具有致病作用的一类时滞捕食-被捕食模型,分析了系统的非负不变性、边界平衡点的性质和全局稳定性,证明了当时滞u=1τ+τ2适当小时,边界平衡点E3是局部渐近稳定的,随着时滞的增加,E3由稳定变为不稳定,系统在E3附近发生Hopf分支;当时滞1τ+2τ2充分小时,边界平衡点E2=(1,0,0)是全局稳定的.

A system of retarded functional differential equations is proposed as a predator- prey model with disease in the prey and predator. The invariance of none - negativity, nature of boundary equilibria and global stability are analyzed. The author shows that boundary equilibrium E3 is locally asymptotically stable when time delays u u=τ1＋τ2 is suitable small, while a loss of stability by a Hopf bifurcation can occur as the delays increase, and shows that boundary equilibrium E2 = （ 1,0,0） is global stability when time delay τ1＋τ2 is suitable small.