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具有时滞的生态传染病系统的稳定性分析
Stability of an Eco-Epidemiological System with Delay

DOI: 10.12677/OJNS.2016.42012, PP. 103-109

Keywords: 时滞,稳定性,Hopf分支,生态传染病系统
Delay
, Stability, Hopf Bifurcation, Eco-Epidemiological System

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Abstract:

本文考虑了疾病在食饵种群中传播和具有Holling II型功能反应的时滞生态系统,主要分析时滞对系统局部稳定性的影响。当时滞不存在时,系统在内部平衡点处是局部渐近稳定的;但随着时滞?τ?的逐渐增加并超过临界值时,系统由稳定状态变为不稳定且产生Hopf分支,从而得到了Hopf分支的存在条件,最后利用数值模拟来验证所得结论。这些结论预测了疾病在种群间的发展趋势,并为控制疾病在种群间传播提供了可靠的理论依据。
In this paper, a delayed eco-epidemiological system with a disease in prey is considered. Its dy-namics of stability and the effect of delay on this system have been studied. The system without delay is locally asymptotically stable at the internal equilibrium point. With the delay gradually increasing, the system will be unstable and occurHopf bifurcation. Finally, the numerical simula-tion is carried out to verify the conclusions. These results can predict the trend of the populations with disease, and provide a reliable theoretical basis for controlling the spread of disease in populations.

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