被捕食者感染疾病的Lotka-Volterra捕食—被捕食模型的研究  

A Lotka-Volterra Predator-Prey Model with Disease Spread in Preys

作　　者：王丽莎 赵建东 

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264039

出　　处：《鲁东大学学报（自然科学版）》2018年第1期38-43,85,共7页Journal of Ludong University:Natural Science Edition

基　　金：山东省自然科学基金(ZR2015AM026)

摘　　要：建立了被捕食者感染疾病的Lotka-Volterra捕食—被捕食模型,讨论了其平衡点及稳定性、中心流形上的周期解,并给出了传染病流行的阈值R_0.结果表明:当R_0>1时,传染病流行;当R_0<1时,传染病将消亡.最后,通过数值模拟验证了本文的主要结果.A Lotka-Volterra predator-prey model with disease spread in preys only was proposed. The equilibria and their stability were discussed,the periodic solutions on the center manifolds were studied,and the threshold R_0 for disease prevalence was given. The results show that the disease will disappear from this ecosystem when R_0< 1,and the disease will prevail in the preys when R_0> 1. Furthermore,some numerical simulations were given to illustrate the results.

关 键 词：捕食—被捕食模型 传染病 零Hopf平衡点 周期解 

分 类 号：O175.12[理学—数学]