动物种群中炭疽模型解的存在性与稳定性分析  

The Existence of Solution and Stability Analysis of the Anthrax Model in Animal Population

作　　者：周可可 薛亚奎[1] ZHOU Ke-ke;XUE Ya-kui(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2019年第1期8-12,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11301491);山西省自然科学基金资助项目(2015011009)

摘　　要：研究了一类具有潜伏期且以Logistic增长的炭疽疾病模型.计算出模型中炭疽流行的基本再生数R0,利用Lyapunov函数和LaSalle不变集原理证明了当R0<1时,系统存在唯一无病平衡点P0且全局渐近稳定,意味着炭疽疾病最终消亡;当R0>1时,系统存在唯一的地方病平衡点P*,并通过Routh-Hurwitz判据证明了该平衡点是局部渐近稳定的,数值模拟发现在一定条件下系统存在Hopf分支,说明炭疽疾病的爆发是周期性的.The anthrax disease model with incubation period and Logistic growth was studied.The reproductive number R0 was calculated.If R0<1,there exists only the disease-free equilibrium which is globally asymptotically stable by the Lyapunov function and theorem of Lasalle invariant set,which means that anthrax disease will eventually disappear;if R0>1,there exists a unique endemic equilibrium which is locally asymptotically stable by Routh-Hurwitz criterion.Numerical simulation shows that the system has Hopf bifurcation under certain conditions,and the outbreak of anthrax is periodic.

关 键 词：炭疽 潜伏期 基本再生数 LYAPUNOV函数 HOPF分支 

分 类 号：O175[理学—数学]