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有Logistic增长的媒介传播模型分析
引用本文:杨博炜,张菊平.有Logistic增长的媒介传播模型分析[J].数学的实践与认识,2014(23).
作者姓名:杨博炜  张菊平
作者单位:中北大学理学院;
基金项目:国家自然科学基金(11226259,11301491);山西省青年科学基金(2011021001-2)
摘    要:建立了贮存宿主鸟类与传染宿主蚊子都具有Logistic增长的西尼罗河病毒传播模型,获得了基本再生数R_0.当R_0<1时,通过构造Lyapunov函数,证明了无病平衡点的全局渐近稳定性.当R_0>1,且满足不同条件时,得到了正平衡点的存在性,数值模拟验证了理论结果的正确性.

关 键 词:西尼罗河病毒  稳定性  平衡点  Lyapunov函数  数值模拟

Analysis of a Vector-Borne Model With Logistic Growth
Abstract:In this paper,we established a West Nile virus model that storage reservoir birds and infected reservoir mosquitoes are both with Logistic growth,and we obtained the basic reproduction number R_0.When R_0 < 1,We proved the disease-free equilibrium is global asymptotically stable by constructing the Lyapunov functions.When R_0 > 1,and meet different conditions,we obtained the existence of positive equilibrium,and we use numerical simulation to verify the theoretical results.
Keywords:west nile virus(WNV)  global stability  equilibrium  lyapunov functions  numerical simulation
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