具有急慢性阶段的媒介传染病的建模与研究

发布时间：2018-04-29 14:09

本文选题：急慢性阶段 + 媒介传染病　；参考：《信阳师范学院》2012年硕士论文

【摘要】：本文建立和研究了具有急慢性阶段的媒介传染病模型.得到该模型基本再生数R0的表达式.运用构造Lyapunov函数和Lasalle不变集原理证明了R0是区分媒介传染病消亡与流行的阈值,即当R01时,无病平衡点全局渐近稳定,此时疾病消亡；当R01时,地方病平衡点全局渐近稳定,此时疾病形成地方病.通过引入对媒介的控制措施,建立了媒介传染病的控制模型,得到最优控制表达式和存在条件,并用数值模拟验证了理论结果.
[Abstract]:In this paper, a vector infectious disease model with acute and chronic stages is established and studied. The expression of the basic reproduction number R _ 0 of the model is obtained. By using the principle of constructing Lyapunov function and Lasalle invariant set, it is proved that R0 is the threshold to distinguish the extinction and prevalence of vector infectious diseases, that is, when R01, the disease-free equilibrium is globally asymptotically stable, the disease dies, and when R01, the endemic equilibrium is globally asymptotically stable. At this time the disease became endemic. By introducing the control measures to the media, the control model of the vector infectious disease is established, the optimal control expression and the existence condition are obtained, and the theoretical results are verified by numerical simulation.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：R181.3

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