殷红燕.一类疟疾传播模型的稳定性和后向分支[J].中南民族大学学报自然科学版,2018,(2):142-146
一类疟疾传播模型的稳定性和后向分支
Stability and Backward Bifurcation of a Malaria Transmission Model
  
DOI:10.12130/znmdzk.20180129
中文关键词: 疟疾  平衡点  稳定性  基本再生数  后向分支
英文关键词: malaria  equilibrium  stability  the basic reproduction number  backward bifurcation
基金项目:中央高校基本科研业务费专项资金资助项目(CZQ13016)
作者单位
殷红燕 中南民族大学 数学与统计学学院武汉 430074 
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中文摘要:
      建立了一类关于疟疾传播的 SIS-SI 模型.首先通过分析模型的病平衡点的局部渐近稳定性,得到了模型的基本再生数公式; 然后证明了当基本再生数大于 1 时, 模型存在唯一的地方病平衡点; 当基本再生数小于 1 时,模型可能存在两个地方病平衡点,这表明模型会存在后向分支. 证明了后向分支的存在性. 讨论了病平衡点的全 局稳定性; 最后对所得理论结果进行了数值模拟.
英文摘要:
      A SIS-SI malaria transmission model is considered. Firstly, the formula of the basic reproduction number is derived by investigating the local asymptotical stability of the infection-free equilibrium. Secondly, it is shown that a unique endemic equilibrium exists when the basic reproduction number is more than unity and two endemic equilibria may exist if the basic reproduction number is less than unity. This indicates that a backward bifurcation may occur when the basic reproduction number is less than unity. The existence of the backward bifurcation is proved, and the global stability of the infection-free equilibrium is also discussed. Finally, numerical simulations are provided to support our theoretical results.
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