| 一类具有饱和发生率的虫媒传染病模型研究 |
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| 引用本文： | 张晋珠,梁娟,苏铁熊.一类具有饱和发生率的虫媒传染病模型研究[J].西南农业大学学报,2020,42(3):88-93. |
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| 作者姓名： | 张晋珠 梁娟 苏铁熊 |
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| 作者单位： | 1. 太原工业学院 经济与管理系, 太原 030008;2. 太原工业学院 理学系, 太原 030008;3. 中北大学 机电工程学院, 太原 030051 |
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| 基金项目： | 山西省自然科学基金项目（2012011002-2）；太原工业学院重点基金项目（2016LZ02）. |
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| 摘 要： | 考虑虫媒传染病具有潜伏期的特征,研究了一类具有饱和发生率的时滞传染病模型的动力学行为,确定了疾病是否流行的阈值R_0.当R_01时,无病平衡点全局渐近稳定,疾病将最终灭绝;当R_01时,唯一地方病平衡点条件稳定,系统会产生Hopf分支.
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| 关 键 词： | 虫媒传染病模型 饱和发生率 时滞 稳定性 Hopf分支 |
| 收稿时间： | 2017/11/20 0:00:00 |
Dynamics Analysis of a Vector-Borne Disease Model with Saturation Incidence Rate |
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| ZHANG Jin-zhu,LIANG Juan,SU Tie-xiong.Dynamics Analysis of a Vector-Borne Disease Model with Saturation Incidence Rate[J].Journal of Southwest Agricultural University,2020,42(3):88-93. |
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| Authors: | ZHANG Jin-zhu LIANG Juan SU Tie-xiong |
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| Institution: | 1. Department of Economics and Management, Taiyuan Institute of Technology, Taiyuan 030008, China;2. Department of Mathematics, Taiyuan Institute of Technology, Taiyuan 030008, China;3. School of Mechatronics Engineering, North University of China, Taiyuan 030051, China |
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| Abstract: | Taking into consideration the fact that insect-borne infectious diseases have a latent period, we study in this paper the dynamic behavior for a delayed vector-borne disease model with saturation infection rate. The threshold value R0, which determines whether the disease dies out, is found. If R0<1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If R0>1, a unique endemic equilibrium is conditionally stable. The conditions for Hopf bifurcation to occur are derived. |
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| Keywords: | vector-borne disease model saturation incidence rate time delay stability Hopf bifurcation |
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