| 结核分枝杆菌动力学模型的稳定性分析 |
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| 引用本文： | 姚苗然,王稳地,张金金,舒梦诗.结核分枝杆菌动力学模型的稳定性分析[J].西南农业大学学报,2017,39(5):113-119. |
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| 作者姓名： | 姚苗然 王稳地 张金金 舒梦诗 |
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| 作者单位： | 西南大学 数学与统计学院，重庆 400715 |
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| 摘 要： | 研究了一个同时考虑结核分枝杆菌胞内和胞外两种增殖方式的动力学模型.分析了此模型的结核菌基本再生数和免疫基本再生数,并借助基本再生数探究了无免疫平衡点的存在性及稳定性,得到了在无病平衡点处出现后向分支的充要条件,且该条件和发生率函数及胞内增殖所产生的裂解释放量紧密相关.
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| 关 键 词： | 结核分枝杆菌 平衡点 后向分支 稳定性 持续性 |
Stability Analysis of a Dynamical Model of Mycobacterium tuberculosis |
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| YAO Miao-ran,WANG Wen-di,ZHANG Jin-jin,SHU Meng-shi.Stability Analysis of a Dynamical Model of Mycobacterium tuberculosis[J].Journal of Southwest Agricultural University,2017,39(5):113-119. |
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| Authors: | YAO Miao-ran WANG Wen-di ZHANG Jin-jin SHU Meng-shi |
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| Abstract: | In this paper, we study a model about Mycobacterium tuberculosis, in which both intracellular proliferation and extracellular proliferation are considered. For the model, we obtain the basic reproductive numbers of the bacterium and the immune system. Then we use the reproductive numbers to study the existence and stability of the non-immune equilibrium point. Besides, we obtain the sufficient and necessary conditions of the backward bifurcation at disease-free equilibrium point, which are closely related to the incidence function and the burst-size of Mtb produced by intracellular proliferation. |
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