| 一类具有垂直传播的HIV模型的稳定性分析 |
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| 引用本文： | 张梅,张凤琴,刘汉武.一类具有垂直传播的HIV模型的稳定性分析[J].工程数学学报,2012,29(3):399-404. |
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| 作者姓名： | 张梅 张凤琴 刘汉武 |
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| 作者单位： | 1. 运城学院应用数学系,运城044000;中北大学理学院,太原030051
2. 运城学院应用数学系,运城,044000 |
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| 基金项目： | 国家自然科学基金(11071283);山西省自然科学基金(2009011005-3);山西省重点学科项目(2011028;20111030)~~ |
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| 摘 要： | 根据艾滋病的传播规律,本文建立了一类传染病模型.在模型中,HIV携带者分为幼年和成年两类,HIV可垂直传染,艾滋病患者有额外死亡.我们用再生矩阵求出了模型的基本再生数,并得出当基本再生数小于1时,模型只有无病平衡点,而当基本再生数大于1时,模型还有地方病平衡点.最后,应用第二加性复合矩阵等理论,文中证明了各平衡点全局渐近稳定性.
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| 关 键 词： | 垂直传播 基本再生数 稳定性 平衡点 |
Stability Analysis of an HIV Model with Vertical Transmission |
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| ZHANG Mei
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ZHANG Feng-qin
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LIU Han-wu.Stability Analysis of an HIV Model with Vertical Transmission[J].Chinese Journal of Engineering Mathematics,2012,29(3):399-404. |
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| Authors: | ZHANG Mei ZHANG Feng-qin LIU Han-wu |
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| Affiliation: | 1(1-Deparment of Applied Mathematics,Yuncheng University,Yuncheng 044000;2-School of Science,North University of China,Taiyuan 030051) |
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| Abstract: | According to the spreading law of AIDS,an epidemic model is formulated.In the model,the carriers of HIV include juveniles and adults,the HIV can be transmitted vertically,AIDS patients may die of disease.By means of the reproductive matrix,we obtain the basic reproductive number.If the basic reproductive number is less than 1,the model has disease-free equilibrium only.However,if the basic reproductive number is larger than 1,the model has another endemic equilibrium.By using second additive compound matrices,we have studied the global stability of all equilibriums. |
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| Keywords: | vertical transmission basic reproductive number stability equilibrium point |
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