| 具有年龄结构的SI传染病模型的分析 |
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| 引用本文： | 张剑,张宏民.具有年龄结构的SI传染病模型的分析[J].东北农业大学学报,2010,41(8). |
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| 作者姓名： | 张剑 张宏民 |
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| 作者单位： | 齐齐哈尔大学理学院,黑龙江,齐齐哈尔,161006;齐齐哈尔大学理学院,黑龙江,齐齐哈尔,161006 |
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| 基金项目： | 黑龙江省教育厅科学技术研究项目 |
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| 摘 要： | 研究了具有年龄结构的单种群模型在成年种群间染病的问题,建立并分析了具有成年和幼年两个年龄结构的SI传染病模型,利用微分方程定性分析方法讨论了该模型平衡点的存在条件,根据平衡点的系数矩阵对应的特征方程的特征根的情况,判断出各个平衡点的类型及局部稳定性,同时利用Hurwitz判别法得到模型的唯一正平衡点局部渐近稳定的充分条件。该结论说明在一定的条件下,疾病对生物种群不会造成较大的影响,不会造成种群的灭绝。
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| 关 键 词： | 年龄结构 SI传染病模型 平衡点 渐近稳定 |
Analysis of stage-structured SI model |
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| ZHANG Jian,ZHANG Hongmin.Analysis of stage-structured SI model[J].Journal of Northeast Agricultural University,2010,41(8). |
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| Authors: | ZHANG Jian ZHANG Hongmin |
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| Abstract: | In the paper, it researched the problem of epidemic single population model with stage-structured with epidemic mature specie. Itanalysed the stage-structured with young and mature specie SI epidemic models, used qualitative analysis method of differential equations to discuss the existential condition ofequilibriums. According to the eigenvalues ofthe equilibriums'coefficient matrix corresponding to differentcharacteristic equations, the paperjudged the types and localstabilities ofequilibriums. Furthermore, by using Hurwitz judgment, the sufficient condition of locally asymptotic stability for the unique positive equilibrium was obtained. The result illustrated that in particular condition, the disease can not cause more effects on the biologic population and the extinction. |
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| Keywords: | stage-structure SIepidemic model equilibrium asymptotic stability |
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