| 未感染概率为一般函数的离散S-I-R模型 |
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| 引用本文： | 郑芳,刘贤宁,袁媛.未感染概率为一般函数的离散S-I-R模型[J].西南农业大学学报,2008,30(2):20-25. |
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| 作者姓名： | 郑芳 刘贤宁 袁媛 |
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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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| 基金项目： | 国家自然科学基金资助项目（10571143） |
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| 摘 要： | 研究了一个离散S-I-R传染病模型,其中未感染概率为关于被感染人群的一般函数.建立了模型的基本再生数,得到了平衡点的存在性和稳定性只依赖于此再生数.此外,还得到了系统一致持久和全局渐近稳定的条件.模型的数学结论表明种群密集是疾病传播的原因,提高医疗技术有利于疾病控制.
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| 关 键 词： | 离散 S-I-R模型 一致持续生存 全局稳定性 |
| 文章编号： | 1673-9868（2008）02-0020-06 |
| 收稿时间： | 2007-04-10 |
| 修稿时间： | 2007年4月10日 |
A Discrete S-I-R Model with a General Function of Remaining Susceptible Probability |
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| ZHENG Fang, LIU Xian-ning, YUAN Yuan.A Discrete S-I-R Model with a General Function of Remaining Susceptible Probability[J].Journal of Southwest Agricultural University,2008,30(2):20-25. |
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| Authors: | ZHENG Fang LIU Xian-ning YUAN Yuan |
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| Abstract: | This paper studies a discrete S-I-R disease transmission model, in which the probability of remaining susceptible is a general function of the infected population. The basic reproduction number is established. Existence and stability of equilibria are studied with conditions only related to this number. Conditions for permanence and global stability of the system are also obtained. The mathematical results of the model suggest that overcrowded population may be the reason for disease spread and improving the medical technology is effective for disease control. |
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| Keywords: | discrete susceptible-infected-recovered(SIR) model uniform persistence global stability |
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