| 裴永珍,刘少英,李长国,高淑京.具有多时滞和垂直传染的脉冲接种流行病模型[J].数学年刊A辑,2009,30(5):669~676 |
| 具有多时滞和垂直传染的脉冲接种流行病模型 |
| A Pulse Vaccination Epidemic Model with Multi-delay and Vertical Transmission |
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| DOI： |
| 中文关键词: 脉冲接种 潜伏期 染病期 持久 全局吸引 |
| 英文关键词:Pulse vaccination, Latent period, Infected period, Permanence,
Global attractivity |
| 基金项目:国家科技支撑计划基金，江西省教育厅科技基金(No.GJJ0931)资助的项目 |
| Author Name | Affiliation | E-mail | | PEI Yongzhen | Department of Mathematics, School of Science, Tianjin Polytechnic University,
Tianjin 300160, China. | peiyongzhen@sina.com | | LIU Shaoying | Department of Mathematics, School of Science, Tianjin Polytechnic University,
Tianjin 300160, China. | liushaoying2008@163.com | | LI Changguo | Department of Basic Science, Institute of Military Traffic, Tianjin 300161,
China. | li_changguo@yahoo.cn | | GAO Shujing | College of Mathematics and Computer Science, Gannan Normal University,
Ganzhou 341000, Jiangxi, China. | gaosjmath@126.com |
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| 中文摘要: |
| 在潜伏期和感染期是常数的情况下,给出了一个具有两个时滞和脉冲免疫的SEIR流行病模型.利用频闪映射的离散动力系统,得到了无病周期解的表达式以及全局吸引的条件是R*<1.此外,还证明了疾病一致持续的条件足R*>1.结论表明较短的脉冲接种间隔或较大的脉冲接种率将导致疾病的灭绝.结论还表明潜伏期和感染期是导致地方病的主要因素. |
| 英文摘要: |
| Assuming the incubation period and infected period of the disease to be con-
stant, a disease transmission model of SEIR type with two delays and pulse vaccination is
formulated. Using the discrete dynamical system determined by the stroboscopic map, the
authors obtain the exact periodic infection-free solution of the impulsive epidemic system
and prove that the infection-free periodic solution is globally attractive if ?? < 1. Moreover,
it is obtained that the disease is uniformly persistent if ?? > 1. The results indicate that a
short interpulse time or a large pulse vaccination rate will lead to eradication of the disease,
and also indicate that the incubation and infected periods of an epidemic are important
factors in these whether or not this disease becomes endemic. |
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