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含潜伏时滞效应和非线性发生率的SEIR模型的长时间行为 被引量：1

Long Time Behavior for an SEIR Epidemic Model with Latent Delay and Nonlinear Incidence Rate
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摘要 研究了一类含有潜伏时滞和非线性发生率的SEIR流行病模型。给出了疾病流行的阈值条件,并且得到了无病平衡点和流行病平衡点的局部稳定性条件。通过构造适当的Lyapunov泛函,结合LaSalle不变集原理,证明了当基本再生数R0≤1时,无病平衡点是全局渐近稳定的;但当R0>1时,流行病平衡点是全局渐近稳定的,同时利用数值模拟验证了分析的结果。 A mathematical model describing the transmission dynamics of disease with nonlinear inci-dence rate and delay is constructed.The local stability of the disease-free equilibrium and epidemic equi-librium is established by analyzing the corresponding characteristic equation.Using suitable Lyapunov function and LaSalle＆#39;s invariance principle,it is proved that if R0  1 then the disease-free equilibrium is globally asymptotically stable,but if R0 ＆gt;1 then the epidemic equilibrium is globally asymptotically sta-ble.Some numerical simulations are also given to explain the conclusions.
作者 杨若晨 马明菊 齐逸飞 李君
机构地区 圣约翰大学托宾商学院 莆田学院数学学院 西北师范大学经济学院 西安电子科技大学
出处 《中山大学学报（自然科学版）》 CAS CSCD 北大核心 2015年第1期24-29,36,共7页 Acta Scientiarum Naturalium Universitatis Sunyatseni
基金 福建省教育厅中青年教师教育科研资助项目(JA13283)
关键词 流行病 数学模型 潜伏期 复发 时滞 全局稳定性 epidemic disease mathematical model incubation period latent relapse delay global stability
分类号 O175 [理学—基础数学]
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参考文献15

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同被引文献11

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中山大学学报（自然科学版）
2015年 第1期

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