Long Time Behavior for an SEIR Epidemic Model with Latent Delay and Nonlinear Incidence Rate

YANG Ruochen; MA Mingju; QI Yifei; LI Jun

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Long Time Behavior for an SEIR Epidemic Model with Latent Delay and Nonlinear Incidence Rate

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- Long Time Behavior for an SEIR Epidemic Model with Latent Delay and Nonlinear Incidence Rate
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 54, Issue 1, Pages: 24-29(2015)
- 作者机构：
  
  1. 圣约翰大学托宾商学院, 39,纽约,美国,NY114
  2. 
  3. 莆田学院数学学院,福建,莆田,351100
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2015，
  
  Published Online：25 January 2015，
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YANG Ruochen, MA Mingju, QI Yifei, et al. Long Time Behavior for an SEIR Epidemic Model with Latent Delay and Nonlinear Incidence Rate. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(1):24-29(2015)
DOI：

YANG Ruochen, MA Mingju, QI Yifei, et al. Long Time Behavior for an SEIR Epidemic Model with Latent Delay and Nonlinear Incidence Rate. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(1):24-29(2015) DOI：

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R

= 1时

无病平衡点是全局渐近稳定的；但当R

＞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。

Abstract

A mathematical model describing the transmission dynamics of disease with nonlinear incidence rate and delay is constructed. The local stability of the disease-free equilibrium and epidemic equilibrium is established by analyzing the corresponding characteristic equation. Using suitable Lyapunov function and LaSalle's invariance principle

it is proved that if R

= 1 then the diseasefree equilibrium is globally asymptotically stable

but if R

＞1 then the epidemic equilibrium is globally asymptotically stable. Some numerical simulations are also given to explain the conclusions.

关键词

流行病数学模型潜伏期复发时滞全局稳定性

Keywords

epidemic diseasemathematical modelincubation periodlatent relapsedelayglobal stability

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