一类埃博拉传染病模型的动力学分析

数学物理学报 ›› 2017, Vol. 37 ›› Issue (3): 577-592.

• 论文 • 上一篇

一类埃博拉传染病模型的动力学分析

韦爱举¹, 张新建¹, 王俊义², 李科赞^1,3

1. 桂林电子科技大学数学与计算科学学院广西桂林 541004;
2. 广西无线宽带通信与信号处理重点实验室广西桂林 541004;
3. 广西密码学与信息安全重点实验室广西桂林 541004

收稿日期:2016-10-13 修回日期:2017-03-07 出版日期:2017-06-26 发布日期:2017-06-26
通讯作者: 李科赞,E-mail:kezanli@163.com E-mail:kezanli@163.com
基金资助:
国家自然科学基金（61663006，61261017）、广西自然科学基金（2015GXNSFBB139002）和广西密码学与信息安全重点实验室研究课题（GCIS201612）

Dynamics Analysis of an Ebola Epidemic Model

Wei Aiju¹, Zhang Xinjian¹, Wang Junyi², Li Kezan^1,3

1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guangxi Guilin 541004;
2 Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guangxi Guilin 541004;
3 Guangxi Key Laboratory of Cryptography and Information Security, Guangxi Guilin 541004

Received:2016-10-13 Revised:2017-03-07 Online:2017-06-26 Published:2017-06-26
Supported by:
Supported by the NSFC (61663006, 61261017) and the Natural Science Foundation Program of Guangxi Province (2015GXNSFBB139002) and Guangxi Key Laboratory of Cryptography and Information Security (GCIS201612)

摘要/Abstract

摘要： 该文考虑了人类和动物耦合传播的情况，提出了一类具有隔离仓室和动物仓室的埃博拉传染病模型.然后运用第二代生成矩阵的方法得到了基本再生数的表达式，利用稳定性和动力系统的相关理论证明了无病平衡点、边界平衡点、共存平衡点的存在性及全局稳定性，并对模型中的参数进行敏感性指数分析.最后通过数值模拟验证了这些结果的正确性.该文工作对于如何有效预防和控制埃博拉病毒的传播具有重要的意义.

关键词: 埃博拉病毒, 基本再生数, 全局稳定性, 敏感性分析

Abstract: In this paper, we consider the human-animal coupling epidemic where an Ebola epidemic model with isolation compartment and animal compartment is proposed. Then, the basic reproductive number is obtained by using the method of the second generation matrix. Applying the stability theory and dynamical system theory, we prove both the existence and global stability of disease-free equilibrium, boundary equilibrium and coexistence equilibrium. Moreover, sensitivity analysis of model's parameters is also performed. Finally, the theoretical results are all verified by numerical simulations. This work has important significance for guiding us to prevent and control the Ebola spread.

Key words: Ebola virus, The basic reproduction number, Global stability, Sensitivity analysis

中图分类号:

O175.1

韦爱举, 张新建, 王俊义, 李科赞. 一类埃博拉传染病模型的动力学分析[J]. 数学物理学报, 2017, 37(3): 577-592.

Wei Aiju, Zhang Xinjian, Wang Junyi, Li Kezan. Dynamics Analysis of an Ebola Epidemic Model[J]. Acta mathematica scientia,Series A, 2017, 37(3): 577-592.

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一类埃博拉传染病模型的动力学分析

Dynamics Analysis of an Ebola Epidemic Model

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