西藏自治区包虫病传播的数学建模及动力学分析

摘要/Abstract

摘要：

该文通过对包虫病传播机理以及西藏地区包虫病流行现状的研究, 构建了一类符合西藏地区实际情况的包虫病动力学模型. 利用 Lyapunov 函数对模型平衡点进行了稳定性分析, 证明了无病平衡点和地方病平衡点的全局稳定性. 并用收集到的数据, 依据模型对基本再生数 $R_{0}$ 和包虫病流行情况进行了估计和模拟, 结果表明构建的模型符合当地实际传播情况, 具有一定的合理性. 最后针对归置流浪犬和宣传教育两种防治措施给出了合理的建议.

关键词: 包虫病, 动力学模型, 平衡点, 基本再生数

Abstract:

In this paper, by studying the transmission mechanism of echinococcosis and the epidemic status of echinococcosis in Tibet, we constructed a dynamic model of echinococcosis in line with the actual situation in Tibet. The stability of the equilibrium point of the model is analyzed by Lyapunov function, and the global stability of disease-free equilibrium point and endemic equilibrium point is proved. Using the collected data, according to the model, the basic regeneration number $R_{0}$ and the prevalence of echinococcosis were estimated and simulated. The results show that the model is in line with the local actual communication situation and has certain rationality. Finally, reasonable suggestions are given for the prevention and treatment of domesticated stray dogs and publicity and education.

Key words: Echinococcosis, Dynamic model, Equilibrium point, Basic regeneration number

中图分类号:

O175.1

许越, 韩晓玲. 西藏自治区包虫病传播的数学建模及动力学分析[J]. 数学物理学报, 2023, 43(2): 646-656.

Xu Yue, Han Xiaoling. Mathematical Modeling and Dynamic Analysis of Echinococcosis Transmission in Tibet Autonomous Region[J]. Acta mathematica scientia,Series A, 2023, 43(2): 646-656.

图/表 9

图1

图2

图3

西藏地区 2016-2020 年实际患病人数与 $H_{e}$ 的比较"

图3

图4

西藏地区未来 $50$ 年 $H_{e}$ 的变化趋势"

图4

图5

西藏地区未来 $50$ 年 $H_{i}$ 的变化趋势"

图5

表1

表2

图6

$R_{0}=1$ 其中 $p, \theta$ 为参数的临界曲线"

图6

图7

犬的归置率 $\theta$ 与宣传教育因素 $p$ 对疾病流行的影响"

图7

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