基于两类媒介的炭疽传播模型的全局动力学分析

摘要/Abstract

摘要：

为了研究动物种群中媒介对炭疽传播的影响, 该文依据尸食性蝇与血食性蝇的传播机制, 建立了一个确定性传染病模型. 利用微分方程基本定理证明了模型解的非负性和有界性, 给出了平衡点存在的充分条件, 定义了模型的几类再生数, 利用线性化方法和M-矩阵等方法对平衡点的稳定性进行了分析, 并研究了疾病的持久性. 利用数值模拟研究了参数对基本再生数的影响. 研究结果表明: 及时清理染病尸体, 尽量消除苍蝇的繁殖地点, 对苍蝇使用杀虫剂对炭疽在动物种群中传播具有一定的抑制作用.中文摘要

关键词: 炭疽, 尸食性蝇, 血食性蝇, 稳定性, 持久性

Abstract:

In order to study the influence of vectors on anthrax transmission in animal populations, a deterministic infectious disease model is established based on the transmission mechanism of necrophilic flies and hematophagous flies. The nonnegativity and boundedness of the solutions of the model are proved by using the basic theorem of differential equations, the sufficient conditions for the existence of equilibria are given, and several kinds of reproduction numbers of the model are defined, the stability of the equilibria is analyzed by means of linearization and M-matrix theory, and the persistence of the disease is also studied. The effects of parameters on the basic reproduction number are studied by numerical simulations. The results show that timely cleaning of infected carcasses, eliminating fly breeding sites as much as possible and the use of insecticides on flies can inhibit the spread of anthrax in animal populations.

Key words: Anthrax, Necrophilic flies, Hematophagous flies, Stability, Persistence

中图分类号:

O175.1

韩梦洁, 刘俊利, 张太雷. 基于两类媒介的炭疽传播模型的全局动力学分析[J]. 数学物理学报, 2024, 44(1): 227-245.

Han Mengjie, Liu Junli, Zhang Tailei. Global Dynamics Analysis of Anthrax Transmission Model Based on Two Kinds of Vectors[J]. Acta mathematica scientia,Series A, 2024, 44(1): 227-245.

图/表 2

图1

系统 (2.2) 存在三个正平衡点, 正平衡点 $E_{83}$ 渐近稳定, 正平衡点 $E_{81}$ 和 $E_{82}$ 不稳定"

图1

图2

$R_{0}$ 与 $k$ 、 $c$ 的关系图. (a) $R_{0}$ 与 $k$ 的关系图; (b) $R_{0}$ 与 $c$ 的关系图"

图2

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