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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 >

2022 , Vol. 39 >Issue 4: 599 - 609

DOI: https://doi.org/10.3969/j.issn.1005-3085.2022.04.008

基于 Beverton-Holt 出生函数的阶段结构传染病模型的稳定性和分支

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  • 1. 西安工程大学理学院，西安 710048
    2. 空军工程大学基础部，西安 710051

网络出版日期: 2022-10-15

基金资助

中国国家留学基金；陕西省教育厅自然科学专项基金 (18JK0336).

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Stability and Bifurcation in a Stage-structured Epidemic Model with the Beverton-Holt Birth Function

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  • 1. School of Science, Xi'an Polytechnic University, Xi'an 710048
    2. Fundamentals Department, Air Force Engineering University, Xi'an 710051

Online published: 2022-10-15

Supported by

The China National Foundation for Studying Abroad; the Scientific Research Program Funded by Shaanxi Provincial Education Department (18JK0336).

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摘要

基于 Beverton-Holt 出生函数，考虑疾病仅在成年个体间传播且患病成年个体具有一定出生率等因素，建立了一类具有幼年和成年两个阶段的传染病模型。分析了模型平衡点的存在性，通过构造恰当的 Lyapunov 函数和定性分析，得到了模型平衡点的稳定性，并确定了模型出现后向分支的条件。最后，借助数值模拟验证了所得分析结果的正确性。

关键词： 阶段结构; 平衡点; 稳定性; 后向分支; 基本再生数

本文引用格式

胡新利, 郑田田, 杨亚莉 . 基于 Beverton-Holt 出生函数的阶段结构传染病模型的稳定性和分支[J]. 工程数学学报, 2022 , 39(4) : 599 -609 . DOI: 10.3969/j.issn.1005-3085.2022.04.008

Abstract

An epidemic model with Beverton-Holt birth rate function and two stage-structure is established, vertical transmission is considered in the model, and the disease is only transmitted among adult individuals. The existence of equilibria of the model is analyzed, and the stability of equilibria of the model is obtained by constructing Lyapunov function, and the condition for the backward bifurcation of the model is determined. Finally, the analysis result is verified by numerical simulation.

Key words： stage structure; equilibrium; stability; backward bifurcation; the basic reproduction number

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