| 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北大核心CSCD |
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| 引用本文： | 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北大核心CSCD[J]. 工程数学学报, 2022, 39(4): 599-609. DOI: 10.3969/j.issn.1005-3085.2022.04.008 |
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| 作者姓名： | 胡新利 郑田田 杨亚莉 |
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| 作者单位： | 1. 西安工程大学理学院，西安 7100482. 空军工程大学基础部，西安 710051 |
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| 基金项目： | 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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| 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。
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| 关 键 词： | 阶段结构 平衡点 稳定性 后向分支 基本再生数 |
Stability and Bifurcation in a Stage-structured Epidemic Model with the Beverton-Holt Birth Function |
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| HU Xinli,ZHENG Tiantian,YANG Yali. Stability and Bifurcation in a Stage-structured Epidemic Model with the Beverton-Holt Birth Function[J]. Chinese Journal of Engineering Mathematics, 2022, 39(4): 599-609. DOI: 10.3969/j.issn.1005-3085.2022.04.008 |
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| Authors: | HU Xinli ZHENG Tiantian YANG Yali |
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| Affiliation: | 1. School of Science, Xi'an Polytechnic University, Xi'an 710048;2. Fundamentals Department, Air Force Engineering University, Xi'an 710051; |
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| 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. |
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| Keywords: | stage structure equilibrium stability backward bifurcation the basic reproduction number |
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