具有环境传播和生理年龄结构的霍乱模型研究

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (2): 157-164.

具有环境传播和生理年龄结构的霍乱模型研究

亢跃男, 郭文丹, 聂麟飞^*

新疆大学数学与系统科学学院, 新疆乌鲁木齐 830046

收稿日期:2022-03-15 出版日期:2023-04-28 发布日期:2023-05-05
通讯作者: 聂麟飞(1978-),男,河南扶沟人,博士,教授.Email:lfnie@163.com
基金资助:
新疆维吾尔自治区自然科学基金(2021D01E12)

Dynamics of a Cholera model with environmental transmission and physiological age structure

KANG Yue-nan, GUO Wen-dan, NIE Lin-fei

College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Received:2022-03-15 Online:2023-04-28 Published:2023-05-05

摘要/Abstract

摘要： 基于霍乱在人群和环境之间的传播规律, 以及生物体间个体的差异性, 提出一类具有环境传播和生理年龄结构的霍乱模型, 并利用半群理论证明了模型全局正解的存在唯一性. 进一步, 通过线性近似方法推导出基本再生数R₀的表达式并得出结论: 当R₀<1时, 无病平衡态是全局渐近稳定的; 当R₀>1时, 无病平衡态是不稳定的, 模型存在唯一的地方病平衡态且在一定条件下是局部渐近稳定的. 通过数值模拟解释了主要的理论结果.

关键词: 霍乱, 年龄结构, 环境传播, 基本再生数, 平衡态与稳定性

Abstract: Based on the rules of Cholera transmission between humans and environment, as well as individual differences between humans, a Cholera model with environmental transmission and physiological age structure is proposed, and the existence and uniqueness of the global positive solution of this model are proved by semigroup theory. Furthermore, the expression of basic reproduction number R₀ is derived by linear approximation method, it is concluded that if R₀<1, the disease-free steady state is globally asymptotically stable; if R₀>1, the disease-free steady state is unstable, and the model has a unique endemic steady state and is locally asymptotically stable under certain conditions. The main theoretical results are explained by numerical simulation.

Key words: cholera, age-structured, environmental transmission, basic reproduction number, steady state and stability

中图分类号:

O175

亢跃男, 郭文丹, 聂麟飞. 具有环境传播和生理年龄结构的霍乱模型研究[J]. 兰州理工大学学报, 2023, 49(2): 157-164.

KANG Yue-nan, GUO Wen-dan, NIE Lin-fei. Dynamics of a Cholera model with environmental transmission and physiological age structure[J]. Journal of Lanzhou University of Technology, 2023, 49(2): 157-164.

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