一类具有不同扩散速率的蚊媒模型的动力学

doi:10.6040/j.issn.1671-9352.0.2023.434

摘要/Abstract

摘要： 为研究宿主的扩散和空间异质性对蚊媒疾病传播的影响,建立一类具有不同扩散速率的反应扩散蚊媒疾病模型。首先,基于下一代算子理论定义模型的基本再生数R0,并分析大扩散和小扩散对R0的影响;其次,利用动力系统的持续性理论,证明R0-1的符号决定模型的全局阈值动力学;最后,通过数值模拟验证理论结果,并表明空间异质性可能会增加疾病传播的风险。

关键词: 蚊媒疾病, 空间异质性, 基本再生数, 阈值动力学

Abstract: In order to study the impact of host dispersal and spatial heterogeneity on the spread of mosquito-borne diseases, a reactive-diffusion mosquito-borne disease model with different diffusion rates is established. Firstly, the next-generation operator theory is applied to define the basic reproduction number R₀ of the model, and the asymptotic behavior of R₀ as the diffusion coefficient tending to zero and infinity is analyzed respectively. Secondly, according to the persistence theory of dynamical systems, it is proved that the sign of R₀-1 determines the global threshold dynamics of the model. Finally, numerical simulations validate the theoretical results and show that spatial heterogeneity may increase the risk of disease transmission.

Key words: mosquito-borne diseases, spatial heterogeneity, basic reproduction number, threshold dynamics

中图分类号:

押宝,何杰. 一类具有不同扩散速率的蚊媒模型的动力学[J]. 《山东大学学报(理学版)》, 2025, 60(12): 38-48.

YA Bao, HE Jie. Dynamics of a mosquito-borne model with distinct dispersal rates[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 38-48.

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