具有两阶段结构的登革热传染病时滞动力学模型
A Time-Delay Dynamic Model of Dengue Fever Infection with Two-Stage Structure
摘要: 建立了一类幼年个体与成年个体因户外活动时间不同而造成被媒介个体叮咬的概率不同以及媒介个体具有潜伏期的登革热传染病时滞动力学模型。首先给出了模型的基本再生数R0，并证明了正平衡点的唯一存在性。其次，通过构造Lyapunov泛函，证明了无病平衡点的全局稳定性，证明了时滞参数τ = 0时地方病平衡点的全局稳定性；结合cardon公式给出了时滞参数τ = 0时地方病平衡点局部渐进稳定的条件和系统存在Hopf分支的条件。最后通过数值模拟验证了结论。
Abstract: A time-delay dynamic model of dengue fever infection was established, in which the probability of being bitten by a vector was different between young and adult due to the different time of outdoor activities and the vector had an incubation period. Firstly, the basic regeneration number R0 of the model is given, and the unique existence of the positive equilibrium point is proved. Secondly, by constructing Lyapunov functional, the global stability of disease-free equilibrium point is proved, and the global stability of endemic equilibrium point with delay parameter τ = 0 is proved; combined with cardon formula, the conditions of local asymptotic stability of endemic equilibrium point with delay parameter τ = 0 and the condition of Hopf branch are given. Finally, the results are verified by numerical simulation.
文章引用：杨艳红, 刘贤宁. 具有两阶段结构的登革热传染病时滞动力学模型[J]. 应用数学进展, 2024, 13(4): 1378-1390. https://doi.org/10.12677/aam.2024.134129

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