一类具有潜伏周期的空间异质反应扩散梅毒模型动力学分析
Dynamical Analysis of a Reaction-Diffusion Syphilis Model with a Fixed Latent Period and Spatial Heterogeneity
方诚 1吴鹏 2何泽荣2
作者信息
- 1. 浙江财经大学数据科学学院,杭州 310018
- 2. 杭州电子科技大学理学院,杭州 310018
- 折叠
摘要
该文研究了一类具有潜伏周期的异质空间扩散的梅毒模型的阈值动力学行为.首先讨论了系统解的全局存在性以及系统全局吸引子的存在性.其次,根据传染病模型下一代再生算子定义推导出模型的动力学阈值-基本再生数R0.具体地,当R0＜1,无病平衡态是全局吸引的;根据耗散系统的持久性理论证明了当R0＞1时疾病是一致持久的.最后,在空间同质情形下,推导出模型基本再生数R0的显示表达式.此外,除了证明无病平衡点的全局稳定之外,还利用波动引理证明了系统正平衡点的全局稳定性.
Abstract
In this paper,a reaction-diffusion Syphilis model with a fixed latent pe-riod and spatial heterogeneity is formulated to study the transmission dynamics of syphilis among population.Firstly,the authors discuss the global existence and at-tractor of the solution for the system.Secondly,based on the definition the next generation operator for the disease compartment model,as the threshold of the dy-namics,the basic reproduction number R0 is derived.Specifically,the authors show that the disease-free steady state is globally attractive when R0＜1 and the uniform persistence of the disease is proved by the persistence theory for dissipative system.Finally,in space homogeneous case,the explicit expression of the basic reproduc-tion number R0 is derived.Moreover,the authors prove the global stability of the disease-free and the endemic equilibria by Fluctuation lemma.
关键词
梅毒模型/潜伏周期/空间异质性/反应扩散/基本再生数/阈值动力学Key words
Syphilis model/latent period/spatial heterogeneity/reaction diffusion/the basic reproduction number/threshold dynamics引用本文复制引用
基金项目
国家自然科学基金(12201557)
国家自然科学基金(11871185)
浙江省教育厅一般项目(Y202249921)
浙江省统计研究项目(23TJQN12)
浙江省一流学科资助课题(浙江财经大学统计A类)()
出版年
2024
NETL
NSTL
万方数据