具有Beddington-DeAngelis发生率的双斑块裂谷热病毒模型研究  

A Two-Patch Rift Valley Fever Virus Model with Beddington-DeAngelis Incidence

作　　者：桑瑞 吴浩 张龙[1] SANG Rui;WU Hao;ZHANG Long(College of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆应用数学重点实验室,乌鲁木齐830017

出　　处：《重庆师范大学学报（自然科学版）》2023年第3期94-105,共12页Journal of Chongqing Normal University:Natural Science

基　　金：新疆应用数学重点实验室开放课题(No.2021D04014);国家自然科学基金面上项目(No.12261087;No.11861065);新疆维吾尔自治区自然科学基金(No.2022D01E41);新疆维吾尔自治区高校科研重点项目(No.XJEDU2021I002)。

摘　　要：【目的】研究人口在斑块间扩散对裂谷热疾病传播的影响,提出了一个具有Beddington-DeAngelis发生率函数的双斑块裂谷热病毒模型。【方法】通过构造Lyapunov函数和运用LaSalle不变性原理,建立了系统无病平衡点的全局渐近稳定性准则,运用了Routh-Hurwit判别准则以及几何方法,建立了系统正平衡点全局渐近稳定性准则。【结果】得到了2个斑块的基本再生数R_(10)、R_(20),建立了系统平衡点局部和全局渐近稳定的阈值准则,并通过数值模拟对理论结果进行验证。【结论】当R_(10)≤1且R_(20)≤1时,该疾病在2个斑块中灭绝;当R_(10)>1时,该疾病在2个斑块中持续生存。[Purposes]In order to study the impact of population migration on the spread of the Rift Valley fever disease,a two-patch Rift Valley fever virus model is proposed based on the Beddington-DeAngelis incidence function.[Methods]By constructing Lyapunov function and applying LaSalle invariance principle,the global asymptotic stability of the disease-free equilibrium of the system is proved.Routh-hurwit criterion and geometric method are used to prove the stability of the positive equilibrium and the positive equilibrium of the system is global asymptotic stable.[Results]The basic regeneration number R_(10) and R_(20) of the two patches is got,established the threshold criteria for local and global asymptotic stability of the equilibrium and the theoretical results were verified by numerical simulation.[Conclusions]In two patches,the disease is extinct if R_(10)≤1,R_(20)≤1,while it is uniform persistent if R_(10)>1.

关 键 词：裂谷热 Beddington-DeAngelis功能反应 斑块模型 基本再生数 阈值动力学 

分 类 号：O175.1[理学—数学]