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


A Two-Patch Rift Valley Fever Virus Model with Beddington-DeAngelis Incidence
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    【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R10、R20,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R10≤1且R20≤1时,该疾病在2个斑块中灭绝;当R10>1时,该疾病在2个斑块中持续生存。

    Abstract:

    [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 R10 and R20 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 R10≤1, R20≤1, while it is uniform persistent if R10>1

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桑瑞,吴浩,张龙.具有Beddington-DeAngelis发生率的双斑块裂谷热病毒模型研究[J].重庆师范大学学报自然科学版,2023,40(3):94-105

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  • 在线发布日期: 2023-07-27