一类Wolbachia氏菌在蚊群传播的数学模型的动力学研究
Dynamics of a Mathematical Model for the Propagation of Wolbachia Bacteria in Mosquito Populations
DOI: 10.12677/AAM.2021.105195, PDF,  被引量    国家自然科学基金支持
作者: 武 丹, 刘 建：广州大学数学与信息科学学院，广东 广州
关键词: 时滞微分方程；种群动力学；Wolbachia；登革热；Hopf分支；Delay Differential Equation； Population Dynamics； Wolbachia； Dengue； Hopf Bifurcation
摘要: 蚊媒传染病是指由蚊子传播的传染病，主要包括登革热，疟疾等。一种新型的控制和预防蚊媒传染病的方式是利用内共生菌Wolbachia (沃尔巴克氏)来阻断病源体的传播。本文建立了一个新的时滞微分方程模型研究Wolbachia氏菌在蚊群中的传播。首先证明了模型解的非负性和有界性，给出了平衡点的存在条件；在各种不同的参数条件下，得到了平衡点的稳定性态；分析了Hopf分支存在的充分条件；利用中心流形定理和规范型理论给出了确定Hopf分支周期解方向和稳定性的计算公式。最后用数值模拟验证了理论结果。
Abstract: Mosquito-borne diseases are infectious diseases transmitted by mosquitoes, including dengue fever and malaria. A new way to control and prevent mosquito-borne infectious diseases is to use the endosymbiotic bacterium Wolbachia to interrupt the transmission of the pathogen. In this paper, a new delay differential equation model was established to study the transmission of Wolbachia in mosquito population. First of all, the nonnegative and boundedness of solutions of the model are proved, and the existence condition of the equilibrium points is given. The asymptotic stability of the equilibrium is obtained in different situations. Sufficient conditions are analyzed which ensures that Hopf bifurcation occurs. The computational formulas for direction and stability of Hopf bifurcation are given by applying the center manifold theorem and norm form theory. Finally, numerical simulations are provided to demonstrate the theoretical results.
文章引用：武丹, 刘建. 一类Wolbachia氏菌在蚊群传播的数学模型的动力学研究[J]. 应用数学进展, 2021, 10(5): 1855-1869. https://doi.org/10.12677/AAM.2021.105195

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