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具有多时滞的血吸虫传染病模型稳定性和Hopf分支分析
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Abstract:
考虑血吸虫在中间宿主钉螺和终极宿主人体内的潜伏期，本文建立一类具有潜伏期时滞的血吸虫传播动力学模型，证明模型全局正解的存在性与最终有界性，给出疾病的基本再生数，研究无病平衡点的存在性与稳定性，讨论模型地方病平衡态的存在性与稳定性，探讨Hopf分支的存在性，以及模型关键参数对基本再生数的影响，探究潜伏期时滞在血吸虫传播和防控中的作用和地位。
Considering the incubation period of Schistosoma in the intermediate host, the snail, and the ultimate host, the human, this paper establishes a Schistosome model with multi-delays, proves the existence and ultimate boundedness of the global positive solutions of this model. And then, the basic reproduction number is given, which describes the existence and stability of the disease free equilibrium, the existence and stability of the endemic equilibrium. Further, the existence of the Hopf bifurcation, the influence of the key parameters on the basic reproduction number and the role of delay in the transmission and control of this disease are discussed.
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