河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
中国期刊方阵入选期刊
中国高校优秀科技期刊
华北优秀期刊
河北省优秀科技期刊

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一类流行性出血热周期模型的动力学分析

李凤¹

刘俊利²

（1.西安医学高等专科学校基础部，陕西西安 710309； 2.西安工程大学理学院，陕西西安 710032）
DOI： 10.13763/j.cnki.jhebnu.nse.202201007

Dynamic Analysis of an Epidemic Hemorrhagic Fever Periodic Model

LI Feng¹，LIU Junli²

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摘要/Abstract

摘要：

考虑到流行性出血热的季节性爆发，建立了一类具有周期系数的流行性出血热模型.利用积分算子的谱半径得到了模型的基本再生数R₀，R₀决定了疾病的灭绝和一致持久性.通过Poincare映射讨论了模型的一致持续生存，并通过数值模拟验证了当R₀=0.168 5＜1时，无病平衡点全局渐近稳定，说明疾病灭绝;当R₀=8.797 1＞1时，无病周期解不稳定，系统的解趋向于一个正周期解，说明疾病持续生存.

Abstract：

Due to the seasonal outbreak of epidemic hemorrhagic fever，an epidemic hemorrhagic fever model with periodic coefficients was established. Using the spectral radius of the integral operator，the basic reproduction number R₀ was obtained，and it determines the extinction and uniform persistence of disease.The uniform persistence of the model was discussed by Poincare map. Finally，the theoretical results are verified by numerical simulations. It shows that when R₀=0.168 5＜1, the disease-free equilibrium point is globally asymptotically stable and the disease dies out; when R₀=8.797 1＞1, the disease-free periodic solution is unstable，and the system solution tends to a positive periodic solution so the disease persists.

关键词

关键词： 流行性出血热 ; 基本再生数 ; 稳定性 ; 周期解 ; 一致持久性

Key words： epidemic hemorrhagic fever ; basic reproduction number ; stability ; periodic solution ; uniform persistence

参考文献 19

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