在线阅读 --自然科学版 2020年3期《考虑信息变量呈Logistic自然增长的SIRS传染病模型》
考虑信息变量呈Logistic自然增长的SIRS传染病模型--[在线阅读]
周苗, 刘茂省
中北大学 理学院, 山西 太原 030051
起止页码: 193--199页
DOI: 10.13763/j.cnki.jhebnu.nse.2020.03.002
摘要
为了研究信息变量对传染病传播动力学的影响,从而对传染病能够进行有效预防,结合现实情况建立了一个信息变量呈Logistic自然增长的SIRS传染病模型.首先计算基本再生数,然后研究了无病平衡点和地方病平衡点的存在性和稳定性的条件,并得到了在地方病平衡点处产生Hopf分支的条件,发现信息自然承载量的变化可能导致传染病的传播呈周期性震荡.

SIRS Epidemic Model with Logistic Natural Growth of Information Variable
ZHOU Miao, LIU Maoxing
School of Science, North University of China, Shanxi Taiyuan 030051, China
Abstract:
In order to study the influence of information variables on the transmission dynamics of infectious diseases and thus effectively prevent infectious diseases,we realistically establish a SIRS epidemic model with information variables showing Logistic natural growth.We first calculate the basic reproduction number,and then study the conditions for the existence and stability of disease-free equilibrium and endemic equilibrium.Finally,we obtain the conditions under which Hopf bifurcation emerges at endemic equilibrium,and find that the change of natural carrying capacity of information may lead to the periodic oscillation of infectious diseases.

收稿日期: 2019-09-12
基金项目: 国家自然科学基金(11571324,11701528);山西省自然科学基金(201601D021015)

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