摘要
性接触是性传播疾病的主要传播途径,通过性关系连接起来的一种社会关系而形成的性接触网络,在性接触网络上研究性传播疾病更加切合实际,建立的性传播疾病模型更加精确.因此,该文在性接触网络上考虑了含有异性恋的性传播疾病,建立了易感者-感染者-易感者(SIS)传播模型.利用网络上对逼近方法,将模型变为一个8维封闭常微分系统,计算出了模型的基本再生数R0.当R0<1时,证明了无病平衡点是局部渐近稳定的;当R0>1时,获得了满足不同条件时正平衡点的存在性.并且满足一定条件时,系统会出现后向分支.最后,通过数值模拟验证了理论结果的正确性,为分析性传播疾病提供了理论依据.
Sexual contact is the main transmission route of sexually transmitted diseases, which is a social relationship by sexual relations forms sexual contact network. It is more practical and accurate to establish a model to study sexually transmitted diseases on the sexual contact network.Therefore, the susceptible-infected-susceptible(SIS) model on the sexual contact network is established in this article. Using pair approximation method, the system becomes 8 dimensions system. We calculate the basic reproduction number R0. When R0<1, the disease-free equilibrium is locally asymptotically stable. When R0>1, the existence of positive equilibrium is obtained under different conditions. When certain condition is met, backward branch appears. Finally, the theoretical results are verified by numerical simulation, which provides a theoretical basis for the analysis of sexually transmitted diseases.
作者
赵小倩
秦鹏
张菊平
ZHAO Xiaoqian;QIN Peng;ZHANG Juping(School of Science,North University of China,Taiyuan 030051,China;School of Electrical and Control Engineering,North University of China,Taiyuan 030051,China;Complex Systems Research Center,Shanxi University,Taiyuan 030051,China)
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2020年第1期5-11,共7页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金项目(11301491)
山西省自然科学基金项目(2018021008)
关键词
规则网络
对逼近
基本再生数
平衡点
稳定性
regular network
pair approximation
peproduction number
equilibrium
stability
