一类具有非线性发生率的时滞戒烟模型  

A Delayed Quit Smoking Model with Nonlinear Incidence Rate

作　　者：张子振[1] 张伟诗 宋志强 ZHANG Zizhen;ZHANG Weishi;SONG Zhiqiang(School of Management Science and Engineering,Anhui University of Finance and Economics,Bengbu 233030,China;College of Mechanical and Electrical Engineering,Hulunbuir University,Hulunbuir 021008,China)

机构地区：[1]安徽财经大学管理科学与工程学院,安徽蚌埠233030 [2]呼伦贝尔学院机电工程学院,内蒙古呼伦贝尔021008

出　　处：《滨州学院学报》2023年第6期44-50,共7页Journal of Binzhou University

基　　金：国家自然科学基金项目(12061033);安徽财经大学研究生科研创新项目(ACYC2022111)。

摘　　要：提出并研究一类具有非线性发生率的时滞戒烟模型,该模型将人群划分为潜在吸烟者、轻度吸烟者、习惯吸烟者和戒烟者4个子群体。推导得到模型的基本再生数和吸烟平衡点后,以戒烟者重新变成潜在吸烟者的临时免疫期时滞为分岔参数讨论了Hopf分岔的存在性,并计算出模型产生Hopf分岔的时滞临界点。最后给出仿真示例验证了所得结果的正确性。A delayed quit smoking model with nonlinear incidence is proposed and investigated.The model includes four compartments:potential smokers,light smokers,habitual smokers and quit smokers.After deriving the basic regeneration number and smoking equilibrium point of the model,the existence of Hopf bifurcation is discussed with the bifurcation parameter of the temporary immunity period for quitters to potential smokers,and the time lag threshold for the Hopf bifurcation of the model is calculated.Finally,a simulation example is given to verify the correctness of the obtained results.

关 键 词：时滞 戒烟模型 HOPF分岔 基本再生数 

分 类 号：O175.12[理学—数学]