人口转型中生育观念传播模型的建立与分析  

Modeling and analysis of a fertility concept epidemic model for the demographic transition

作　　者：刘子建 刘铭 谭远顺 杨金 庞建华[2] LIU Zi-jian;LIU Ming;TAN Yuan-shun;YANG Jin;PANG Jian-hua(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China;School of Science,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074 [2]广西科技大学理学院,广西柳州545006

出　　处：《高校应用数学学报(A辑)》2023年第4期433-457,共25页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12271068);重庆市自然科学基金创新发展联合基金(CSTB2022NSCQ-LZX0026);重庆市高校创新研究群体项目(CXQT21021);重庆市研究生联合培养基地建设项目(JDLHPYJD2021016);广西自然科学基金(2018GXNSFBA281185)。

摘　　要：借助传染病模型的思想,建立了在无或有国家鼓励生育政策下刻画人口转型中生育观念传播的常微分方程模型,给出了低生育群体到高生育群体的生育观念是否传播的阈值.基于该阈值,讨论了模型解的指数增长性,周期性,全局渐近稳定性等动力学行为.数值例子验证了理论所得结果的正确性并对模型解随参数的变化进行了更全面的讨论.In this paper,a fertility concept epidemic model for the demographic transition is presented and studied based on ideas of infectious disease models.Thresholds of fertility concepts from low tohigh fertility groups are established under conditions with or without national pronatalist policy.Dynamical behaviors such as exponential growth,periodicity,global asymptotic stability are investi-gated.Theoretical results are verifed and more discussions are conducted by using some numerical examples.

关 键 词：人口转型 侵入指数 生育观念 生育率 传播模型 

分 类 号：O193[理学—数学] O29[理学—基础数学]