基于体卫融合的青少年特发性脊柱侧弯微分方程模型建构及分析  

Construction and analysis of differential equation model for adolescent idiopathic scoliosis based on sports and health integration

作　　者：张玉华 李海银 毕远宏 Zhang Yuhua;Li Haiyin;Bi Yuanhong(Institute of Physical Education,Henan University of Economics and Law,Zhengzhou 450046,China;Department of Mathematics and Information,Henan University of Economics and Law,Zhengzhou 450046,China;School of Statistics and Mathematics,Inner Mongolia University of Finance and Economics,Hohhot 010070,China;Inner Mongolia Key Laboratory for Economic Date Analysis and Mining,Inner Mongolia University of Finance and Economics,Hohhot 010070,China)

机构地区：[1]河南财经政法大学体育学院,郑州450046 [2]河南财经政法大学数学与信息科学学院,郑州450046 [3]内蒙古财经大学统计与数学学院,呼和浩特010070 [4]内蒙古财经大学内蒙古经济数据分析与挖掘重点实验室,呼和浩特010070

出　　处：《河南师范大学学报（自然科学版）》2024年第5期101-107,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12062017);河南省科技攻关项目(232102320306);内蒙古自治区自然科学基金(2021ZD01).

摘　　要：以体卫融合为切入点,根据青少年特发性脊柱侧弯转变机理构建两个微分方程模型.模型Ⅰ把青少年分为健康者和患有青少年特发性脊柱侧弯两类人群,得到正平衡点渐近稳定的条件.模型Ⅱ把青少年细分为健康者、轻度患者、中度患者和重度患者(需要手术)4类人群,得到3个边界平衡点的稳定性.由微分方程特征方程理论和构造李雅普诺夫函数得到,当运动形成的恢复率和支具形成的恢复率大于转移率时,患有青少年特发性脊柱侧弯的人群(模型Ⅰ)或中度患有青少年特发性脊柱侧弯的人群(模型Ⅱ)都会无限趋向于零.充分体现了运动对青少年特发性脊柱侧弯整体病情的正作用干预.In this paper,sports and health integration is taken as the entry point,we construct two differential equation models basing on the transformation mechanism of adolescent idiopathic scoliosis.Model I divides adolescents into two groups:healthy individuals and those with adolescent idiopathic scoliosis,and obtains the condition for asymptotic stability of the positive equilibrium.Model II divides adolescents into four groups:healthy individuals,mild patients,moderate patients,and severe patients(requiring surgery),and obtains the stability of three boundary equilibria.By the theory of characteristic equation for differential equations and constructing Lyapunov function,it is found that when the recovery rate formed by exercise and the recovery rate formed by braces are greater than the transfer rate,the population with adolescent idiopathic scoliosis(Model I)or the population with moderate adolescent idiopathic scoliosis(Model II)will infinitely approach zero.This fully reflects the positive effect of exercise intervention on the overall condition of adolescent idiopathic scoliosis.

关 键 词：青少年特发性脊柱侧弯 体卫融合 微分方程模型 稳定性 

分 类 号：O175.13[理学—数学]