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

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 constructtwo differentialequation models basing on the transformation mechanism ofadolescentidiopathicscoliosis. ModelIdividesadolescents into two groups:  healthy individuals and thosewith adolescentidiopathic scoliosis, and obtains the condition forasymptotic stability ofthe posi- tive equilibrium. ModelIIdivides adolescents into four groups:healthy individuals, mild patients, moderate patients, and se- vere patients(requiring surgery) , and obtains the stability ofthree boundary equilibria. By the theory ofcharacteristic equation fordifferentialequationsand constructingLyapunov function, itisfound thatwhen therecoveryrateformed byexerciseand the recovery rate formed by braces are greater than the transfer rate, the population with adolescentidiopathic scoliosis(ModelI)  or the population with moderate adolescentidiopathic scoliosis(Model II)  willinfinitely approach zero. This fully reflects the positive effectofexercise intervention on the overallcondition ofadolescentidiopathic scoliosis.

作者：

张玉华,李海银,毕远宏

Zhang Yuhua , LiHaiyin , BiYuanhong

机构地区：

河南财经政法大学体育学院；数学与信息科学学院；内蒙古财经大学统计与数学学院；

内蒙古经济数据分析与挖掘重点实验室

引用本文：

张玉华,李海银,毕远宏.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[J].betway官方app 学报(自然科学版),2024,52(5):101-107. 

Zhang Yuhua,LiHaiyin,BiYuanhong. Construction and analysis of differentialequation modelforadolescentidiopathic scoliosis based on sports and health integration[J] .Journal of Henan NormalUniversity(NaturalScience Edition) ,2024,52(5) : 101-107. DOI: 10. 16366/j. cnki.1000-2367.  2023. 06. 13. 0004.

基金：

国家自然科学基金;河南省科技攻关项目;内蒙古自治区自然科学基金

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

adolescentidiopathic scoliosis; sports and health integration; differentialequation model; stability

分类号：

O175. 13

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.pdf