{"title":"阿尔茨海默病模型中低聚物对[公式省略]-淀粉样蛋白和Ca2+相互作用的病理影响的研究","authors":"Mingyan Dong , Yongxin Zhang , Gui-Quan Sun , Zun-Guang Guo , Jiao Zhang","doi":"10.1016/j.aml.2024.109407","DOIUrl":null,"url":null,"abstract":"<div><div>Alzheimer’s disease (AD) is characterized by the progressive deposition of <span><math><mi>β</mi></math></span>-amyloid (A<span><math><mi>β</mi></math></span>) plaques in the brain, where the A<span><math><mi>β</mi></math></span> oligomers have been confirmed to produce the critical cytotoxicity during the disease process. In this study, a model is established to describe the effect of A<span><math><mi>β</mi></math></span> oligomers on the interplay between A<span><math><mi>β</mi></math></span> and Ca<sup>2＋</sup>. Mathematical analysis demonstrates the existence and stability of the equilibria and the conditions under which backward bifurcation and saddle–node bifurcation occur are proposed. In addition, the aggregate reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is introduced to characterize the progression of AD. These results may offer valuable insights for studying AD-related medical strategies.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109407"},"PeriodicalIF":2.9000,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A study in Alzheimer’s disease model for pathological effect of oligomers on the interplay between β-amyloid and Ca2＋\",\"authors\":\"Mingyan Dong , Yongxin Zhang , Gui-Quan Sun , Zun-Guang Guo , Jiao Zhang\",\"doi\":\"10.1016/j.aml.2024.109407\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Alzheimer’s disease (AD) is characterized by the progressive deposition of <span><math><mi>β</mi></math></span>-amyloid (A<span><math><mi>β</mi></math></span>) plaques in the brain, where the A<span><math><mi>β</mi></math></span> oligomers have been confirmed to produce the critical cytotoxicity during the disease process. In this study, a model is established to describe the effect of A<span><math><mi>β</mi></math></span> oligomers on the interplay between A<span><math><mi>β</mi></math></span> and Ca<sup>2＋</sup>. Mathematical analysis demonstrates the existence and stability of the equilibria and the conditions under which backward bifurcation and saddle–node bifurcation occur are proposed. In addition, the aggregate reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is introduced to characterize the progression of AD. These results may offer valuable insights for studying AD-related medical strategies.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"163 \",\"pages\":\"Article 109407\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-11-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924004270\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924004270","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A study in Alzheimer’s disease model for pathological effect of oligomers on the interplay between β-amyloid and Ca2＋
Alzheimer’s disease (AD) is characterized by the progressive deposition of -amyloid (A) plaques in the brain, where the A oligomers have been confirmed to produce the critical cytotoxicity during the disease process. In this study, a model is established to describe the effect of A oligomers on the interplay between A and Ca2＋. Mathematical analysis demonstrates the existence and stability of the equilibria and the conditions under which backward bifurcation and saddle–node bifurcation occur are proposed. In addition, the aggregate reproduction number is introduced to characterize the progression of AD. These results may offer valuable insights for studying AD-related medical strategies.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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