考虑到空间扩散扰动、集中影响和环境曲率的传染病动力学建模

IF 0.1
S. Baranovsky
{"title":"考虑到空间扩散扰动、集中影响和环境曲率的传染病动力学建模","authors":"S. Baranovsky","doi":"10.17721/2706-9699.2021.1.02","DOIUrl":null,"url":null,"abstract":"While the study of the interaction patterns of the immune system and the viruses detected in the body wide variety of models is used. Well-known infectious disease model by Marchuk which describes the most common mechanisms of immune defense, was obtained under the assumption that the environment of the \"organism\" is homogeneous and unlimited, in which all the active factors of the process are instantly mixed. The approach proposed by the authors to take into account the influence of spatially distributed diffusion \"redistributions\" on the nature of the infectious disease provides an opportunity to detect the reducing effect the model level of maximum antigen concentration at the infection epicenter due to their diffusion \"erosion\" in the disease development. In particular, in cases where the viral particles concentration at the initial time or the intensity of a concentrated source of viruses in any part of the body of infection exceeds a certain critical level of the immunological barrier such an effect of diffusion \"redistribution\" in a short time reduces supercritical concentrations of viral particles to values, in particular, already below the critical level and their further neutralization may be ensured by the existing level of own antibodies concentration or requires a more economical procedure of injection with a lower donor antibodies concentration. In this article the infectious disease mathematical model is generalized to take into account the curvature of the bounded environment in the conditions of spatial diffusion perturbations, convection and the presence of various concentrated influences. The corresponding singularly perturbed model problem with delay is reduced to a sequence of \"solvable\" problems without delay. The influence of \"curvature\" of a limited environment on the development of an infectious disease in the conditions of diffusion perturbations, convection and concentrated influences is illustrated.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"MODELING THE DYNAMICS OF AN INFECTIOUS DISEASE TAKING INTO ACCOUNT SPATIAL-DIFFUSE PERTURBATIONS, CONCENTRATED INFLUENCES AND ENVIRONMENT CURVATURE\",\"authors\":\"S. Baranovsky\",\"doi\":\"10.17721/2706-9699.2021.1.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"While the study of the interaction patterns of the immune system and the viruses detected in the body wide variety of models is used. Well-known infectious disease model by Marchuk which describes the most common mechanisms of immune defense, was obtained under the assumption that the environment of the \\\"organism\\\" is homogeneous and unlimited, in which all the active factors of the process are instantly mixed. The approach proposed by the authors to take into account the influence of spatially distributed diffusion \\\"redistributions\\\" on the nature of the infectious disease provides an opportunity to detect the reducing effect the model level of maximum antigen concentration at the infection epicenter due to their diffusion \\\"erosion\\\" in the disease development. In particular, in cases where the viral particles concentration at the initial time or the intensity of a concentrated source of viruses in any part of the body of infection exceeds a certain critical level of the immunological barrier such an effect of diffusion \\\"redistribution\\\" in a short time reduces supercritical concentrations of viral particles to values, in particular, already below the critical level and their further neutralization may be ensured by the existing level of own antibodies concentration or requires a more economical procedure of injection with a lower donor antibodies concentration. In this article the infectious disease mathematical model is generalized to take into account the curvature of the bounded environment in the conditions of spatial diffusion perturbations, convection and the presence of various concentrated influences. The corresponding singularly perturbed model problem with delay is reduced to a sequence of \\\"solvable\\\" problems without delay. The influence of \\\"curvature\\\" of a limited environment on the development of an infectious disease in the conditions of diffusion perturbations, convection and concentrated influences is illustrated.\",\"PeriodicalId\":40347,\"journal\":{\"name\":\"Journal of Numerical and Applied Mathematics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17721/2706-9699.2021.1.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17721/2706-9699.2021.1.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在研究免疫系统与体内检测到的病毒的相互作用模式时,使用了各种各样的模型。Marchuk著名的传染病模型描述了最常见的免疫防御机制,该模型是在假设“有机体”的环境是同质的和无限的,其中所有过程的活性因素都是瞬间混合的情况下得到的。作者提出的考虑到空间分布的扩散“再分布”对传染病性质的影响的方法,提供了一个机会来检测由于它们在疾病发展中的扩散“侵蚀”而导致的感染中心最大抗原浓度模型水平的降低效应。特别是,当病毒颗粒在初始时刻的浓度或感染身体任何部位的病毒浓缩源的强度超过免疫屏障的某一临界水平时,这种在短时间内扩散“再分配”的作用将病毒颗粒的超临界浓度降低到值,特别是,已经低于临界水平,其进一步的中和可以通过现有的自身抗体浓度水平来保证,或者需要更经济的注射程序,使用较低的供体抗体浓度。本文将传染病数学模型推广到考虑有界环境在空间扩散扰动、对流和各种集中影响存在的条件下的曲率。将相应的具有时滞的奇摄动模型问题简化为一系列无时滞的“可解”问题。说明了在扩散扰动、对流和集中影响条件下,有限环境的“曲率”对传染病发展的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
MODELING THE DYNAMICS OF AN INFECTIOUS DISEASE TAKING INTO ACCOUNT SPATIAL-DIFFUSE PERTURBATIONS, CONCENTRATED INFLUENCES AND ENVIRONMENT CURVATURE
While the study of the interaction patterns of the immune system and the viruses detected in the body wide variety of models is used. Well-known infectious disease model by Marchuk which describes the most common mechanisms of immune defense, was obtained under the assumption that the environment of the "organism" is homogeneous and unlimited, in which all the active factors of the process are instantly mixed. The approach proposed by the authors to take into account the influence of spatially distributed diffusion "redistributions" on the nature of the infectious disease provides an opportunity to detect the reducing effect the model level of maximum antigen concentration at the infection epicenter due to their diffusion "erosion" in the disease development. In particular, in cases where the viral particles concentration at the initial time or the intensity of a concentrated source of viruses in any part of the body of infection exceeds a certain critical level of the immunological barrier such an effect of diffusion "redistribution" in a short time reduces supercritical concentrations of viral particles to values, in particular, already below the critical level and their further neutralization may be ensured by the existing level of own antibodies concentration or requires a more economical procedure of injection with a lower donor antibodies concentration. In this article the infectious disease mathematical model is generalized to take into account the curvature of the bounded environment in the conditions of spatial diffusion perturbations, convection and the presence of various concentrated influences. The corresponding singularly perturbed model problem with delay is reduced to a sequence of "solvable" problems without delay. The influence of "curvature" of a limited environment on the development of an infectious disease in the conditions of diffusion perturbations, convection and concentrated influences is illustrated.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信