应用于HIV感染数学模型的无条件稳定非标准有限差分法

Hasim A. Obaid, R. Ouifki, K. Patidar
{"title":"应用于HIV感染数学模型的无条件稳定非标准有限差分法","authors":"Hasim A. Obaid, R. Ouifki, K. Patidar","doi":"10.2478/amcs-2013-0027","DOIUrl":null,"url":null,"abstract":"We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.","PeriodicalId":253470,"journal":{"name":"International Journal of Applied Mathematics and Computer Sciences","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection\",\"authors\":\"Hasim A. Obaid, R. Ouifki, K. Patidar\",\"doi\":\"10.2478/amcs-2013-0027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.\",\"PeriodicalId\":253470,\"journal\":{\"name\":\"International Journal of Applied Mathematics and Computer Sciences\",\"volume\":\"45 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Applied Mathematics and Computer Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/amcs-2013-0027\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mathematics and Computer Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/amcs-2013-0027","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 17

摘要

本文提出并分析了HIV传播动力学数学模型的一种无条件稳定非标准有限差分方法。用动力系统的定性理论研究了该模型的动力学。本文提出的数值方法保留了连续模型的这些定性特征。该方法还保留了解的正性,这是传染病建模的基本要求之一。提供了可靠的数值结果,证实了理论研究。还与其他常规方法进行了比较,这些方法通常用于解决此类问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection
We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.
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:604180095
Book学术官方微信