{"title":"Numerical analysis of an age-structured model for HIV viral dynamics with latently infected T cells based on collocation methods","authors":"Mengna Li, Zhanwen Yang","doi":"10.1016/j.matcom.2024.09.028","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we consider the numerical threshold for an age-structured HIV model with latently infected T cells. Based on the continuous collocation methods, a semi-discrete scheme is constructed by discretizing the age variable and a numerical basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> is provided. With the study of higher-order convergence to the real basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the relations between <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> and local stability of disease-free are presented. From the viewpoint of full discretization, an equivalent block-Leslie matrix expression is obtained by embedding into a piecewise-discontinuous polynomial space rather than the piecewise-continuous polynomial space. An implicit full-discrete scheme is considered based on a linearly implicit Euler (IMEX) method, of which the computational cost is almost the same as an explicit scheme. It is more important that the dynamical behavior of the age-semi-discretization system is also preserved for any time step whenever <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> is the threshold for the numerical dynamical system of the age-semi-discretization. Finally, numerical applications are shown to HIV models to illustrate our analysis.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"230 ","pages":"Pages 289-305"},"PeriodicalIF":4.4000,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378475424003835","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the numerical threshold for an age-structured HIV model with latently infected T cells. Based on the continuous collocation methods, a semi-discrete scheme is constructed by discretizing the age variable and a numerical basic reproduction number is provided. With the study of higher-order convergence to the real basic reproduction number , the relations between and local stability of disease-free are presented. From the viewpoint of full discretization, an equivalent block-Leslie matrix expression is obtained by embedding into a piecewise-discontinuous polynomial space rather than the piecewise-continuous polynomial space. An implicit full-discrete scheme is considered based on a linearly implicit Euler (IMEX) method, of which the computational cost is almost the same as an explicit scheme. It is more important that the dynamical behavior of the age-semi-discretization system is also preserved for any time step whenever is the threshold for the numerical dynamical system of the age-semi-discretization. Finally, numerical applications are shown to HIV models to illustrate our analysis.
期刊介绍:
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
Topics covered by the journal include mathematical tools in:
•The foundations of systems modelling
•Numerical analysis and the development of algorithms for simulation
They also include considerations about computer hardware for simulation and about special software and compilers.
The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research.
The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.