Mathematical analysis for a HIV model with quadratic logistic growth term

在过去的三十多年中，对于导致艾滋病（AIDS）的人类免疫缺陷病毒（HIV）的研究，已经建立过大量的数学模型。过去的研究方向主要分为两类：(i)艾滋病传染病学；(ii)艾滋病毒作为病原体的免疫学。在本文中，我们主要采用第二种途径。 艾滋病毒感染的主要目标是淋巴细胞，或白血细胞，统称为CD4$^+$T细胞。CD4$^+$T细胞个数正常标准大约是1000个/mm$^{3}$，当病人体内减少到200个/mm$^{3}$或以下时，病人便被诊断为患有艾滋病了。 数学模型是了解艾滋病毒动力过程的非常有价值的工具。人们建立了大量的模型来描述人体免疫系统，它与艾滋病毒的相互作用以及CD4$^+$T细胞数的减...Over the past thirty years, there has been much research in the mathematical modeling of Human Immunodeficiency Virus (HIV), the virus which causes AIDS (Acquired Immune Deficiency Syndrome). The research directions have been twofold: (i) the epidemiology of AIDS; (ii) the immunology of HIV as a pathogen. In this thesis we are interested in the latter approach. The major target of HIV infection...学位：理学博士院系专业：数学科学学院信息与计算数学系_计算数学学号：1902009015360

THE FINITE ELEMENT INTERPOLATED CORRECTION METHOD FOR NONSELFADJOINT ELLIPTIC EIGENVALUE PROBLEMS

本文研究非自共轭椭圆特征值问题有限元插值校正方案.基于插值校正和广义rAylEIgH商加速技巧,用三角形线性元二次插值、双二次元双四次插值得到了较好的结果,并用三线性元的三二次插值将插值校正推广到三维.This paper discusses interpolated correction method for nonselfadjoint elliptic eigenvalue problem.Based on the interpolated correction method and acceleration of the generalized Rayleigh quotient,by quadratic interpolation for linear triangle elements and bi-quartic interpolation for bi-quadratic elements,we obtained elegant results.Furthermore,we generalized the correction of interpolation to 3D case by the tri-quadratic interpolation for trilinear elements.国家自然科学基金资助项目(No.10761003

TWO-DIMENSIONAL STABILITY ANALYSIS IN A HIV MODEL WITH QUADRATIC LOGISTIC GROWTH TERM

Fujian Administration of Foreign Expert Affairs, China [SZ2011008]We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-dimensional environment. The model consists of two ODEs for the concentrations of the target T cells, the infected cells, and a parabolic PDE for the virus particles. We study the stability of the uninfected and infected equilibria, the occurrence of Hopf bifurcation and the stability of the periodic solutions