具有高危易感年龄和潜伏期年龄的HIV传播模型研究

王雅萍; 王生福; 聂麟飞

doi:10.13568/j.cnki.651094.651316.2022.04.06.0001

您当前的位置：

首页 >

文章列表页 >

具有高危易感年龄和潜伏期年龄的HIV传播模型研究

数理科学 | 更新时间：2026-01-21

- 具有高危易感年龄和潜伏期年龄的HIV传播模型研究
- 具有高危易感年龄和潜伏期年龄的HIV传播模型研究
- 新疆大学学报（自然科学版中英文） 2023年40卷第2期页码：160-168
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金“多宿主传染病模型动力学分析及应用”（11961066）;新疆维吾尔自治区自然科学基金“基于异质性的艾滋病传播的数学建模与防控分析――以新疆为例”（2021D01C070）
- DOI：10.13568/j.cnki.651094.651316.2022.04.06.0001
  中图分类号： R181;O175
- 纸质出版：2023
- 稿件说明：
移动端阅览
[1]王雅萍,王生福,聂麟飞.具有高危易感年龄和潜伏期年龄的HIV传播模型研究[J].新疆大学学报(自然科学版)(中英文),2023,40(02):160-168+174.
[1]王雅萍,王生福,聂麟飞.具有高危易感年龄和潜伏期年龄的HIV传播模型研究[J].新疆大学学报(自然科学版)(中英文),2023,40(02):160-168+174. DOI： 10.13568/j.cnki.651094.651316.2022.04.06.0001.

DOI：10.13568/j.cnki.651094.651316.2022.04.06.0001.

摘要

基于HIV的传播特点，将易感人群分为普通易感人群和高危易感人群，提出一类具有高危易感年龄和潜伏期年龄的HIV传播模型．利用下一代算子方法给出基本再生数R0的精确表达式．讨论无病平衡态和地方病平衡态的存在性与稳定性，即：当R0<1时无病平衡态全局渐近稳定，当R0>1时地方病平衡态全局渐近稳定．

Abstract

Based on the transmission characteristics of HIV

the susceptible population is divided into general susceptible population and high-risk susceptible population

and an HIV transmission model with high-risk susceptible age and latent age is developed. The exact expression of the basic reproduction number R0 is obtained by using the next generation operator method. The existence and stability of disease-free steady state and endemic steady state are discussed

that is

the disease-free steady state is globally asymptotically stable for R0<1 and the endemic steady state is globally asymptotically stable for R0>1.

关键词

Keywords

references

董晨,张欢,莫兴波.传染病流行病学[M].苏州:苏州大学出版社, 2018.

CAI L M, GUO S L, WANG S P. Analysis of an extended HIV/AIDS epidemic model with treatment[J]. Applied Mathematics and Computation, 2014, 236:621-627.

ZOHRAGUL O, XAMXINUR A. Stability analysis of an HIV/AIDS model with vertical transmission[J]. Journal of Xinjiang University(Natural Science Edition), 2015, 32(3):297-303.

何楠,王稳地,周爱蓉,等.基于饱和发生率的随机HIV模型的动力学研究[J].西南大学学报(自然科学版), 2018, 40(3):109-114.

MCCLUSKEY C C. Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes[J]. Mathematical Biosciences and Engineering, 2012, 9(4):819-841.

LIU L L, WANG J L, LIU X N. Global stability of an SEIR epidemic model with age-dependent latency and relapse[J]. Nonlinear Analysis:Real World Applications, 2015, 24:18-35.

WANG J L, ZHANG R, KUNIYA T. The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes[J]. Journal of Biological Dynamics, 2015, 9(1):73-101.

梁霜霜,聂麟飞,胡琳.具有年龄结构和水平传播的媒介传染病模型研究[J].华东师范大学学报(自然科学版), 2021, 3:47-55.

YAN D X, CAO H, XU X X, et al. Hopf bifurcation for a predator-prey model with age structure[J]. Physica A:Statistical Mechanics and its Applications, 2019, 526:120953.

HIRSCH W M, HANISCH H, GABRIEL J P. Differential equation models of some parasitic infections:methods for the study of asymptotic behavior[J]. Communications on Pure and Applied Mathematics, 1985, 38(6):733-753.

IANNELLI M. Mathematical theory of age-structured population dynamics[M]. Pisa:Giardini Editori E Stampatori, 1995.

MAGAL P. Compact attractors for time-periodic age-structured population models[J]. Electronic Journal of Differential Equations,2001, 2001(65):1-35.

BROWNE C J, PILYUGIN S S. Global analysis of age-structured within-host virus model[J]. Discrete and Continuous Dynamical Systems B, 2013, 18(8):1999-2017.

MARTCHEVA M. An introduction to mathematical epidemiology[M]. New York:Springer, 2015.

浏览量

120

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

一类具有媒体报道和环境传播的SEVIQBR传染病模型的动力学分析

含水量对路基土压实机理影响分析

一类具有饱和发生率和治疗的SIS传染病模型的后向分支及动力学行为

一类与环境有关的传染病模型的稳定性分析

具有染病年龄结构的SEIS流行病模型的稳定性