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Mathematical analysis of HIV/AIDS stochastic dynamic models

机译：HIV / AIDS随机动态模型的数学分析

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摘要

In this paper, we present a group of stochastic dynamic models of the infection of the HIV/AIDS in a host population of four classes of epidemiological classes: susceptible individuals, HIV infected, AIDS infected individuals and treatment class (i.e. infected individuals who are under ARV treatment). The mathematical analysis of the deterministic model has been previously consider by Emvudu and Bongor (2012). The mathematical analysis of the group of the stochastic models associated to the deterministic model is performed to determine the conditions for the stability of the random equilibriums. The results of this mathematical analysis are the next one: the global and asymptotic stability of the disease free equilibrium of the mean system when the effective reproduction number is less than 1; the global, asymptotical, and p-exponential stability of the disease free equilibrium of the stochastic model occurs when the basic reproduction number is less than 1; the stability in probability of the trivial equilibrium of the stochastic perturbations model occurs if the basic reproduction number is bigger than 1.
机译：在本文中，我们提出了一组流行病学类别的宿主种群中的艾滋病毒/艾滋病感染的随机动态模型，这些宿主流行病类别为四类：易感人群，艾滋病毒感染者，艾滋病感染者和治疗人群（即，抗逆转录病毒治疗）。 Emvudu和Bongor（2012）曾考虑过对确定性模型的数学分析。对与确定性模型相关的一组随机模型进行数学分析，以确定随机均衡稳定性的条件。该数学分析的结果是下一个：有效繁殖数小于1时，平均系统的无病平衡的全局稳定性和渐近稳定性。当基本繁殖数小于1时，随机模型的无病平衡的全局，渐近和p指数稳定性就会发生；如果基本再生产数大于1，则随机扰动模型的琐碎平衡概率保持稳定。

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  • 来源
    《Applied Mathematical Modelling》 |2016年第22期|9131-9151|共21页
  • 作者

    Yves Emvudu; Danhree Bongor; Rodoumta Koiena;

  • 作者单位

    Applied Mathematical Laboratory, Postgraduate School of Science, Technology & Geoscience, University of Yaounde 1, URFD-MIBA, P.O. Box 918, Yaounde, Cameroon;

    Applied Mathematical Laboratory, Postgraduate School of Science, Technology & Geoscience, University of Yaounde 1, URFD-MIBA, P.O. Box 918, Yaounde, Cameroon;

    Department of Mathematics, Faculty of the Exact and Applied Sciences, University of NDjamena, P.O. Box 1024, Djamena, Chad;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Stochastic model; Stability analysis; Endemic equilibrium; Brownian motion; Ito process; Numerical simulation;

    机译：随机模型稳定性分析;地方平衡布朗运动伊藤制程;数值模拟;

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