具有常恢复率的艾滋病梯度传染模型

本文建立了一个具有常恢复率的同质人群艾滋病梯度传染模型，其中的性接触数是人群变量的函数，讨论了平衡点的存在性和稳定性，推广和改进了一些相关的已有结果。     

一类HIV/AIDS流行病模型

结合某市的艾滋病现状给出了相应的传染病动力学模型,研究了其平衡点的稳定性,讨论了流行病的阈值,并对不同的说服率、不同的因病死亡率、不同的传染率分别进行了数值模拟,对该市艾滋病的预防和控制给出了理论上的指导和建议.     

Modelling circumcision and condom use as HIV/AIDS preventive control strategies

We present a sex-structured model for heterosexual transmission of HIV/AIDS with explicit incubation period for modelling the effect of male circumcision as a preventive strategy for HIV/AIDS. The model is formulated using integro-differential equations, which are shown to be equivalent to delay differential equations with delay due to incubation period. The threshold and equilibria for the model are determined and stabilities are examined. We extend the model to incorporate the effects of condom use as another preventive strategy for controlling HIV/AIDS. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of male circumcision and condom use in a community. The models are numerically analysed to assess the effects of the two preventive strategies on the transmission dynamics of HIV/AIDS. We conclude from the study that in the continuing absence of a preventive vaccine or cure for HIV/AIDS, male circumcision is a potential effective preventive strategy of HIV/AIDS to help communities slow the development of the HIV/AIDS epidemic and that it is even more effective if implemented jointly with condom use. The study provides insights into the possible community benefits that male circumcision and condom use as preventive strategies provide in slowing or curtailing the HIV/AIDS epidemic.     

香港艾滋病近期传播特征与动态预测

首次研究出香港艾滋病目前传播势态为一元线性回归方程,并由方程的预测值和斜率的变化动态监测香港艾滋病近期发病趋势,艾滋病病毒感染者年平均发病率为255至271个,艾滋病病患者年平均发病率为56个左右.本文研究方法简单易行,对香港政府近期预防艾滋病有重要的理论和实用价值.     

女性吸毒者在HIV/AIDS传播中的作用

利用数学模型,探讨了女性吸毒者在HIV/AIDS传播中的作用.通过理论分析和数值模拟,揭示了女性吸毒者对HIV/AIDS传播和流行的重要作用:当HIV/AIDS在吸毒人群和一般男性人群中流行时,若切断女性吸毒人群和一般男性人群间的传播途径(商业性行为),则疾病不但在一般男性人群中会消亡,在一定的条件下,甚至会在吸毒人群中消亡.     

一类具有说服率的HIV/AIDS流行病模型

根据某市艾滋病出现的新特点,即外来人口对艾滋病的影响,给出了相应的传染病动力学模型,并进行了数值模拟.     

HIV/AIDS epidemic fractional-order model

In this paper a non-linear mathematical model with fractional order ?, 0 < ? ≤ 1 is presented for analyzing and controlling the spread of HIV/AIDS. Both the disease-free equilibrium E₀ and the endemic equilibrium E^* are found and their stability is discussed using the stability theorem of fractional order differential equations. The basic reproduction number R₀ plays an essential role in the stability properties of our system. When R₀ < 1 the disease-free equilibrium E₀ is attractor, but when R₀ > 1, E₀ is unstable and the endemic equilibrium (EE) E^* exists and it is an attractor. Finally numerical Simulations are also established to investigate the influence of the system parameter on the spread of the disease.     

A CA-based epidemic model for HIV/AIDS transmission with heterogeneity

The complex dynamics of HIV transmission and subsequent progression to AIDS make the mathematical analysis untraceable and problematic. In this paper, we develop an extended CA simulation model to study the dynamical behaviors of HIV/AIDS transmission. The model incorporates heterogeneity into agents’ behaviors. Agents have various attributes such as infectivity and susceptibility, varying degrees of influence on their neighbors and different mobilities. Additional, we divide the post-infection process of AIDS disease into several sub-stages in order to facilitate the study of the dynamics in different development stages of epidemics. These features make the dynamics more complicated. We find that the epidemic in our model can generally end up in one of the two states: extinction and persistence, which is consistent with other researchers’ work. Higher population density, higher mobility, higher number of infection source, and greater neighborhood are more likely to result in high levels of infections and in persistence. Finally, we show in four-class agent scenario, variation in susceptibility (or infectivity) and various fractions of four classes also complicates the dynamics, and some of the results are contradictory and needed for further research.     

具有年龄结构的离散HIV/AIDS模型的全局分析

本文根据艾滋病传播的特点建立了有年龄结构的高维离散SIA模型,和有干预的具有年龄结构的离散HIV模型.对每种模型,我们首先给出了建模思想,用差分方程建立了数学模型,然后对模型平衡点的稳定性进行了理论分析,得出一定条件下模型无病平衡点和地方病平衡点的稳定性.另外,本文还给出了模型的基本再生数,其意义为一个病人在染病期内平均感染的人数,基本再生数决定了模型无病平衡点和地方病平衡点的存在性和稳定性.     

A QUALITATIVE ANALYSIS OF A VACCINATION MODEL OF HIV/AIDS WITH STAGED PROGRESSION AND AMELIORATION

An epidemic vaccination model with multiple stages of infection is presented and analyzed. The model allows infected individuals to move from advanced stages of infection back to less advanced stages of infection. A threshold parameter which determines the local stability of the disease-free equilibrium is found. The existence and stability of endemic equilibrium for 2-dimensional phase space are analyzed. At the same time, we put forward an optimal vaccine efficacy.     

艾滋病防治资源投入的效果分析

基于GOALS模型的基本思想,建立了效果分析模型,并针对两种不同的资金分配方案,模拟了两种方案对2006—2010年某地艾滋病流行的影响,并对模拟结果进行了分析.     

Analytic solutions to compartmental models of the HIV/AIDS epidemic

For many years compartmental models have provided useful insightsinto the spread of epidemics. Such models are usually fairlyeasy to set up, but even the simpler models have the disadvantagethat they are intractable to analytic solution. In this paperwe examine models of the HIV/AIDS epidemic, and show that theequations may be linearized in a piecewise manner over time,thus allowing analytic solutions to be obtained. Indicationsof the usefulness of this approach are provided. In particular,an analytic solution gives insight into the mechanism of theepidemic, together with a clearer picture of the sensitivityof results to changes in parameter values. Further, the processesof parameter estimation and the methodology of back-calculationalso benefit from the provision of functional forms for thestate variables.     

Stability analysis of an HIV/AIDS epidemic model with treatment

An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number _ℜ0${\Re }_0$. If _ℜ0≤1${\Re }_0\le 1$, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if _ℜ0>1${\Re }_0>1$. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.     

Global stability for an HIV/AIDS epidemic model with different latent stages and treatment

An HIV/AIDS epidemic model with different latent stages and treatment is constructed. The model allows for the latent individuals to have the slow and fast latent compartments. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are determined by the basic reproduction number under some conditions. If R₀ < 1, the disease free equilibrium is globally asymptotically stable, and if R₀ > 1, the endemic equilibrium is globally asymptotically stable for a special case. Some numerical simulations are also carried out to confirm the analytical results.     

Asymptotic properties of an HIV/AIDS model with a time delay

A mathematical model for HIV/AIDS with explicit incubation period is presented as a system of discrete time delay differential equations and its important mathematical features are analysed. The disease-free and endemic equilibria are found and their local stability investigated. We use the Lyapunov functional approach to show the global stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The HIV/AIDS model is numerically analysed to asses the effects of incubation period on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Zimbabwe.     

Optimal strategies for mitigating the HIV/AIDS epidemic in the Philippines

The human immunodeficiency virus (HIV) impairs a person's immune system against many infections and some types of cancer, leading to acquired immunodeficiency syndrome (AIDS), which is characterized by severe illnesses. The number of HIV infections in the Philippines has increased, more than doubled, within the last decade. This alarming HIV crisis in the country requires urgent actions. In this study, a mathematical model is developed to describe the disease transmission in the Philippines. Disease-free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Sensitivity analyses and subset selection are performed to identify influential parameters and to determine an identifiable parameter set given measurements, respectively. Available data on the number of asymptomatic aware infectious, those who are in the AIDS stage, and those under treatment are utilized to estimate key epidemiological parameters such as transmission, treatment, and screening rates. Uncertainty of these parameter estimates is quantified through bootstrapping method. Furthermore, intervention strategies are investigated in the framework of optimal control theory. Control measures include precaution, HIV screening, antiretroviral treatment, and pre-exposure prophylaxis (PrEP) treatment. These various control efforts are compared with regard to cost efficiency and effectiveness in reducing the number of infected individuals. Given limited available control measures, the PrEP-only scenario is shown to be the most cost-effective, followed by other scenarios that combine PrEP with other controls.     

The coupled within- and between-host dynamics in the evolution of HIV/AIDS in China

In this work, we develop and analyze mathematical models for thecoupled within-host and between-host dynamics caricaturing the evolutionof HIV/AIDS. The host population is divided into susceptible, the infectedwithout receiving treatment and the infected receiving ART treatment in accordancewith China’s Four-Free-One-Care Policy. The within-host model is a typicalODE model adopted from literatures. The between-host model incorporatesage-since-infection described by a system of integrodifferential equations. Thetwo models are coupled via the viral load and number of CD4+ T cells ofwithin the hosts. For the between-host model with an arbitrarily selectedHIV infected individual, we focus on the analyses of the basic reproductionnumber R0 and the stabilities of equilibria. Through simulations we also findthat the within-host dynamics does influence the between-host dynamics, andthe nesting of within-host and between-host play a very important role in theHIV/AIDS evolution.     

SWEIA艾滋病毒传染模型及应用

人类免疫缺陷病毒(HIV)是一种严重威胁生命的病毒,感染艾滋病毒患者一般经历四个阶段:i)艾滋病毒阴性的窗口期(W);ii)阳性的无症状潜伏期(E);iii)有症状期(Ⅰ);以及iv)移除阶段(A).为深入研究艾滋病传播过程,建立SWEIA艾滋病毒传染模型,定义基本再生数,分析无病与地方病平衡点的存在性和局部稳定性,根据2004至2015年中国艾滋病患者数据,采用遗传算法对SWEIA模型中参数进行估计.通过对基本再生数敏感性分析以及模型数值随参数不同而产生的变化,揭示艾滋病窗口期的接触率是影响艾滋病流行的主要原因之一.     

具有商业性行为的女性吸毒者对HIV/AIDS传播的影响

利用数学模型,研究了具有商业性行为的女性吸毒者对HIV/AIDS传播的影响.通过理论分析,讨论了系统的一致持续性和地方病平衡点的存在性,从理论上揭示了女性吸毒者的商业性行为可加强HIV/AIDS的传播和流行.特别地,若无商业性行为且吸毒人群和一般男性人群中均无疾病流行时,商业性行为的存在将会导致两类人群中的疾病均流行起来.这为防控工作的开展提供了重要参考.