Dynamical analysis of public health education on HIV/AIDS transmission

An Human Immunodeficiency Virus/Acquired Immuno‐Deficiency Syndrome (HIV/AIDS) epidemic model for sexual transmission with asymptomatic and symptomatic phase is proposed as a system of differential equations. The threshold and steady state for the model are determined and stabilities of disease free steady state is investigated. We use the model and study the effect of public health education on the spread of HIV/AIDS as a single‐strategy in HIV prevention. The education, including basic reproduction number for the model with public health education, is compared with the basic reproduction number for the HIV/AIDS in the absence of public health education. By comparing these two values, influence of public health education appears. According to property of , threshold proportion of educated adolescents, education rate for susceptible individuals and education efficacy is obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Effect of a preventive vaccine on the dynamics of HIV transmission

A deterministic mathematical model for the transmission dynamics of HIV infection in the presence of a preventive vaccine is considered. Although the equilibria of the model could not be expressed in closed form, their existence and threshold conditions for their stability are theoretically investigated. It is shown that the disease-free equilibrium is locally–asymptotically stable if the basic reproductive number (thus, HIV disease can be eradicated from the community) and unstable if (leading to the persistence of HIV within the community). A robust, positivity-preserving, non-standard finite-difference method is constructed and used to solve the model equations. In addition to showing that the anti-HIV vaccine coverage level and the vaccine-induced protection are critically important in reducing the threshold quantity , our study predicts the minimum threshold values of vaccine coverage and efficacy levels needed to eradicate HIV from the community.     

Modelling the Spread of HIV/AIDS Epidemic

In this paper, a deterministic mathematical model for the spread of HIV/AIDS in a variable size population through horizontal transmission is considered. The existence of a threshold parameter, the basic reproduction number, is established, and the stability of both the disease-free equilibrium and the endemic equilibrium is discussed in terms of $R_0$.     

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.     

A nonlinear HIV/AIDS model with contact tracing

A nonlinear mathematical model is proposed and analyzed to study the effect of contact tracing on reducing the spread of HIV/AIDS in a homogeneous population with constant immigration of susceptibles. In modeling the dynamics, the population is divided into four subclasses of HIV negatives but susceptibles, HIV positives or infectives that do not know they are infected, HIV positives that know they are infected and that of AIDS patients. Susceptibles are assumed to become infected via sexual contacts with (both types of) infectives and all infectives move with constant rates to develop AIDS. The model is analyzed using the stability theory of differential equations and numerical simulation. The model analysis shows that contact tracing may be of immense help in reducing the spread of AIDS epidemic in a population. It is also found that the endemicity of infection is reduced when infectives after becoming aware of their infection do not take part in sexual interaction.     

Assessing the impact of educational campaigns on controlling HCV among women in prison settings

Prior studies have shown that imprisonment is a major risk factor for hepatitis C infection, with the risk of infection directly proportional to the length of incarceration. Women are at least twice as likely as men to contract HCV as they have limited access to information, health services and safe intravenous drug injecting equipments. We develop a mathematical model to assess the impact of educational campaigns on controlling HCV among women in prison settings. Equilibria for the model are determined and their stability are examined. Population-level effects of increased educational campaigns to encourage safe injecting practices among women in prison are evaluated through numerical simulations. The results suggest that educating women prisoners about abstaining from intravenous drug misuse may significantly reduce HCV prevalence among women in prison settings. Targeted education campaigns, which are effective at stopping transmission of HCV more than 80% of the time, will be highly effective at controlling the disease among women in prisons.     

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.     

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.     

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.     

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.     

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.     

Modelling the effect of tuberculosis on the spread of HIV infection in a population with density-dependent birth and death rate

A nonlinear mathematical model is proposed to study the effect of tuberculosis on the spread of HIV infection in a logistically growing human population. The host population is divided into four sub classes of susceptibles, TB infectives, HIV infectives (with or without TB) and that of AIDS patients. The model exhibits four equilibria namely, a disease free, HIV free, TB free and an endemic equilibrium. The model has been studied qualitatively using stability theory of nonlinear differential equations and computer simulation. We have found a threshold parameter R₀ which is if less than one, the disease free equilibrium is locally asymptotically stable otherwise for R₀>1, at least one of the infections will be present in the population. It is shown that the positive endemic equilibrium is always locally stable but it may become globally stable under certain conditions showing that the disease becomes endemic. It is found that as the number of TB infectives decreases due to recovery, the number of HIV infectives also decreases and endemic equilibrium tends to TB free equilibrium. It is also observed that number of AIDS individuals decreases if TB is not associated with HIV infection. A numerical study of the model is also performed to investigate the influence of certain key parameters on the spread of the disease.     

A discrete epidemic model for SARS transmission and control in China

Severe acute respiratory syndrome (SARS) is a rapidly spreading infectious disease which was transmitted in late 2002 and early 2003 to more than 28 countries through the medium of international travel. The evolution and spread of SARS has resulted in an international effort coordinated by the World Health Organization (WHO).

We have formulated a discrete mathematical model to investigate the transmission of SARS and determined the basic reproductive number for this model to use as a threshold to determine the asymptotic behavior of the model. The dependence of the basic reproductive number on epidemic parameters has been studied. The parameters of the model have been estimated on the basis of statistical data and numerical simulations have been carried out to describe the transmission process for SARS in China. The simulation results matches the statistical data well and indicate that early quarantine and a high quarantine rate are crucial to the control of SARS.     

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.