Study on a HIV/AIDS model with application to Yunnan province,China

This paper presents an epidemic model aiming at the prevalence of HIV/AIDS in Yunnan, China. The total population in the model is restricted within high risk population. By the epidemic characteristics of HIV/AIDS in Yunnan province, the population is divided into two groups: injecting drug users (IDUs) and people engaged in commercial sex (PECS) which includes female sex workers (FSWs), and clients of female sex workers (C). For a better understanding of HIV/AIDS transmission dynamics, we do some necessary mathematical analysis. The conditions and thresholds for the existence of four equilibria are established. We compute the reproduction number for each group independently, and show that when both the reproduction numbers are less than unity, the disease-free equilibrium is globally stable. The local stabilities for other equilibria including two boundary equilibria and one positive equilibrium are figured out. When we omit the infectivity of AIDS patients, global stability of these equilibria are obtained. For the simulation, parameters are chosen to fit as much as possible prevalence data publicly available for Yunnan. Increasing strength of the control measure on high risk population is necessary to reduce the HIV/AIDS in Yunnan.     

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.     

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.     

System Dynamic simulation of treatment policies to address colliding epidemics of tuberculosis,drug resistant tuberculosis and injecting drug users driven HIV in Russia

The explosive increase in the number of people infected with tuberculosis (TB),multi drug resistant tuberculosis (MDRTB), and injecting drug users (IDU)HIV/AIDS has become a serious public health challenge in Russia. The WorldHealth Organization is recommending policies including simultaneous use ofhighly active antiretroviral therapy (HAART) to treat HIV/AIDS and second linedrugs to treat MDRTB. We developed a System Dynamics simulation model torepresent the dynamic transmission of TB, MDRTB and human immunodeficiency virus(HIV). The model simulated scenarios regarding MDRTB cure rate and HAARTcoverage, that is the HIV/AIDS population covered by HAART. The results over a20-year period indicate that reduction in TB and HIV-associated TB deaths wouldbe negligible for HAART coverage up to 50%. The reduction is onlysignificant for HAART coverage of 70% and above. Similarly, high MDRTBcure rate reduces significantly deaths from TB and MDRTB and this reduction ismore important as the HAART coverage is increased.     

一类非线性动力系统的数值分析及控制策略研究

根据艾滋病在新疆的流行特点,建立了一个非线性动力系统的数学模型来研究艾滋病在新疆高危人群中传播的规律.通过查阅大量的统计数据和文献资料,确定了模型中部分参数的具体数值,然后通过数据拟合的方法得到了各个高危人群中的HIV病毒的传染性系数.在模型中,选择2004年底(2005年初)作为系统的初始点,预测了艾滋病未来几年内在新疆的流行趋势.最后,提出并比较遏止艾滋病传播的各项干预措施.     

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.     

Modelling treatment effects in the HIV/AIDS epidemic

Advances in recent treatments for HIV/AIDS patients have shown dramatic outcomes in extending the incubation period and AIDS survival time, while also providing significant improvements in the quality of patients' lives. A compartmental model is proposed to analyse the effects of the various treatment regimens which have been introduced. The results produced are in good agreement with routinely collected data relating to levels of HIV/AIDS incidence and prevalence in the UK homosexual population. Some parameter values within the model are obtained from surveys, census results, etc, but others are derived using a maximum likelihood estimation procedure. Finally, the model is used to project levels of incidence and prevalence over the next few years, and to investigate several possible scenarios.     

A linked risk group model for investigating the spread of HIV

This paper describes a model that simulates the spread of HIV and progression to AIDS. The model is based on classical models of disease transmission. It consists of six linked risk groups and tracks the numbers of infectives, AIDS cases, AIDS related deaths, and other deaths of infected persons in each risk group. Parametric functions are used to represent risk-group-specific and time-dependent average contact rates. Contacts are needle sharing, sexual contacts, or blood product transfers.

An important feature of the model is that the contact rate parameters are estimated by minimizing differences between AIDS incidence and reported AIDS cases adjusted for undercounting biases. This feature results in an HIV epidemic curve that is analogous to one estimated by backcalculation models but whose dynamics are determined by simulating disease transmission. The model exhibits characteristics of both the disease transmission and the backcalculation approaches, i.e., the model:

• reconstructs the historical behavior patterns of the different risk groups,

• includes separate effects of treatment and changes in average contact rates,

• accounts for other mortality risks for persons infected with HIV,

• calculates short-term projections of AIDS incidence, HIV incidence, and HIV prevalence,

• calculates cumulative HIV infections (the quantity calculated by backcalculation approaches) and HIV prevalence (the quantity measured by seroprevalence and sentinel surveys). This latter feature permits the validation of the estimates generated by two distinct approaches.

We demonstrate the use of the model with an application to U.S. AIDS data through 1991.     

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.     

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.     

河北省女性人口平均预期寿命变化的度量分析

本文应用ＥｄｕａｒｄｏＥ．Ａｒｉａｇａ在１９８４年提出的平均预期寿命变化度量理论对河北省女性人口平均预期寿命进行分析     

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.     

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 $R_0$.     

A nonlinear AIDS epidemic model with screening and time delay

A nonlinear mathematical model to study the effect of time delay in the recruitment of infected persons on the transmission dynamics of HIV/AIDS is proposed and analyzed. In modeling the dynamics, the population is divided into four subclasses: the susceptibles, the HIV positives or infectives that do not know they are infected, the HIV positives that know they are infected and the AIDS patients. Susceptibles are assumed to become infected via sexual contacts with (both types of) infectives. The model is analyzed using stability theory of delay differential equations. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation. Numerical simulations are also carried out to investigate the influence of key parameters on the spread of the disease, to support the analytical conclusion and to illustrate possible behavioral scenario of the model.     

The persistence of HIV-1 spreading in MSM population in China

In this work, we develop and analyze mathematical models for the dynamics about the evolution of HIV/AIDS in men who have sex with men in China. We focus on the analyses of the basic reproduction number $R_0$ and the persistence of infection. Through simulations we also find that the interventions including antiviral therapy, condom using and potential vaccinations play very important roles in the HIV/AIDS spreading in MSM population in China.     

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.     

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.     

带有发病年龄的HIV/AIDS传播的数学建模及分析

所建的模型是用含有常微分方程和偏微分方程的方程组来描述的,考虑了垂直感染,发病年龄,AIDS病人有希望恢复到潜伏期以及不同患者接受治疗的能力不同等诸多因素.利用导出的方程,直接推出:当AIDS引起死亡率增加时,社会总人口衰减.利用泛函分析方法和有界线性算子半群理论分析了系统的适定性,并证明了系统方程存在正解.     

Modeling and dynamics of HIV transmission among high-risk groups in Guangzhou city, China

In this paper, a multicompartmental model is formulated to study how HIV is transmitted among different HIV high-risk groups, including MSM (men who have sex with men), FRs (foreigner residents), FSWs (female sex workers), and IDUs (injection drug users). The explicit expression for the basic reproduction number is obtained via the next generation matrix approach. We show that the disease free equilibrium is locally as well as globally asymptotically stable (the disease goes to extinction) when the basic reproduction number is less than unity, and the disease is always present when the basic reproduction number is larger than unity. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct a case study where model parameters are estimated from the demographic and epidemiological data from Guangzhou. Using the parameter estimates, we predict the HIV/AIDS trend for each high-risk group. Furthermore, our study suggests that reducing the transmission routes of the disease and increasing condom use will be useful for control of HIV transmission.     

中国城市人口死亡率的预测

死亡率是随时间变动的具有不确定性的变量,基本养老保险的养老金给付必须考虑动态死亡率的影响,因此需要对中国城市人口的未来死亡率变动进行预测。针对部分年的中国城市分性别人口死亡率数据缺失的实际状况,本文运用死亡人数服从Poisson分布的Lee-Carter模型进行了预测,结果表明该模型的拟合较好。由上述预测得出,随时间的延续,中国城市人口的预期寿命将明显增加,为基本养老保险的支付带来严重的风险,该风险导致基本养老保险个人账户的收入远不足以支付未来的养老金,必须引起重视。本文就如何规避这一风险给出了一些政策建议。