具有桥梁人群的HIV模型的研究

研究了具有桥梁人群(从事性服务的女性静脉吸毒者)的艾滋病模型.在桥梁人群内部建立一个DI模型.通过定性分析,证明了各类平衡点的稳定性,从而判断艾滋病流行与否.     

HIV病毒传播的动力学研究的同伦映射解法

研究了艾滋病病毒的传播的一个动力学模型．利用同伦映射理论和方法得到了HIV流行性传染病区域的人群传播规律．     

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.     

多因素双线性HIV模型的研究

建立了具有桥梁人群的艾滋病模型,在桥梁人群内部建立了双线性型DI模型,将桥梁人群中的病毒携带者分为n组人群.通过定性分析,证明了边界平衡点的局部渐进稳定性和全局渐进稳定性.     

行为改变下的艾滋病流行预测

基于亚洲艾滋病流行模型(Asian Epidemic Model,AEM)基本思想,建立我国艾滋病流行预测模型.利用该模型,估计某地1989—2007年艾滋病流行状况,同时设计不同行为改变方案,预测该地2008—2020年艾滋病流行趋势.     

基于捕获再捕获模型的新冠肺炎传染高危人群估计

利用手机定位大数据识别和监测新冠肺炎高危人群,既是流行病学调查方法的创新,也是疫情防控的重要支撑.本文聚焦于构造基于手机定位大数据的捕获再捕获模型,估计特定区域新冠肺炎传染高危人群总量,并利用互联网企业提供的,经脱敏处理的天津市手机APP定位大数据验证了方法的实践有效性.数据分析结果显示,2020年1月24日至1月31日期间天津每日传染高危人群规模约为12500人.本文的研究为当前疫情防控与复产复工中传染高风险人群的识别与监测提供了大数据方法支持.     

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.     

新疆艾滋病发病率的组合预测模型研究

近年来新疆艾滋病发病率较高,预防控制工作严峻,此种情况下,基于2008年1月至2014年12月的艾滋病发病率数据,采用ARIMA方法及广义回归神经网络方法建立了ARIMA-GRNN组合预测模型,并用2015年1月至5月的数据检验模型预测能力,结果模型能较好地对新疆艾滋病发病率做预测,这可为新疆艾滋病的预防控制提供一定的科学参考.     

多因素标准型HIV模型的研究

建立了具有桥梁人群的艾滋病模型,在桥梁人群内部建立了标准型DI模型,将桥梁人群中的病毒携带者分为n组人群.证明了其边界平衡点的局部渐进稳定性和全局渐进稳定性.     

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.     

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.     

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 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.     

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.     

Modelling and analysis of the spread of AIDS epidemic with immigration of HIV infectives

We propose and analyze, a nonlinear mathematical model of the spread of HIV/AIDS in a population of varying size with immigration of infectives. It is assumed that susceptibles become infected via sexual contacts with infectives (also assumed to be infectious) and all infectives ultimately develop AIDS. The model is studied using stability theory of differential equations and computer simulation. Model dynamics is also discussed under two particular cases when there is no direct inflow of infectives. On analyzing these situations, it is found that the disease is always persistent if the direct immigration of infectives is allowed in the community. Further, in the absence of inflow of infectives, the endemicity of the disease is found to be higher if pre-AIDS individuals also interact sexually in comparison to the case when they do not take part in sexual interactions. Thus, if the direct immigration of infectives is restricted, the spread of infection can be slowed down. A numerical study of the model is also carried out to investigate the influence of certain key parameters on the spread of the disease.