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1.
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.  相似文献   

2.
数学-艾滋病   总被引:1,自引:1,他引:0  
本文介绍HIV/AIDS传播数学模型,主要包括AIDS患者初期增长数、性传染病传播的经典模型、HIV/AIDS传播动态模型和危险行为模型等。此外,还介绍这些数学模型目前研究结果和未解决的问题。  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
莫嘉琪  张伟江  何铭 《应用数学》2007,20(3):441-445
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.  相似文献   

6.
通过考虑同性接触与异性接触来研究HIV/AIDS的传播,建立带有性别结构的HIV/AIDS模型.根据下一代矩阵法求出基本再生数.证明当R0<1时,无病平衡点是全局渐近稳定的,当R0> 1时,地方病平衡点是存在的,并且疾病是一致持续的,并通过数值模拟来验证结论.提出一个最优控制问题并利用庞特里亚金极大值原理进行了求解.拟合结果表明我国未来几年患病人数仍会不断攀升.  相似文献   

7.
根据人类感染梅毒的方式建立了一种新的数学模型,整个人口被分成四个组:注射吸毒者,女性性工作者,性工作者的客人以及MSM人群.通过对模型的研究和分析得到了模型的基本再生数R_0,还进一步研究了平衡点的存在性和稳定性,当R_01时,无病平衡点是全局渐近稳定的,疾病将会被消除;当R_0 1时,疾病是一致持续的而且给出了地方病平衡点全局渐近稳定的充分性条件,疾病将持续流行.  相似文献   

8.
针对HIV/AIDS传播的具有常数移民和指数出生的SI型模型,为了更加符合实际意义,对具有双线性传染率的模型进行局部改进,并对改进后的动力学模型进行了简化.对于改进后的模型,证明了平衡点的存在与局部稳定性,并证明了传染病毒的灭绝与持续性,得到了传染病毒的基本再生数.结果表明:当单位时间内从外界迁入人口中染病者的比例系数c近似等于零时,基本再生数小于1时,传染病毒最终灭绝;当基本再生数大于1时,模型存在唯一的正平衡点,且是局部渐近稳定的,说明传染病毒一致持续存在.  相似文献   

9.
建立了一类具有自愿咨询和检测(VCT)意识的随机HIV/AIDS传染病模型,利用停时理论等方法证明了随机模型正解的全局存在唯一性.其次,分析了该随机模型的解在相应确定性模型的无病平衡点与地方病平衡点附近的渐近行为,并得到了随机模型解的平均持续与灭绝性的充分条件.最后,通过数值模拟进一步显示了模型的动力学行为.  相似文献   

10.
讨论用脉冲隔离的方案控制HIV的传播.假定艾滋病感染者发展成艾滋病人和感染年龄有关,我们建立了带脉冲隔离类和感染年龄的HIV模型.在一定条件下证明该模型的无病平衡态是全局稳定的.  相似文献   

11.
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.  相似文献   

12.
A model for HIV transmission among intravenous drug users is studied. We show that the disease dies out when the reproductive number R0 1 and remains endemic when R0>1. By employing the comparison method, we provide an iterative scheme to estimate the bounds of the global attractor in the case R0>1. Numerical examples are presented to demonstrate how to use this iterative scheme.  相似文献   

13.
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.  相似文献   

14.
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.  相似文献   

15.
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.  相似文献   

16.
In this paper, we study the impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. Initially we consider constant controls and thereafter treat control measures as time dependent control parameters. In the constant controls case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit transcritical bifurcation. For the time dependent controls, we formulate the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of unaware infectives in the spread of HIV/AIDS. We observed that unawareness by infectives has a great cost impact on the community. We further investigate the impact of combinations of the strategies in the control of HIV/AIDS. Carrying out cost-effectiveness analysis, we found that the most cost-effective strategy is the combination of all the control strategies.  相似文献   

17.
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.  相似文献   

18.
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.  相似文献   


19.
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.  相似文献   

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