一个具有干预策略的肺结核模型的阈值动力学行为（英文）

文献[4]研究了肺结核传播的动力学行为.该文献仅从数值模拟上分析了疾病的传播和不同策略对疾病传播的影响.本文从理论上对疾病传播和不同策略对疾病传播的影响进行了分析.主要结论如下：得到了模型的基本再生数R_0.R_0决定了疾病传播的动力学行为：如果R_0〈1,则模型仅有一个无病平衡点且是局部渐近稳定的,若R_0〉1则模型存在一个地方病平衡点并且疾病是一致持续的.本文还得到了无病平衡点全局渐近稳定的充分条件.     

鼠疫传播动力学模型的构建研究

目的:采用疾病传播动力学模型描述鼠疫的流行特征,为科学地制定鼠疫的防控措施提供理论依据。方法:运用微分方程建立鼠间鼠疫和人间鼠疫的传播动力学模型,分析模型中各参数与疫情发展变化的关系。结果:使用基本繁殖率,平均鼠密度,感染者平均病死率,感染者平均治愈率等参数描述感染率随时间的变化趋势。结论:根据鼠间传播期、疫区传播期和人群扩散期的传播特点,分别开展各项防控工作,能够更好地控制鼠疫疫情。     

一类随机包虫病传播模型及CDC数据拟合

研究了一类具有随机环境波动的包虫病传播动力学模型,得到了地方病平衡点的随机渐近稳定的充分条件,通过对随机模型的数值仿真来拟合中国疾病预防控制中心(CDC)包虫病月报数据,并揭示了随机环境因素对疾病传播的影响.     

一类包虫病传播动力学模型的研究

研究了一类具有终宿主产卵期和中间宿主虫卵成熟期两时滞的包虫病传播动力学模型,得到了决定系统动力学行为的阈值R_0,当R_0〈1时,证明了未感染平衡点是局部渐近稳定的;当R_0〉1时,得到了感染平衡点是局部渐近稳定的充分条件。通过数值仿真验证了理论结果并探讨了时滞对系统动力学行为的影响,且发现若时滞在一定的范围内系统存在周期解.     

电离辐射对蛋白质分子作用的量子孤波分析

本文运用量子力学方法对蛋白质分子中孤波传播的非线性动力学特征进行了探讨。研究表明：电离辐射产生的自由基对蛋白质分子的伤害将会对携带能量、信息的孤立子波传播产生较为显著的影响。     

具垂直传播的林龄结构病虫害模型平衡态的稳定性

讨论连续使用杀虫剂和具有垂直传播的林龄结构病虫害模型,对模型的动力学性态进行了分析,得到模型的基本再生数,讨论了模型无病平衡态的稳定性和病虫害平衡态的不稳定性,分析了病虫害的机理参数对病害流行的影响.     

霍乱动力学模型中的疫情增长率以及疫情最终大小的计算

旨在通过流行病动力学的常微分数学模型来计算疫情增长率以及疫情最终大小,并讨论基本再生数与这二者之间的关系.2011年Mukandavire等人~([1])针对2008-2009年津巴布韦霍乱建立ODE模型,包含了环境与人之间的传播(用参数β-e表示)以及人与人之间的传播(用参数β_h表示)两种传播途径.我们首先计算出疫情初始增长率,并判断两种传播途径的敏感性强弱.并且还推导出疫情最终大小公式,其只与基本再生数相关.     

一类计算机病毒SEIR模型稳定性分析

建立数学模型已经成为研究计算机病毒传播机理的重要手段.依照分离的时间间隔来模拟计算机病毒传播更能反映现实情况.文章对一类SEIR模型进行了改进,假设对全部新的计算机节点进行免疫策略,研究其对计算机病毒动力学模型的影响.利用Lyapunov第一方法和圆盘定理分别求得两类平衡点的渐近稳定条件.     

一类具有饱和接触率的SIQRS模型的动力学分析

本文研究了在网络环境下一种具有饱和接触率的SIQRS模型,并对所建模型平衡点的存在性进行了深入的讨论,利用Liapunov函数和Dulac定理对模型进行分析,得到了流行病传播的无病平衡点以及地方病平衡点.紧接着,通过对模型平衡点的动力学分析,推断出了流行病传播的一般性趋势.最后,我们设计了一个数值实验,通过计算机仿真验证了模型的合理性与有效性.     

持续性疾病流行和血吸虫病在多个脊椎动物宿主中的瞬时振动

血吸虫是一种寄生在脊椎动物上有助于消化的地方或血管中的寄生虫．它们共有复杂的生活史,其中包括中间阶段的软体动物和一个脊椎动物宿主．根据MacDonald和May的工作,我们研究了一个基于血吸虫生活史的多个时滞的动力学模型,并且包含了一个由May和Wo11house提出的交配函数,当我们改变交配函数中的一个参数,血吸虫病的动力学行为从一个持久的疾病传播变成了疾病消失．如果增加雌性血吸虫的成熬周期,或交配周期和产卵周期,我们能够观察到长时间疾病传播的瞬时振动,这说明了对疾病的预测不依赖在一个特定时间的疾病水平,而是依赖一个充分长时间的疾病水平。     

广义Lotke-Volterra生态模型的非线性奇摄动近似解

非线性奇摄动问题在国际学术界中是一个重要的研究对象。它涉及到许多学科。在一些生态现象中,原始的研究方法只是采取某些简单观察和统计数据来得到结论。但是它对生态现象的实质的研究达不到效果。近来在国际上提出了研究生态学的动力学方法,即人们首先把它归化为代表它的现象本质的微分方程的模型,然后用数学方法来求解对应的方程,最后研究关于生物和数学理论的动力学方面的规律。目前,非线性摄动问题已经被广泛地研究。许多学者已经研究了一些近似理论。近似求解方法已被发展,包括平均法,边界层法,匹配渐近展开和多尺度法等等。研究非线性广义Lotke-Volterra捕食-被捕食生态模型,一个简单而有效的摄动方法被应用到捕食-被捕食生态模型。提出了捕食-被捕食的一个模型,它是一个微分方程系统,并用小的正参数按幂级数展开未知函数,然后得到关于幂级数的系数的方程,并求出它们的解。于是利用摄动方法得到了原问题解的渐近展开式。得到了它是原模型解是一个好的近似的结论,它是一个解析展开式并且能保持其解析运算。最后,给出了一个对应的例子,它说明得到的解具有很好的精度。     

Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals

This paper presents a sex-structured model for heterosexual transmission of HIV/AIDS in which the population is divided into three subgroups: susceptibles, infectives and AIDS cases. The subgroups are further divided into two classes, consisting of individuals involved in high-risk sexual activities and individuals involved in low-risk sexual activities. The model considers the movement of individuals from high to low sexual activity groups as a result of public health educational campaigns. Thus, in this case public health educational campaigns are resulting in the split of the population into risk groups. The equilibrium and epidemic threshold, which is known as the basic reproductive number (R0), are obtained, and stability (local and global) of the disease-free equilibrium is investigated. The model is extended to incorporate sex workers, and their role in the spread of HIV/AIDS in settings with heterosexual transmission is explored. Comprehensive analytic and numerical techniques are employed in assessing the possible community benefits of public health educational campaigns in controlling HIV/AIDS. From the study, we conclude that the presence of sex workers enlarges the epidemic threshold R0, thus fuels the epidemic among the heterosexuals, and that public health educational campaigns among the high-risk heterosexual population reduces R0, thus can help slow or eradicate the epidemic.     

An HIV Epidemic Model Based on Viral Load Dynamics: Value in Assessing Empirical Trends in HIV Virulence and Community Viral Load

Trends in HIV virulence have been monitored since the start of the AIDS pandemic, as studying HIV virulence informs our understanding of HIV epidemiology and pathogenesis. Here, we model changes in HIV virulence as a strictly evolutionary process, using set point viral load (SPVL) as a proxy, to make inferences about empirical SPVL trends from longitudinal HIV cohorts. We develop an agent-based epidemic model based on HIV viral load dynamics. The model contains functions for viral load and transmission, SPVL and disease progression, viral load trajectories in multiple stages of infection, and the heritability of SPVL across transmissions. We find that HIV virulence evolves to an intermediate level that balances infectiousness with longer infected lifespans, resulting in an optimal SPVL∼4.75 log₁₀ viral RNA copies/mL. Adaptive viral evolution may explain observed HIV virulence trends: our model produces SPVL trends with magnitudes that are broadly similar to empirical trends. With regard to variation among studies in empirical SPVL trends, results from our model suggest that variation may be explained by the specific epidemic context, e.g. the mean SPVL of the founding lineage or the age of the epidemic; or improvements in HIV screening and diagnosis that results in sampling biases. We also use our model to examine trends in community viral load, a population-level measure of HIV viral load that is thought to reflect a population''s overall transmission potential. We find that community viral load evolves in association with SPVL, in the absence of prevention programs such as antiretroviral therapy, and that the mean community viral load is not necessarily a strong predictor of HIV incidence.     

Validation of the Modes of Transmission Model as a Tool to Prioritize HIV Prevention Targets: A Comparative Modelling Analysis

Background

The static Modes of Transmission (MOT) model predicts the annual fraction of new HIV infections acquired across subgroups (MOT metric), and is used to focus HIV prevention. Using synthetic epidemics via a dynamical model, we assessed the validity of the MOT metric for identifying epidemic drivers (behaviours or subgroups that are sufficient and necessary for HIV to establish and persist), and the potential consequence of MOT-guided policies.

Methods and Findings

To generate benchmark MOT metrics for comparison, we simulated three synthetic epidemics (concentrated, mixed, and generalized) with different epidemic drivers using a dynamical model of heterosexual HIV transmission. MOT metrics from generic and complex MOT models were compared against the benchmark, and to the contribution of epidemic drivers to overall HIV transmission (cumulative population attributable fraction over t years, PAF_t). The complex MOT metric was similar to the benchmark, but the generic MOT underestimated the fraction of infections in epidemic drivers. The benchmark MOT metric identified epidemic drivers early in the epidemics. Over time, the MOT metric did not identify epidemic drivers. This was not due to simplified MOT models or biased parameters but occurred because the MOT metric (irrespective of the model used to generate it) underestimates the contribution of epidemic drivers to HIV transmission over time (PAF_5–30). MOT-directed policies that fail to reach epidemic drivers could undermine long-term impact on HIV incidence, and achieve a similar impact as random allocation of additional resources.

Conclusions

Irrespective of how it is obtained, the MOT metric is not a valid stand-alone tool to identify epidemic drivers, and has limited additional value in guiding the prioritization of HIV prevention targets. Policy-makers should use the MOT model judiciously, in combination with other approaches, to identify epidemic drivers.     

Fitting the HIV Epidemic in Zambia: A Two-Sex Micro-Simulation Model

Background

In describing and understanding how the HIV epidemic spreads in African countries, previous studies have not taken into account the detailed periods at risk. This study is based on a micro-simulation model (individual-based) of the spread of the HIV epidemic in the population of Zambia, where women tend to marry early and where divorces are not frequent. The main target of the model was to fit the HIV seroprevalence profiles by age and sex observed at the Demographic and Health Survey conducted in 2001.

Methods and Findings

A two-sex micro-simulation model of HIV transmission was developed. Particular attention was paid to precise age-specific estimates of exposure to risk through the modelling of the formation and dissolution of relationships: marriage (stable union), casual partnership, and commercial sex. HIV transmission was exclusively heterosexual for adults or vertical (mother-to-child) for children. Three stages of HIV infection were taken into account. All parameters were derived from empirical population-based data. Results show that basic parameters could not explain the dynamics of the HIV epidemic in Zambia. In order to fit the age and sex patterns, several assumptions were made: differential susceptibility of young women to HIV infection, differential susceptibility or larger number of encounters for male clients of commercial sex workers, and higher transmission rate. The model allowed to quantify the role of each type of relationship in HIV transmission, the proportion of infections occurring at each stage of disease progression, and the net reproduction rate of the epidemic (R ₀ = 1.95).

Conclusions

The simulation model reproduced the dynamics of the HIV epidemic in Zambia, and fitted the age and sex pattern of HIV seroprevalence in 2001. The same model could be used to measure the effect of changing behaviour in the future.     

Development,Calibration and Performance of an HIV Transmission Model Incorporating Natural History and Behavioral Patterns: Application in South Africa

Understanding HIV transmission dynamics is critical to estimating the potential population-wide impact of HIV prevention and treatment interventions. We developed an individual-based simulation model of the heterosexual HIV epidemic in South Africa and linked it to the previously published Cost-Effectiveness of Preventing AIDS Complications (CEPAC) International Model, which simulates the natural history and treatment of HIV. In this new model, the CEPAC Dynamic Model (CDM), the probability of HIV transmission per sexual encounter between short-term, long-term and commercial sex worker partners depends upon the HIV RNA and disease stage of the infected partner, condom use, and the circumcision status of the uninfected male partner. We included behavioral, demographic and biological values in the CDM and calibrated to HIV prevalence in South Africa pre-antiretroviral therapy. Using a multi-step fitting procedure based on Bayesian melding methodology, we performed 264,225 simulations of the HIV epidemic in South Africa and identified 3,750 parameter sets that created an epidemic and had behavioral characteristics representative of a South African population pre-ART. Of these parameter sets, 564 contributed 90% of the likelihood weight to the fit, and closely reproduced the UNAIDS HIV prevalence curve in South Africa from 1990–2002. The calibration was sensitive to changes in the rate of formation of short-duration partnerships and to the partnership acquisition rate among high-risk individuals, both of which impacted concurrency. Runs that closely fit to historical HIV prevalence reflect diverse ranges for individual parameter values and predict a wide range of possible steady-state prevalence in the absence of interventions, illustrating the value of the calibration procedure and utility of the model for evaluating interventions. This model, which includes detailed behavioral patterns and HIV natural history, closely fits HIV prevalence estimates.     

Assessing the variability of stochastic epidemics.

In predicting the course of individual realizations of an epidemic it is important to know the magnitude of the variability of such realizations about their mean. In this paper and in the context of the general stochastic epidemic, some methods of obtaining approximate estimates of this variability are investigated; one is a multivariate normal approximation based on an asymptotic Gaussian diffusion process, and another uses an approximating linear stochastic process. The extension of these methods to the more detailed models used to describe the transmission dynamics of HIV infection and AIDS is discussed.     

An integral equation model for the control of a smallpox outbreak

An integral equation model of a smallpox epidemic is proposed. The model structures the incidence of infection among the household, the workplace, the wider community and a health-care facility; and incorporates a finite incubation period and plausible infectivity functions. Linearisation of the model is appropriate for small epidemics, and enables analytic expressions to be derived for the basic reproduction number and the size of the epidemic. The effects of control interventions (vaccination, isolation, quarantine and public education) are explored for a smallpox epidemic following an imported case. It is found that the rapid identification and isolation of cases, the quarantine of affected households and a public education campaign to reduce contact would be capable of bringing an epidemic under control. This could be used in conjunction with the vaccination of healthcare workers and contacts. Our results suggest that prior mass vaccination would be an inefficient method of containing an outbreak.     

Assessing the effects of drug misuse on HIV/AIDS prevalence

Drug misuse (injecting drug users-IDU) has been recognized to have a significant effect on the spread of HIV/AIDS epidemic. A deterministic model to assess the contribution of drug misuse and sex in the spread of HIV/AIDS is investigated. The threshold parameters of the model are determined and stabilities are analysed. Analysis of the reproduction number has shown that increase in drug misuse results in an increase in HIV infections. Furthermore, numerical simulations of the model show that drug misuse enhances HIV transmission and progression to AIDS. Thus, in a population with intravenous drug users, advocating for safe sex alone will not be enough to control the HIV/AIDS epidemic.     

Judge attacks South African government's response to AIDS

During the 13th international AIDS conference in Durban, Judge Edwin Cameron of the High Court in Johannesburg, castigated the South African government for its flirtation with those who claim that AIDS is not caused by HIV, and for its slow response to the epidemic. In his deliberation of the Jonathan Mann memorial lecture, the government was admonished for failing to adopt a program to prevent vertical transmission of HIV infection by providing pregnant women with antiretroviral therapy. Quoting an article by the African intellectual Dr. Mamphela Ramphele, he commented that failure to recognize HIV as the country's utmost priority is an irresponsibility that borders on criminality on the part of the government. Moreover, Cameron called on the pharmaceutical industry and developed countries to take steps to lower the prices of drugs and make them more readily available to poverty stricken countries that are more affected by the epidemic.