具有年龄结构的结核病模型的平衡解

本文根据结核病的传染特征,利用数学建模的思想改进了结核病微分方程模型,通过偏微分方法得到该模型平衡解唯一存在的条件.     

具有年龄结构的结核病模型平衡解的稳定性

结核病是由结核杆菌感染引起的慢性传染病,也是中国发病、死亡人数最多的重大传染病之一,几乎一半的中国人是结核杆菌的带菌者.本文在结核病传播的数学模型的动力学系统基础上,不仅考虑了年龄对结核病的影响,还考虑了处于潜伏期的人群,采用建立数学模型的方法来分析结核病的传播机理,建立了一个具有年龄结构的结核病微分方程模型.利用微分方程理论,对模型的无病平衡解的全局渐近稳定性,结核病平衡解的局部稳定性,做了比较系统的分析研究.得到了具有年龄结构的结核病模型平衡解的存在性和稳定性的阀值,为结核病的控制与治疗提供了理论依据,并展示了方程的应用前景.     

浙江省结核病疫情预测和防控策略分析

探究结核病疫情发展趋势是制定结核病防控策略的前提,而采取不同防控策略对疫情控制效果不同.文章根据浙江省结核病流行特点,构建动力学模型,并利用浙江省结核病监测数据和调查数据拟合模型.应用该模型预测浙江省2009-2050年结核病流行过程,发现浙江省总结核发病率呈缓慢下降趋势,但现行结核病防控策略难以达到消灭结核的全球目标(发病率1/100,000/年).其次,文章对比4种防控策略的效果,即提高治疗成功率,降低传染率,治疗潜伏结核感染,和加强耐药控制.分析显示,降低传染率可在短期大幅控制结核病发病率,而治疗潜伏结核感染的防控措施远期控制效果显著.评估各防控策略效果可为制定结核病防控策略提供科学依据.     

诊断与治疗延误对结核病传播作用

通过建立包含结核病诊断和治疗延误因素的数学模型,探讨诊断和治疗延误存在情况的结核病基本再生数(R_0);理论解析证明,当R_0≤1时,该模型存在全局稳定的无病平衡点P_0,当R_01时,模型存在唯一局部稳定的正平衡点;继而利用全国涂阳结核病现况调查数据,拟合诊断和治疗延误对结核病疫情的作用,为制定针对延误的结核病干预措施提供科学依据.     

对角膨胀双变量Poisson回归模型在结核病影响因素分析中的应用

结核病的传播过程比较复杂,易感人群在受到结核病菌传染后可能会患上结核病或结核性胸膜炎,前者具有传染性,而后者暂时不具有传染性,但可能又会发展成结核病,具有传染性.为了探讨结核病的影响因素,利用对角膨胀双变量Poisson回归模型,将受结核病菌传染所发生的结核病患者数和结核性胸膜炎患者数作为模型中的2维响应变量,拟合D市在校学生受结核病菌传染的患病数据.计算结果表明:结核病患者与结核性胸膜炎患者不具有相关性;强阳率、痰菌检验阳性状态、宿舍密度、季节与通风状态差等因素是对结核病的影响因素,数据拟合效果较好,为对结核病的预防工作提供参考依据.     

应用寿命表法和灰色模型分析结试阳转维持率

半个多世纪以来,卡介苗接种已成为安全有效的结核病预防方法,为减少儿童结核病的发病和死亡发挥了巨大作用～(1).卡介苗接种后,结试阳转率是考核接种质量、推算保护效期的重要指标.在观察卡介苗接种后的远期保护效应时,常要计算n年结试阳转维持率,目前多用直接法计算,丢失的信息较多,不便于统计比较.本文试用定群寿命表分析阳转维持率,并应用灰色理论建立阳转维持率的GM(1,1)模型现报告如下. 资料整理 本文所引资料来源于湖北省医科院结防所1985年至1989年在公安县雷州乡卡介苗监测点,对357例新生儿接种卡介苗后五年结试监测结果.种苗者一…     

78例风湿科患者T- SPOT.TB检查结果分析及应用评价

我国是全球22个结核病高负担国家之一,结核病可累及全身各个系统,临床表现多样,尤其是肺外结核病临床诊断更为困难。结核杆菌感染人体后,可以通过“自身免疫”机制使人体对结核菌的抵抗力增强,仅约5%的患者表现为活动性结核,另外95%的患者为无症状的潜伏性结核感染者[1]。潜伏性结核感染者体内长时间存留活菌,当各种因素致机体免疫力下降时结核复发风险显著增加。对风湿病患者使用激素和免疫抑制剂,尤其是肿瘤坏死因子拮抗剂（TNFi）,更应重视患者结核病的风险。我科从2010年起采用T细胞斑点试验（T-SPOT.TB）检查筛查结核高危患者,现报道如下。     

具有测量误差的非线性模型的Bayes估计

测量中大量的函数模型都是非线性回归模型．当回归变量含有一定的测量误差时，我们得到非线性测量误差模型．本讨论了这种模型中未知参数具有正态先验分布时的参数Bayes估计方法，并对这种估计进行了影响分析，证明了删除模型与均值漂移模型中参数的Bayes估计相同，利用Cook统计量给出了删除模型下参数的Bayes估计的影响度量．     

软件可靠性M-O模型和逆线性模型的参数估计

Musa-Okumoto模型和逆线性模型是研究软件可靠性的重要模型，给出了在分组数据下，M－O模型和逆线性模型中参数的最大似然估计及其存在的充分性条件，指出了[4]中的错误，并且给出了一个实例。     

股票价格波动的塑性性质及模型探讨

首先基于股票价格和成交量，根据股票的量价规律，分析了股价波动的塑性性质；然后使用计量经济学方法建立描述股价波动的塑性模型，包括股价塑性基本模型、基本模型的一阶自回归模型、幂指数模型及幂指数模型的一阶自回归模型，基于12支样本股对这些模型进行参数估计和检验；最后对4种形式的股价塑性模型进行了总结。由4种模型均能够通过经济学检验和统计学检验可知股价波动具有塑性性质，且幂指数模型描述股价塑性较为科学、合理。     

Mathematical analysis of a three-strain tuberculosis transmission model

In recent years, bacteria have become resistant to antibiotics, leading to a decline in the effectiveness of antibiotics in treating infectious diseases. A mathematical model for multi-strain tuberculosis transmission dynamics to assess the burden of drug-sensitive, multidrug-resistant and extensively drug-resistant tuberculosis is formulated and analyzed. Each single strain submodel is shown to exhibit backward bifurcation when the threshold parameter is less than unity. Both analytical and numerical results show that resistance to drugs increase with increase in drug use, that is, active tuberculosis treatment results in a reduction of drug sensitive and increase in multidrug-resistant tuberculosis. Furthermore, use of second line drugs results in a decrease of the multidrug-resistant and increase of extensively drug resistant tuberculosis as most cases of multidrug resistant tuberculosis occur as a result of inappropriate, misuse or mismanaged treatment. Both the analytic results and numerical simulations suggest that quarantine of extensively drug resistant TB cases in addition to treatment of other forms of TB may be able to reduce the spread of the epidemic in poor resource-settings.     

Global stability of two models with incomplete treatment for tuberculosis

Two tuberculosis (TB) models with incomplete treatment are investigated. It is assumed that the treated individuals may enter either the latent compartment due to the remainder of Mycobacterium tuberculosis or the infectious compartment due to the treatment failure. The first model is a simple one with treatment failure reflecting the current TB treatment fact in most countries with high tuberculosis incidence. The second model refines the simple one by dividing the latent compartment into slow and fast two kinds of progresses. This improvement can be used to describe the case that the latent TB individuals have been infected with some other chronic diseases (such as HIV and diabetes) which may weaken the immunity of infected individuals and shorten the latent period of TB. Both of the two models assume mass action incidence and exponential distributions of transfers between different compartments. The basic reproduction numbers of the two models are derived and their intuitive epidemiological interpretations are given. The global dynamics of two models are all proved by using Liapunov functions. At last, some strategies to control the spread of tuberculosis are discussed.     

基于灰色预测模型的新疆肺结核疫情分析

借助灰色系统理论对新疆2004-2010年肺结核发病率进行研究,建立不同维度的静态GM(1,1)模型与动态等维递补灰预测模型对数据进行模拟和预测.针对新疆肺结核疫情发病率数据,探索建立新疆肺结核疫情传播预测模型,为肺结核防治提供科学依据.     

Optimal intervention strategies for tuberculosis

This paper deals with the problem of optimal control of a deterministic model of tuberculosis (abbreviated as TB for tubercle bacillus). We first present and analyze an uncontrolled tuberculosis model which incorporates the essential biological and epidemiological features of the disease. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated basic reproduction number is less than the unity. Based on this continuous model, the tuberculosis control is formulated and solved as an optimal control problem, indicating how control terms on the chemoprophylaxis and detection should be introduced in the population to reduce the number of individuals with active TB. Results provide a framework for designing the cost-effective strategies for TB with two intervention methods.     

The dynamics of an age-structured TB transmission model with relapse

This paper deals with the global dynamics for a tuberculosis transmission model with age-structure and relapse. The time delay in the progression from the latent individuals to becoming the infectious individuals is also considered in our model. We perform some rigorous analyses for the model, including presenting an explicit formula for the basic reproduction number of the model, addressing the persistence of the solution semiflow and the existence of a global attractor. Based on these analyses, we establish some results about stability and instability of the solutions for our model. At end, the model is applied to describe tuberculosis transmission in China. The number of the total population and the number of the annual newly reported TB cases both match the statistical data well. The number of the total population, the latent individuals, the infectious individuals, the Purified Protein Derivative (PPD) positive rate, and the prevalence rate from 2020 to 2035 all are presented.     

一类带有疫苗注射和常比率输入的传染病模型系统分析

卡介苗注射是目前很多国家控制肺结核传播的有效方法.疫苗注射并非完全有效,考虑疫苗注射后的免疫丧失率,疫苗注射的覆盖率等因素建立一个描述肺结核传播的数学模型,证明了无病平衡点全局渐进稳定性,对地方病平衡点的稳定性进行了计算机模拟,最后用2011年数据验证了理论的实际应用价值.     

Stability and traveling waves of an epidemic model with relapse and spatial diffusion

An epidemic model with relapse and spatial diffusion is studied. Such a model is appropriate for tuberculosis, including bovine tuberculosis in cattle and wildlife, and for herpes. By using the linearized method, the local stability of each of feasible steady states to this model is investigated. It is proven that if the basic reproduction number is less than unity, the disease-free steady state is locally asymptotically stable; and if the basic reproduction number is greater than unity, the endemic steady state is locally asymptotically stable. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem, the existence of a traveling wave solution which connects the two steady states is established. Furthermore, numerical simulations are carried out to complement the main results.     

Lie integrable cases of the simplified multistrain/two-stream model for tuberculosis and dengue fever

We apply the techniques of Lie's symmetry analysis to a caricature of the simplified multistrain model of Castillo-Chavez and Feng [C. Castillo-Chavez, Z. Feng, To treat or not to treat: The case of tuberculosis, J. Math. Biol. 35 (1997) 629-656] for the transmission of tuberculosis and the coupled two-stream vector-based model of Feng and Velasco-Hernández [Z. Feng, J.X. Velasco-Hernández, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol. 35 (1997) 523-544] to identify the combinations of parameters which lead to the existence of nontrivial symmetries. In particular we identify those combinations which lead to the possibility of the linearization of the system and provide the corresponding solutions. Many instances of additional symmetry are analyzed.     

Tuberculosis model with relapse via fractional conformable derivative with power law

The present study explores the tuberculosis dynamics with relapse with a nonlocal conformable derivative in the Caputo sense. The real data of tuberculosis cases since 2002 to 2017 are used to the set the parameters. The numerical results with the realistic parameters are chosen and present the graphical results. Further, we assign different values to the fractional parameters α and β and discuss its effect on the system variables. The use of these two fractional operators on the model simultaneously with realistic data gives reliable results.