基于时滞动力学模型对钻石公主号邮轮疫情的分析

2019年末以来,新型冠状病毒肺炎迅速蔓延的疫情引发了全球关注.文献[5-6]提出了一类时滞动力学系统的新冠肺炎传播模型用以描述疫情的发展趋势.文献[7]在此基础上,结合CCDC统计数据,提出了一类基于CCDC统计数据的随机时滞动力学模型.本文将使用以上两类模型研究分析"钻石公主号"邮轮的疫情发展.基于日本厚生劳动省公布的数据,本文准确反演出模型参数,进而有效模拟当前疫情的发展,并预测疫情未来的趋势,发现在疫情爆发初期基本再生数R0(t)较大,而后随着防控措施加强而逐渐减小;约在2月下旬,累计确诊人数增长速度放缓,在3月上旬,累计确诊人数趋于稳定,即无新增确诊人数,疫情得到有效控制;最终累计确诊人数对隔离率变化敏感,隔离率升高,最终累计确诊人数将有显著下降.针对传染率较高、隔离率较低的问题,本文建议日本政府进一步加强防控措施,抑制疫情的大规模爆发.     

基于新增确诊数据和光滑算子对FUDAN-CCDC模型反演算法的改进

2019年12月,新型冠状病毒肺炎(Corona-Virus-Disease,COVID-19)的疫情被人们识别认知,全世界都开始重视这个疫情.截至2020年4月21日24时,全球已累计确诊2 568 603例.科学地预测疫情发展趋势对疫情防控至关重要.FUDAN-CCDC模型用于国内疫情的预测产生了很好的效果,但是在用于欧美国家的疫情分析预测时效果不是很理想.本文对FUDAN-CCDC模型的优化目标进行了改进,考虑了新增数据的拟合,并考虑了欧美疫情数据的周末现象,提出对数据进行光滑预处理.新加入的两种可能的反演优化目标的改变,会对零增时间有较大的影响.在此基础上进一步发展的算法,可以得到更好的拟合和预测效果.     

基于一类时滞动力学系统对新型冠状病毒肺炎疫情的建模和预测

2019年12月,新型冠状病毒肺炎(novel coronavirus pneumonia, NCP)疫情从武汉开始暴发,几天内迅速传播到全国乃至海外.科学有效地掌控疫情发展对疫情防控至关重要.本文基于全国各级卫生健康委员会每日公布的累计确诊数和治愈数,提出一类基于时滞动力学系统的传染病动力学模型.在模型中引入时滞过程,用来描述病毒潜伏期和治疗周期.通过公布的疫情数据,首先准确反演模型的参数;其次有效地模拟目前疫情的发展,并预测疫情未来的趋势;最后分析各级政府防控措施手段的有效程度,并发现在现有的高效防控措施下,疫情将在近期好转.     

COVID-19疫情时滞模型构建与确诊病例驱动的追踪隔离措施分析

新型冠状病毒肺炎(COVID-19)疫情自暴发以来,众多研究者基于公开的疫情数据和经典的SEIR模型研究了疫情的发展趋势、传播风险等,为早期COVID-19疫情预测预警提供了重要的决策依据.本论文首先讨论在突发性传染病疫情发展期间,传染病数学模型是如何助力疫情防控的,能在公共卫生重大突发事件中发挥什么样的重要作用.然后集中介绍如何建立数学模型来刻画COVID-19疫情期间密切跟踪隔离措施的实施以及措施强度的变化,重点讨论有症状感染者和确诊病例驱动的追踪隔离措施在建模上的异同,最后得到确诊病例驱动的COVID-19时滞非自治传染病模型.主要结论揭示了确诊滞后不仅能有效延迟感染者类峰值到来的时间,而且使得其出现多峰,甚至最终感染规模可能增大的现象,但是我国强有力的综合防控策略能够有效减缓确诊滞后带来的不利影响.这为分析复杂疫情数据提供了新的重要的模型参考.     

基于动力学模型的COVID-19疫情预测与控制策略研究

本文基于COVID-19的传播机理以及追踪隔离染病者的密切接触者、治疗等公共干预措施,建立了非自治的动力学模型,对湖北省疫情发展进行预测并评估相应控制策略的有效性.首先基于湖北省卫生健康委员会公布的数据,利用最小二乘法以及MCMC估计动力学模型中的待估计参数值.然后基于估计得到的参数值,验证模型预测的有效性,估计湖北省总病例数达峰时间,峰值规模以及流行时间.此外,研究发现湖北省每天的总病例数中隔离的潜伏者以及现存确诊者占比重较大,因此,加快对于隔离人群的筛查、对于确诊人群的治疗能够加快疫情的结束.最后对有效再生数进行敏感性分析,揭示了即使在疫情发展的后期,加强对密切接触者的追踪隔离依然是疫情控制最有效的措施.     

关于SARS的预测模型

建立了确诊病例和疑似病例累计人数随时间变化的差分方程模型.通过对其求解和合理的假设讨论了确诊病例数在不同的阶段随时间变化的情况.进一步,用我们的模型来模拟北京疫情(2003.4.20—2003.5.29)的变化情况.说明我们的模型具有一定的实用性.     

新型冠状病毒肺炎疫情控制策略研究:效率评估及建议

基于传播动力学及普适SEIR (susceptible-exposed-infectious-recovered/removed)模型和程序Epi SIX (模型总参数只有10个),实时跟踪国家及各地卫生健康委员会(简称卫健委)自2019年12月12日以来发布的确诊数据,对新型冠状病毒肺炎(简称新冠肺炎)疫情的流行趋势进行了研判,对疾控策略的效率进行了评估,并将相应的建议提供给疾控方参考.特别地,厘清了这次疫情的流行病学基本参数,如基本再生数、平均潜伏期、平均传染期、非典型患者占比和流行趋势,包括流行时间、疫情拐点、流行规模,并分析了控制强度对传播的影响等.同时创建了一个网页来更新预测结果.     

具有跟踪隔离措施的新冠肺炎传播模型分析及应用

报道于2019年12月底的新型冠状病毒肺炎(COVID-19)疫情, 由于2020年春运期间人口的大规模流动, 使得其迅速蔓延.自2020年1月23日起, 我国采取了各种措施使得疫情得到了有效的控制, 例如武汉封城、确诊病例的密切接触者跟踪隔离、湖北人员的居家隔离等.该文基于COVID-19在山西省的实际传播情况, 建立了具有输入病例和确诊病例密切接触者跟踪隔离的动力学模型.在不考虑输入病例的情况下, 分析了模型的动力学行为.利用山西省COVID-19病例数据, 计算了实时再生数, 发现山西省2020 年1月25日全省封村封街道有效控制了COVID-19疫情的传播, 即实时再生数小于1, 从宏观角度验证了防控措施的有效性.进一步通过模型的数值拟合得到: 早期染病者隔离14天的防控策略是合理有效的; 武汉封城时间越早, 染病者的规模越小; 跟踪隔离到大量确诊病例的接触者时, 染病者的规模越小.     

动态传播率模型及其在疫情分析中的应用

应用数据驱动的动态传播率来代替基本传染数$R_0$,在全国和省市两个层面上研究COVID-19疫情发展的特点和趋势。首先,基于动态增长率建立传染病常微分方程,推导得出动态传播率模型。其次,选择幂函数作为动态传播率的拟合函数,以3天作为最优滑窗期,对各地拐点进行了估计。最后,通过动态模型对各地不同程度尾声开始的起点进行了预测,并在13个省市间进行9个疫情相关指标的对比分析。结果显示,各地动态传播率在经过短暂的波动后均稳步下降,疫情得到有效控制;估计的拐点主要集中在2月中旬,而预测的尾声都将在3月底之前到来;同时,各地疫情发展特点和趋势、防控措施力度和效果存在一定差异。     

北京市SARS疫情统计分析

本文对严重急性呼吸道综合症 SA RS疾病进行了统计分析 .文章首先以北京市海淀区 SARS确诊病例和疑似病例为研究对象 ,分别按照地区、人口进行了统计分析 ,得出海淀区不同小区疫情发展的显著程度 .然后利用正交试验设计 ,分别就年龄、性别、职业等因素对海淀区 SARS确诊病人和疑似病人影响程度进行了统计分析 ,得出 2 1岁到 50岁的学生和干部得病率最高的统计结果 ,这完全符合海淀区的疫情事实 .这个统计结果已经被海淀区政府“海淀区政府应急管理信息系统 ( H EMIS)”[6]采用 . H EMIS系统作为中国第一个政府应急系统在海淀区 SARS防治中起到了一定作用 [1 ] .文章最后研究了北京市每天新增的确诊病例和每天疑似病例转为确诊病例之间的相关系数 ,从它们的相关性分析可以反映出防治 SARS疫情措施的有效性 .     

Assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of HIV/AIDS in heterosexual settings

A deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of the disease in heterosexual settings in which homosexuality and bisexuality issues have remained taboo is presented. The epidemic threshold and equilibria for the model are determined and stabilities are investigated. Comprehensive qualitative analysis of the model including invariance of solutions and permanence are carried out. The epidemic threshold known as the basic reproductive number suggests that heterosexuality, homosexuality, and bisexuality influence the growth of the epidemic in HIV/AIDS affected populations and the partial reproductive number (homosexuality induced or heterosexuality and bisexuality induced) with the larger value influences the overall dynamics of the epidemic in a setting. Numerical simulations of the model show that as long as one of the partial reproductive numbers is greater than unity, the disease will exist in the population. We conclude from the study that homosexuality and bisexuality enlarge the epidemic in a heterosexual setting. The theoretical study highlights the need to carry out substantial research to map homosexuals and bisexuals as it has remained unclear as to what extent this group has contributed to the epidemic in heterosexual settings especially in southern Africa, which has remained the epidemiological locus of the epidemic.     

Local and global bifurcations in an SIRS epidemic model

This paper studies the existence and stability of the disease-free equilibrium and endemic equilibria for the SIRS epidemic model with the saturated incidence rate, considering the factor of population dynamics such as the disease-related, the natural mortality and the constant recruitment of population. Analytical techniques are used to show, for some parameter values, the periodic solutions can arise through the Hopf bifurcation, which is important to carry different strategies for the controlling disease. Then the codimension-two bifurcation, i.e. BT bifurcation, is investigated by using a global qualitative method and the curves of saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation are obtained at the degenerate equilibrium. Moreover, several numerical simulations are given to support the theoretical analysis.     

脉冲接种作用下具有垂直传染的SIR模型的定性分析

研究了脉冲接种作用下的具有垂直传染的SIR传染病模型,得到了无病周期解的全局稳定性和基本再生数.通过数值仿真验证以上这些结论.     

Dynamics of SIS Epidemic Model with Varying Total Population and Multivaccination Control Strategies

In this paper, two susceptible‐infected‐susceptible epidemic models with varying total population size, continuous vaccination, and state‐dependent pulse vaccination are formulated to describe the transmission of infectious diseases, such as diphtheria, measles, rubella, pertussis, and so on. The first model incorporates the proportion of infected individuals in population as monitoring threshold value; we analytically show the existence and orbital asymptotical stability of positive order‐1 periodic solution for this control model. The other model determines control strategy by monitoring the proportion of susceptible individuals in population; we also investigate the existence and global orbital asymptotical stability of the disease‐free periodic solution. Theoretical results imply that the disease dies out in the second case. Finally, using realistic parameter values, we carry out some numerical simulations to illustrate the main theoretical results and the feasibility of state‐dependent pulse control strategy.     

Bifurcation analysis of a delayed epidemic model

In this paper, Hopf bifurcation for a delayed SIS epidemic model with stage structure and nonlinear incidence rate is investigated. Through theoretical analysis, we show the positive equilibrium stability and the conditions that Hopf bifurcation occurs. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. In addition, we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.     

Threshold conditions for a discrete nonautonomous SIRS model

In this paper, a discrete nonautonomous SIRS epidemic model is studied. The model is constructed by applying a nonstandard finite difference scheme. Under weaker assumptions, the sufficient and necessary conditions on the permanence and strong persistence of the disease and the sufficient condition on the extinction of the disease are established. In order to illustrate our theoretical analysis, some numerical simulations are included in the end. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of awareness program and delay in the epidemic outbreak

In the present paper, an epidemic model has been proposed and analyzed to investigate the impact of awareness program and reporting delay in the epidemic outbreak. Awareness programs induce behavioral changes within the population, and divide the susceptible class into two subclasses, aware susceptible and unaware susceptible. The existence and the stability criteria of the equilibrium points are obtained in terms of the basic reproduction number. Considering time delay as the bifurcating parameter, the Hopf bifurcation analysis has been performed around the endemic equilibrium. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated by using the normal form theory and central manifold theorem. To verify the analytical results, comprehensive numerical simulations are carried out. Copyright © 2016 John Wiley & Sons, Ltd.     

A fractional order epidemic model and simulation for avian influenza dynamics

We present a nonlinear fractional order epidemic model to investigate the spreading dynamical behavior of the avian influenza. The population of the model contains susceptible individuals, asymptomatic but infective latent individuals, and infective individuals. We first establish the existence, uniqueness, nonnegativity, and positive invariance of the solution, then we study the reproduction number of the model and the stability of the disease‐free equilibrium. We observe that the reproduction number varies with the order of the fractional derivative ν. In terms of epidemics, this suggests that varying ν induces a change in the avian's epidemic status. Furthermore, we derive the sufficient conditions for the existence and the stability of the endemic equilibrium. Finally, we carry out some numerical simulations to validate the analytical results. We find from simulations that the solution of the fractional order model tends to a stationary state over a longer period of time with decreasing the value of the fractional derivative, and the size of epidemic decreases with decreasing ν.     

Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa

We formulate a deterministic HIV/AIDS model to theoretically investigate how counselling and testing coupled with the resulting decrease in sexual activity could affect the HIV epidemic in resource-limited communities. The threshold quantities are determined and stabilities analyzed. Theoretical analysis and numerical simulations support the idea that increase in the number of sexually inactive HIV positive individuals who voluntarily abstain from sex has a positive impact on HIV/AIDS control. Results from this theoretical study suggest that effective counselling and testing have a great potential to partially control the epidemic (especially when HIV positive individuals either willingly withdraw from risky sexual activities or disclose their status beforehand) even in the absence of antiretroviral therapy (ART). Therefore, more needs to be done in resource-limited settings, such as sub-Saharan Africa, as far as the HIV/AIDS epidemic is concerned and a formalized information, education, and communication strategy should be given prominence in educational campaigns.     

Threshold conditions for a non-autonomous epidemic model with vaccination

In this article, we wish to investigate the dynamical behaviour of an SIRVS epidemic model with time-dependent coefficients. Under the quite weak assumptions, we give some new threshold conditions which determine whether or not the disease will go to extinction. The permanence and extinction of the infectious disease is studied. When the system degenerates into periodic or almost periodic system, the corresponding sharp threshold results are obtained for permanent endemicity versus extinction in terms of asymptotic time. In order to illustrate our theoretical analysis, some numerical simulations are also included in the end.