媒体报道对一类具有潜伏期的传染病控制的影响

针对媒体报道产生的信息对一类具有潜伏期的传染病控制的影响问题,建立了一类带时滞的传染病模型.计算得到模型的基本再生数R_0并证明了当R0<1时,无病平衡点局部渐近稳定.通过分析模型正平衡点处对应的特征方程,得到了模型在正平衡点处稳定的条件,给出了正平衡点处会出现Hopf分支的临界条件并得到相关结论.     

具周期性潜伏期的SEIR传染病模型的动力学

研究了一类具有周期性潜伏期的常微分SEIR传染病模型.首先借助于染病年龄分布函数导出了模型.紧接着定义了模型的基本再生数R_0并利用耗散动力系统的相关理论证明R_0是决定疾病是否继续流行的阈值.最后,利用数值方法进一步验证了结论,并分析了忽略潜伏期的周期性对估计疾病传播能力的影响.     

一类潜伏期有传染性的传染病模型动力学分析

建立了一类潜伏期具备传染性的传染病传播模型,根据疾病传播规律求解了疾病消失和持续生存的阈值——基本再生数.对系统的稳定性进行了讨论,得到了系统稳定性条件.最后,以COVID-19为例,解释了各种举措在疾病控制中的作用,并对疫情传播扩散做了探讨和预测.     

一类具有饱和发生率的SEIR模型的全局稳定性

建立并分析了一类具有饱和发生率、在潜伏期具有传染性的SEIR模型.得到了模型的无病平衡点与地方病平衡点全局渐近稳定的充分条件.     

一类潜伏期具有常数输人率的SEIR模型在流感防控中的应用

针对流感病毒具有的潜伏性、隐性感染者的流动难于防控性、较高的病死率及治愈后拥有的免疫力等特性建立了潜伏期具有常数输入率的SEIR传染病模型.证明了疾病模型仅存在地方病平衡点,并且是全局渐近稳定的,给出了流感防控过程中总人口输入控制及针对染病者占总人数百分比不同情况下的对隐性染病者输入比例控制值的计算公式,并对甲型H1N1流感病毒相应数据数值模拟.     

潜伏期变化的随机流行病模型及其贝叶斯推断

本文讨论了潜伏期和传染期均服从威布尔分布、易感性随机变化的一类随机流行病模型,并利用M CM C算法对潜伏期、传染期的参数和易感性的超参数作了贝叶期推断.这种分析方法比以往各种方法更适用于各类疾病.     

基于ARIMA模型对我国服务价格指数的预测

基于ARIMA模型对2005年1月至2017年10月的我国服务价格指数月度数据进行预测分析.利用对统计数据的变化趋势及季节性进行验证结果表明该模型合理、有效.运用模型对2017年11月至2018年6月份的我国服务价格指数进行了预测,预测值与实际值的估计误差控制在有效范围内,预测效果比较理想,预测结果为到2018年上半年我国服务价格指数涨幅在3.5%左右,全国居民消费价格指数维持于2%左右,2018上半年出现严重通胀的可能性较小.     

一类潜伏期与传染期均传染的SEIQR传染病模型

研究了一类潜伏期和感染期均传染的SEIQR模型的全局稳定性,找到疾病绝灭和持续生存的阈值——基本再生数R0,证明了无病平衡点和地方病平衡点的存在性和全局渐近稳定性,揭示了隔离对疾病控制的积极作用。     

一类具有离散双时滞的SEIR传染病模型的稳定性与持久性

针对一类潜伏期和恢复期描述为离散双时滞的SEIR传染病模型,给出无病平衡点和地方病平衡点存在条件,证明了无病平衡点和地方病平衡点的稳定性,以及疾病的持久性.应用数值模拟验证了疾病的持久性与灭绝性,分析了接触率对疾病流行趋势的影响.     

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.     

Spatial Spread of Rabies in China

The reported data on human rabies in China in the past 10 years demonstrate that the number of counties with human rabies cases has increased dramatically and the disease has spread from southern provinces to northern provinces. The aim of this paper is to study how the movement of dogs impacts the spatial spread of rabies and to find effective strategies for controlling rabies. We firstly construct a reaction-diffusion model for dogs and humans and obtain the minimal wave speed. Then we consider the existence of traveling waves and the influences of parameters on human rabies cases and the minimal wave speed by numerical simulations. Lastly, we discuss the local stability of the endemic equilibrium. Our analysis indicates that dog movement leads to the traveling wave of dog and human rabies and has a large influence on the minimal wave speed. Thus restricting the movement of dogs, in particular the exposed and infected dogs, is an effective way to prevent the spatial spread of rabies.     

Basic Reproduction Number of Rabies Model with Stage Structure

The mathematical model is proposed to simulate the dynamics of rabies transmissions in the raccoon population where juveniles stay with their mother and become adults until they establish their own habitats. The basic reproduction number of rabies transmission is formulated and is shown to be a threshold value of disease invasion. The bifurcation direction from the disease-free equilibrium is proved to be forward when the basic reproduction number passes through unity for spatial homogenous environment. The global stability of the disease-free steady state is also studied.     

A schistosomiasis compartment model with incubation and its optimal control

A new mathematical model included an exposed compartment is established in consideration of incubation period of schistosoma in human body. The basic reproduction number is calculated to illustrate the threshold of disease outbreak. The existence of the disease free equilibrium and the endemic equilibrium are proved. Studies about stability behaviors of the model are exploited. Moreover, control measure assessments are investigated in order to seek out effective control interventions for anti‐schistosomiasis. Then, the corresponding optimal control problem according to the model is presented and solved. Theoretical analyses and numerical simulations induce several prevention and control strategies for anti‐schistosomiasis. At last, a discussion is provided about our results and further work. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Traveling Epizootic Waves of a Fox Rabies Model with Small Spatial Diffusion

In this paper, to describe the spread of fox rabies, a degenerate SEI epidemic model with small spatial diffusion equipped by infectious foxes due to rabies is investigated. In particular, the existence of traveling waves is established by the geometric singular perturbation theory for the larger speeds, while the non-existence of traveling wave is still derived for the smaller speeds. Moreover, some numerical simulations are implemented to illustrate the propagation dynamics driven by traveling waves.     

Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.     

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.     

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.     

Global dynamics of a Vector‐Borne disease model with two delays and nonlinear transmission rate

In this paper, we investigate a Vector‐Borne disease model with nonlinear incidence rate and 2 delays: One is the incubation period in the vectors and the other is the incubation period in the host. Under the biologically motivated assumptions, we show that the global dynamics are completely determined by the basic reproduction number R₀. The disease‐free equilibrium is globally asymptotically stable if R₀≤1; when R₀>1, the system is uniformly persistent, and there exists a unique endemic equilibrium that is globally asymptotically. Numerical simulations are conducted to illustrate the theoretical results.