航班延误传播模型研究

为研究航班延误传播规律,利用真实航班运行数据构建机场航班网络。基于易感-感染-免疫(Susceptible-Infected-Recovered,SIR)模型建立航班延误传播模型,选用梯度下降法求解模型参数;以最大连通子图比例(S)作为网络抗毁性指标,使用选择性攻击和随机攻击策略分析抗毁性;将航班延误传播模型与长短期记忆(Long Short-Term Memory,LSTM)网络预测模型、马尔科夫模型进行延误预测比较,引用历史数据进行实例分析。结果表明:机场航班网络平均路径长度为2.387,聚类系数为0.58,度分布呈双幂率分布,具有小世界和无标度特性;随机攻击删除节点累计300个,S>0.5,网络抗毁性强,选择性攻击删除节点比例15%~20%,S=0,网络抗毁性差;航班延误传播模型平均绝对百分比误差(Mean Absolute Percentage Error,MAPE)分别与LSTM预测模型、马尔科夫模型相差4.41百分点、50.98百分点,具有更高精度。所提出的模型为航班延误提供了预测工具,为航空公司、机场等单位制定有效延误缓解措施提供参考。

Location of emergency rescue center based on SIR epidemiological model

In view of the pressure time of emergency rescue against the infectious diseases,a mathematical model to optimize the location of emergency rescue centers is proposed.The model takes full account of the spread function of infectious diseases,the cycle of pulse vaccination,the distance between the demand area and the emergency rescue centers,as well as the building and maintenance cost for the emergency rescue center,and so on.At the same time,the model integrates the traditional location selection models which are the biggest cover model,the p-center model and the p-median model,and it embodies the principles of fairness and efficiency for the emergency center location.Finally,a computation of an example arising from practice provides satisfactory results.

一种反病毒策略传播模型

针对目前流行的反病毒策略不能有效抑制病毒传播和开销大的不足,提出了一种叫策略竞争策略(Countermeasure Competing Strategy,CMC)的反病毒策略传播模型,策略扮演同病毒竞争的角色。通过对几种流行的反病毒策略模型(RANDOM,TARGE,KS)和CMC进行仿真测试,证明了当策略传播网络具有较高的连通性时,CMC是一种高效的反病毒策略,对病毒传播具有较好的抑制作用。

Evaluation of regional energy security in eastern coastal China based on the DPSIR model

The DPSIR assessment method, which implies the relationships among driving force （D）, pressure （P）, status （S）, impact （I）, and response （R）, is widely applied by scholars. This paper aims to establish a comprehensive assessment system for regional energy security in eastern coastal China based on the above model using different indicators. Factor analysis and the SPSS statistical analysis software were used to carry out scientific and quantitative assessments. The results indicated that con- tradictions of energy supply and demand as well as environmental pollution are the critical factors that present great challenges to regional energy security in this area. The authors argued that a sustainable, stable, and safe supply energy supply is crucial in solving the aforesaid dilemma, and improving the energy use efficiency is one of the best choices. Some countermeasures and suggestions regarding regional energy supply stability and utilization security were pointed out.

Optimal parameterization of COVID-19 epidemic models

At the time of writing,coronavirus disease 2019(COVID-19)is seriously threatening human lives and health throughout the world.Many epidemic models have been developed to provide references for decision-making by governments and the World Health Organization.To capture and understand the characteristics of the epidemic trend,parameter optimization algorithms are needed to obtain model parameters.In this study,the authors propose using the Levenberg–Marquardt algorithm(LMA)to identify epidemic models.This algorithm combines the advantage of the Gauss–Newton method and gradient descent method and has improved the stability of parameters.The authors selected four countries with relatively high numbers of confirmed cases to verify the advantages of the Levenberg–Marquardt algorithm over the traditional epidemiological model method.The results show that the Statistical-SIR(Statistical-Susceptible–Infected–Recovered)model using LMA can fit the actual curve of the epidemic well,while the epidemic simulation of the traditional model evolves too fast and the peak value is too high to reflect the real situation.

On the Reproduction Number and a Presentation of Results for Infectious Diseases Models

The classical Kermack-McKendrick homogeneous SIR （susceptible, infected and removed） model is well known, Its general solution is a function of the unique parameter （the reproduction number） that is equal to a mean number of secondary cases produced by a typical infected individual in a completely susceptible population. If the reproduction number is more than one （the threshold value） its value describes an epidemic scope： larger values correspond to more severe epidemics. In the more complex compartment SIR models the population is divided into several non-overlapping groups. It allows us to partly remove assumptions of the classical model. It is well known that for this kind of models, just as for the classical model there is the threshold parameter R0. Usually it is called by the same name--the reproduction number--though the physical meaning of this parameter has changed. The main purpose of the paper is to show that this new parameter is a not unique measure of an epidemic severity for any compartment SIR model. In particular it means that for such models comparison of the severity of two epidemics by simple comparing values of their reproduction numbers is incorrect. For compartment models these statements were proved with the help of the corresponding ODEs analysis. Very popular now individual-based models （IBMs） are more complex in comparison with the compartment ones since they use overlapping groups （school children are members of families also, for example）. In such a case Diekmann＇s calculation method for the reproduction number used in many papers is inapplicable as well as a presentation the simulation results obtained as functions of this parameter.

一类复杂流行病学模型的混沌研究

研究了一类周期变化的非线性复杂发病率的广义流行病学模型(SIR(susceptible,infected,recovered)模型).通过一系列坐标变换将原模型转化为Hamilton系统,运用Melnikov方法证明了该系统存在混沌运动,给出了发生同宿分岔的条件,并用数值模拟验证了上述结果.

GLOBAL STABILITY OF AN AGE-STRUCTURED SIR EPIDEMIC MODEL WITH PULSE VACCINATION STRATEGY

This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age （duration since infection）. The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infectiomfree situation if the impulsive period T and proportion p satisfy Ro（p,T） 〈 1. Optimal problem is discussed： Pulse vaccination strategy with minimal costs at given R0（p, T） 〈 1.

Traveling wave solutions of a nonlocal dispersal SIRS model with spatio-temporal delay

This paper is mainly concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal SIRS model with nonlocal delayed transmissions. We find that the existence and nonexistence of traveling wave solutions are determined by the critical wave speed c^＊. More specifically, we establish the existence of traveling wave solutions for every wave speed c〉c^＊ and R0 〉 1 by means of upper-lower solutions and Schauder＇s fixed point theorem. Nonexistence of traveling wave solutions is obtained by Laplace transform for any wave speed c ∈ （0, c^＊） and R0 〉 1.

TRAVELING WAVES FOR A SIRS MODEL WITH NONLOCAL DIFFUSION

In this paper, we study a delayed SIRS model with nonlocal diffusion. The well posedness of the model is investigated. Furthermore, we concern with the problem of traveling wave solutions. By using the partial quasi-monotone condition, cross-iteration scheme and fixed-point theorem, sufficient conditions are derived for the existence of traveling waves connecting the two equilibria which depends on the existence of a pair of upper solution and lower solution. We in fact construct a pair of upper solution and lower solution concretely to guarantee the existence of traveling waves.

DYNAMIC ANALYSIS OF AN SIR MODEL WITH STOCHASTIC PERTURBATIONS

In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solution, and we utilize stochastic Lyapunov functions to show the asymptotic behavior of the solution.

A SIMPLE DISCRETE-TIME ANALOGUE PRESERVING THE GLOBAL STABILITY OF A CONTINUOUS SIRS EPIDEMIC MODEL

In this paper, we consider the backward Euler discretization derived from a continuous SIRS epidemic model, which contains a remaining problem that our discrete model has two solutions for infected population; one is positive and the other is negative. Under an additional positiveness condition on infected population, we show that the backward Euler discretization is one of simple discrete-time analogue which preserves the global asymptotic stability of equilibria of the corresponding continuous model.

Rumor Spreading Model with Trust Mechanism in Complex Social Networks

In this paper, to study rumor spreading, we propose a novel susceptible-infected-removed （SIR） model by introducing the trust mechanism. We derive mean-field equations that describe the dynamics of the SIR model on homogeneous networks and inhomogeneous networks. Then a steady-state analysis is conducted to investigate the critical threshold and the finaJ size of the rumor spreading. We show that the introduction of trust mechanism reduces the final rumor size and the velocity of rumor spreading, but increases the critical thresholds on both networks. Moreover, the trust mechanism not only greatly reduces the maximum rumor influence, but also postpones the rumor terminal time, which provides us with more time to take measures to control the rumor spreading. The theoretical results are confirmed by sufficient numerical simulations.

PREVENTING RUMOR SPREADING ON SMALL-WORLD NETWORKS

Since the spreading of harmful rumors can deeply endanger a society, it is valuable to investigate strategies that can efficiently prevent hazardous rumor propagation. To conduct this investigation, the authors modify the SIR model to describe rumor propagation on networks, and apply two major immunization strategies, namely, the random immunization and the targeted immunization to the rumor model on a small-world network. The authors find that when the average degree of the network is small, both two strategies are effective and when the average degree is large, neither strategy is efficient in preventing rumor propagation. In the latter case, the authors propose a new strategy by decreasing the credibility of the rumor and applying either the random or the targeted immunization at the same time. Numerical simulations indicate that this strategy is effective in preventing rumor spreading on the small-world network with large average degree.

STUDYING THE IDENTIFIABILITY OF EPIDEMIOLOGICAL MODELS USING MCMC

Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against mea- sured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo （MCMC） methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identi- fiability： a basic SIR model, an influenza model with vaccination and treatment and a HIV-Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The pre- sented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.