A Restricted SIR Model with Vaccination Effect for the Epidemic Outbreaks Concerning COVID-19

This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms

In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.

Modeling and dynamics analysis of the fractional-order Buck-Boost converter in continuous conduction mode

In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode （CCM） are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck- Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.

Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus

The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.

Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping

A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.

Intelligent Networks for Chaotic Fractional-Order Nonlinear Financial Model

The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system.The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation(LMB),named the ANNs-LMB.This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution.Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model.The selection of the data to solve the fractional-order chaotic financial model are selected as 75%for training,10%for testing,and 15%for certification.The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise.The obtained results are testified to reduce the mean square error(MSE)for solving the fractional model and verified through the various measures including correlation,MSE,regression histogram of the errors,and state transition(ST).

一类具有进化效应的时滞SIR模型的动力学分析

主要研究具有进化效应和受时滞影响的SIR传染病模型的动力学行为.首先,将时滞参数作为分支参数,在常微分和偏微分系统中研究带时滞因素的SIR模型的正平衡点稳定性,并得到在健康个体的防御能力和已感染个体的感染能力相互作用的情况下产生Hopf分支的条件;其次,利用规范型理论和中心流形定理,判断Hopf分支方向及分支周期解的稳定性;最后,通过MATLAB进行数值模拟以验证理论结果的正确性.

On a new fractional-order Logistic model with feedback control

In this paper,we formulate and analyze a new fractional-order Logistic model with feedback control,which is different from a recognized mathematical model proposed in our very recent work.Asymptotic stability of the proposed model and its numerical solutions are studied rigorously.By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function,we show that a unique positive equilibrium point of the new model is asymptotically stable.As an important consequence of this,we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability.Furthermore,we construct unconditionally positive nonstandard finite difference(NSFD)schemes for the proposed model using the Mickens’methodology.It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model.Finally,we report some numerical examples to support and illustrate the theoretical results.The results indicate that there is a good agreement between the theoretical results and numerical ones.

具有Logistic增长和心理作用的随机SIRS传染病模型定性分析

基于流行病受环境噪声和心理作用的影响,建立了一类具有Logistic增长和心理作用的随机SIRS传染病模型,目的在于讨论Logistic增长和心理作用对模型全局动力学的影响。首先,通过构造Lyapunov函数并利用Itˆo公式,证明了该模型全局正解的存在唯一性;然后,在适当的条件下,利用随机Lyapunov函数方法,应用LaSalle不变性原理得到该模型正解存在遍历平稳分布的充分条件。结果表明:环境和心理变化在一定条件下会对疾病起抑制作用。最后,通过数值模拟验证了理论结果的正确性。

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

一类时间周期SIRS扩散传染病模型的渐近传播速度

利用渐近传播速度理论,研究了一类模拟时间周期变化传播环境中疾病传播的SIRS反应扩散传染病模型的渐近传播性质。区别于已有针对SI二维系统的传播速度的结果,该模型中R仓室无法解耦于整个系统,为此需要克服高维和非自治性耦合带来的困难,以证明高维系统渐近传播速度的存在性。首先,借助单调系统渐近传播速度的抽象理论和比较原理证明了染病者I仓室在疾病未入侵区域的传播性质,以此结论为基础,利用整体解结合最大值原理进一步验证了恢复者R仓室在未入侵区域具有类似的传播性质。其次,分别对I和R方程运用比较原理结合一致持久思想和最大值原理分析了其在疾病已入侵区域的一致持久性。由此,得到了划分这两个变化区域的渐近传播速度阈值,即证明了整个系统渐近传播速度的存在性。最后,利用数值方法进一步模拟了时间周期传播环境下疾病已入侵区域更具体的传播动态。

基于SIR模型的直播电商供应链运营风险传播与控制研究

为正确识别直播电商供应链的风险因素,分析、研判风险在直播电商供应链的传播规律,构建了直播电商供应链的结构框架,利用复杂网络模拟了供应链的运营过程。首先,识别出直播电商供应链的22个风险因素,引入SIR风险传染模型。其次,根据风险因素的分类,设置不同初始风险状态和传播规则,对风险传播过程进行模拟仿真分析。结果发现:品牌方的销售策略、主播的直播状态、直播间消费者对产品和主播的负面评价等风险需要重点关注。最后,结合风险传播路径和关键风险因素,提出控制直播电商供应链运营风险的管理措施。

Dynamics of Caputo fractional-order SIRV model:The effects of imperfect vaccination on disease transmission

Though vaccination protects individuals against many infectious diseases,such protection does not always last forever since a few vaccinated individuals could lose their lifelong immunity and eventually become infected.This study,therefore,determines the effects of imperfect vaccination and memory index on the spread of diseases through the Caputo fractional-order SIRV(Susceptible-Infected-Recovered-Vaccinated)epidemic model.Vital properties of the new model including the conditions for the existence of a unique solution determined through the fixed-point theory and the conditions for the existence of a positive solution of the model obtained via the Mittag-Leffler function along with the Laplace transformation-are thoroughly studied.Consequently,our simulation results report that an increase in the imperfect vaccination force increases the population of infected individuals.For the memory effect,the higher“memory”the epidemic system has of past states(which corresponds to decreasing values of fractionalorder parameter),the greater the peaks and magnitudes of infection shaping the epidemiological system dynamics.

基于改进SIR模型的项目隐性知识转移因素解析

隐性知识作为组织重要资产,其成功转移与吸收对项目成败具有重要作用。隐性知识转移绩效受到转移主体比例、知识模糊性、接触率、学习意愿、遗忘率等因素的影响。通过类比分析传染病传播机制与项目隐性知识转移过程,引入SIR模型(susceptible infected recovered model),基于项目成员类型与知识传递过程,建立项目隐性知识转移改进SIR模型,围绕各因素变化对知识转移绩效影响进行仿真分析,进而发现隐性知识转移规律。结果表明,知识模糊性、遗忘率对知识转移绩效具有负向作用;组织成员接触率、学习意愿对转移绩效具有正向作用,可以有效降低其他因素的负向作用。因此,为促进隐性知识转移,应增加知识传播途径、知识学习者人数,提高成员间接触率,降低知识遗忘率,构建项目学习型组织共同体。

基于迁移的SIR模型的行人违章过街传播过程研究

针对城市中普遍存在的红灯期间行人违章过街现象,建立了具有迁移的SIR模型,对行人违章过街的传播机理进行分析,并通过采集大连西安路人行横道处红灯期间行人违章数据,应用最小二乘法对模型的参数β和γ值进行估计,进而对建立的具有迁移性的SIR模型进行参数灵敏度分析,得到违章过街人数的变化趋势,以此提出减少行人违章过街人数的有效措施。

GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.

GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].

GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

基于lévy噪声的随机SIRS模型的拟最优控制

建立了一类基于lévy跳跃的不确定参数随机SIRS传染病模型.利用该模型研究了疫苗接种条件下的拟最优控制问题,使得治疗疾病过程中所花费的成本尽可能地小.根据伴随方程,给出了易感人群、感染人群和恢复人群的先验估计,并利用Hamiltonian函数和Gronwall不等式建立了拟最优控制的充分条件.