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HOW DOES THE LATENCY PERIOD IMPACT THE MODELING OF COVID-19 TRANSMISSION DYNAMICS? 潜伏期如何影响COVID-19传播动力学建模?
Q4 MATHEMATICS, APPLIED Pub Date : 2022-03-30 Epub Date: 2022-02-20 DOI: 10.5206/mase/14537
Ben Patterson, Jin Wang

We introduce two mathematical models based on systems of differential equations to investigate the relationship between the latency period and the transmission dynamics of COVID-19. We analyze the equilibrium and stability properties of these models, and perform an asymptotic study in terms of small and large latency periods. We fit the models to the COVID-19 data in the U.S. state of Tennessee. Our numerical results demonstrate the impact of the latency period on the dynamical behaviors of the solutions, on the value of the basic reproduction numbers, and on the accuracy of the model predictions.

我们引入两个基于微分方程组的数学模型,研究潜伏期与COVID-19传播动态之间的关系。我们分析了这些模型的平衡和稳定性,并在小潜伏期和大潜伏期方面进行了渐近研究。我们将这些模型与美国田纳西州的COVID-19数据拟合。我们的数值结果证明了潜伏期对解的动力学行为、对基本再现数的值以及对模型预测精度的影响。
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引用次数: 3
Dynamics of discrete predator- prey system with fear effect and density dependent birth rate of the prey species 具有恐惧效应的离散捕食-食饵系统动力学和密度依赖的食饵物种出生率
Q4 MATHEMATICS, APPLIED Pub Date : 2022-02-06 DOI: 10.5206/mase/14496
D. Mukherjee
This paper analyses a discrete predator-prey system with fear effect and density dependent birth rate of the prey species. The fixed points of the system are determined and their stability is examined. The criterion for Neimark-Sacker bifurcation and flip bifurcation is developed. The chaotic orbit at an unstable fixed point can be stabilized by applying the state feedback control method. Numerically, we illustrate our analytical findings and observe the complex behaviour of the system that leads to stable state to chaotic one.
本文分析了一个具有恐惧效应和密度依赖的离散捕食系统。确定了系统的不动点,并对其稳定性进行了检验。建立了Neimark-Sacker分岔和翻转分岔的判据。应用状态反馈控制方法可以稳定不稳定不动点的混沌轨道。从数字上讲,我们说明了我们的分析结果,并观察了系统的复杂行为,该行为导致稳定状态变为混沌状态。
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引用次数: 0
Dynamics of a stoichiometric producer-grazer model with maturation delay 具有成熟延迟的化学计量生产者-食草动物模型的动力学
Q4 MATHEMATICS, APPLIED Pub Date : 2022-02-06 DOI: 10.5206/mase/14332
Hua Zhang, Hao Wang, Ben Niu
Ecological stoichiometry provides a multi-scale approach to study macroscopic phenomena via microscopic lens. A stoichiometric producer-grazer model with maturation delay is proposed and studied in this paper. The interaction between stoichiometry and delay is novel and leads to more interesting insights beyond classical delay-driven periodic solutions. For example, the period doubling route to chaos can occur as the minimal phosphorous:carbon ratio in producer decreases. Mathematically, we establish the conditions for the existence and stability of positive equilibria, and study the occurrence of Hopf bifurcation at positive equilibria. Analytic results show that delay can change the number and stability of positive equilibria through transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation, and it further determines the grazer's extinction. Our model with a small delay behaves like LKE model in terms of light intensity, and Rosenzweig's paradox of enrichment exists in a suitable light intensity. We plot bifurcation diagrams and show rich dynamics driven by delay, light intensity, phosphorous availability, and conversion efficiency, including that a large delay can drive the grazer to go extinct in an intermediate light intensity that is favorable for the survival of the grazer when there is no delay; a limit cycle can appear, then disappear as the delay increases; given the same initial condition, solutions with different delay values can tend to different attractors.
生态化学计量提供了一种通过微观透镜研究宏观现象的多尺度方法。本文提出并研究了一个具有成熟延迟的化学计量生产者-食草动物模型。化学计量和延迟之间的相互作用是新颖的,并在经典延迟驱动的周期解之外带来了更有趣的见解。例如,当生产者中的最小磷碳比降低时,可能会出现周期加倍的混沌途径。在数学上,我们建立了正平衡存在和稳定的条件,并研究了正平衡下Hopf分岔的发生。分析结果表明,时滞可以通过跨临界分岔、鞍节点分岔和Hopf分岔改变正平衡的个数和稳定性,并进一步决定了掠器的灭绝。我们的小延迟模型在光强方面与LKE模型类似,在适当的光强下存在Rosenzweig富集悖论。我们绘制了分叉图,显示了由延迟、光强、磷有效性和转化效率驱动的丰富动力学,包括大的延迟可以在中等光强下驱动食草动物灭绝,这有利于食草动物在没有延迟的情况下生存;极限循环可能出现,然后随着延迟的增加而消失;给定相同的初始条件,具有不同延迟值的解可以趋向于不同的吸引子。
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引用次数: 0
Application of ant colony optimization metaheuristic on set covering problems 蚁群优化元启发式算法在集覆盖问题中的应用
Q4 MATHEMATICS, APPLIED Pub Date : 2022-01-20 DOI: 10.5206/mase/14018
C. A. Buhat, Jerson Ken Villamin, G. Cuaresma
Ant Colony Optimization (ACO) metaheuristic is a multi-agent system in which the behaviour of each ant is inspired by the foraging behaviour of real ants to solve optimization problem. Set Covering Problems (SCP), on the other hand, deal with maximizing the coverage of every subset while the weight nodes used must be minimized. In this paper, ACO was adapted and used to solve a case of Set Covering Problem. The adapted ACO for solving the SCP was implemented as a computer program using SciLab 5.4.1. The problem of determining the optimal location of Wi-Fi Access Points using the 802.11n protocol in the UP Los Banos Math Building was solved using this metaheuristic. Results show that in order to have 100% coverage of the MB, 7 access points are required. Methodology of the study can be adapted and results of the study can be used by decision makers on related optimization problems.
蚁群优化(ACO)元启发式是一个多智能体系统,其中每个蚂蚁的行为都受到真实蚂蚁觅食行为的启发,以解决优化问题。另一方面,集覆盖问题(SCP)处理的是最大化每个子集的覆盖,而使用的权重节点必须最小化。本文将ACO方法应用于一个集覆盖问题的求解。使用SciLab 5.4.1将用于解决SCP的自适应ACO实现为计算机程序。使用这种元启发式方法解决了在UP Los Banos数学大楼中使用802.11n协议确定Wi-Fi接入点的最佳位置的问题。结果显示,为了实现MB的100%覆盖,需要7个接入点。研究方法可以进行调整,决策者可以将研究结果用于相关的优化问题。
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引用次数: 0
On approximating initial data in some linear evolutionary equations involving fraction Laplacian 关于部分拉普拉斯算子线性演化方程中初始数据的逼近
Q4 MATHEMATICS, APPLIED Pub Date : 2022-01-19 DOI: 10.5206/mase/13511
R. Karki
We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy. 
我们研究了一个具有Dirichlet边界条件的一维线性方程的初始数据恢复逆问题,当已知在适当固定的空间位置上的解的有限多个值(样本)和适当选择的有限多稍后的时间实例时。更具体地说,我们这样做。我们考虑了一个一维线性进化方程,该方程包含Dirichlet分数拉普拉斯算子和未知的初始数据f,假设初始数据f在Sovolev空间的合适子集中。然后,我们研究如何构建未来时间序列,并选择n,以便从在适当固定的空间位置采集的n个样本和时间序列的前n项中,我们可以构造出具有所需精度的f的近似值。
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引用次数: 0
Long-time behavior of a nonlocal dispersal logistic model with seasonal succession 具有季节演替的非局部扩散logistic模型的长时间行为
Q4 MATHEMATICS, APPLIED Pub Date : 2021-11-29 DOI: 10.5206/mase/15415
Zhenzhen Li, B. Dai
This paper is devoted to a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat, where the seasonal succession accounts for the effect of two different seasons. Firstly, we provide the persistence-extinction criterion for the species, which is different from that for local diffusion model. Then we show the asymptotic profile of the time-periodic positive solution as the species persists in long run.
本文研究了一维有界生境中具有季节序列的非局部扩散逻辑模型,其中季节序列考虑了两个不同季节的影响。首先,我们给出了该物种的持续灭绝准则,该准则不同于局部扩散模型。然后,我们给出了当种群长期存在时,时间周期正解的渐近轮廓。
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引用次数: 0
A diffusive SEIR model for community transmission of Covid-19 epidemics: application to Brazil Covid-19流行病社区传播的弥漫性SEIR模型:在巴西的应用
Q4 MATHEMATICS, APPLIED Pub Date : 2021-11-18 DOI: 10.5206/mase/14150
W. Fitzgibbon, J. Morgan, Geoffrey I. Webb, Yixiang Wu
A mathematical model incorporating  diffusion is developed to describe the spatial spread of COVID-19 epidemics in geographical regions. The dynamics of the spatial spread are based on community transmission of the virus. The model is applied to the outbreak of the COVID-19 epidemic in Brazil.
建立了一个包含扩散的数学模型来描述COVID-19流行病在地理区域的空间传播。空间传播的动态是基于病毒的社区传播。该模型应用于巴西新冠肺炎疫情的爆发。
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引用次数: 1
Prevailing winds and spruce budworm outbreaks: a reaction-diffusion-advection model 盛行风与云杉芽虫爆发:一个反应-扩散-平流模型
Q4 MATHEMATICS, APPLIED Pub Date : 2021-11-03 DOI: 10.5206/mase/14112
Abby Anderson, O. Vasilyeva
We extend the classical reaction-diffusion model for spatial population dynamics of spruce budworm on a finite domain with hostile boundary conditions by including an advection term representing biased unidirectional movement of individuals due to a prevailing wind. We use phase-plane techniques to establish existence of a critical value of advection speed that prevents outbreak solutions on any finite domain while possibly allowing an endemic solution. We obtain lower and upper bounds for this critical advection value in terms of biological parameters involved in the reaction term. We also perform numerical simulations to illustrate the effect of advection on the dependence of the domain size on the maximal population density of a steady state solution and on critical domain sizes for endemic and outbreak solutions. The results are also applicable to other ecological settings (rivers, climate change) where a logistically growing population is subject to predation by a generalist, diffusion and biased movement.
在具有敌对边界条件的有限域上,我们扩展了经典的反应扩散模型,加入了一个平流项,表示由于盛行风而导致的个体有偏的单向运动。我们使用相平面技术来建立平流速度临界值的存在性,该临界值可以在任何有限域上阻止爆发解决方案,同时可能允许地方性解决方案。根据反应项中涉及的生物参数,我们得到了这个临界平流值的下界和上界。我们还进行了数值模拟,以说明平流对区域大小对稳态解决方案的最大种群密度和流行病和爆发解决方案的临界区域大小的依赖性的影响。研究结果也适用于其他生态环境(河流、气候变化),在这些环境中,逻辑上不断增长的人口会受到通才、扩散和偏颇运动的捕食。
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引用次数: 0
Modeling SARS-CoV-2 spread with dynamic isolation 动态隔离下SARS-CoV-2传播建模
Q4 MATHEMATICS, APPLIED Pub Date : 2021-10-10 DOI: 10.5206/mase/13886
Md. Azmir Ibne Islam, Sharmin Sultana Shanta, Ashrafur Rahman
Background: The SARS-CoV-2 pandemic is spreading with a greater intensity across the globe. The synchrony of public health interventions and epidemic waves signify the importance of evaluation of the underline interventions. Method: We developed a mathematical model to present the transmission dynamics of SARS-CoV-2 and to analyze the impact of key nonpharmaceutical interventions such as isolation and screening program on the disease outcomes to the people of New Jersey, USA. We introduced a dynamic isolation of susceptible population with a constant (imposed) and infection oriented interventions. Epidemiological and demographic data are used to estimate the model parameters. The baseline case was explored further to showcase several critical and predictive scenarios.Results and analysis: The model simulations are in good agreement with the infection data for the period of 5 March 2020 to 31 January 2021. Dynamic isolation and screening program are found to be potential measures that can alter the course of epidemic. A  7% increase in isolation rate may result in a 31% reduction of epidemic peak whereas a 3 times increase in screening rate may reduce the epidemic peak by 35%. The model predicts that nearly 9.7% to 12% of the total population of New Jersey may become infected within the middle of July 2021 along with 24.6 to 27.3 thousand cumulative deaths. Within a wide spectrum of probable scenarios, there is a possibility of third wave Conclusion: Our findings could be informative to the public health community to contain the pandemic in the case of economy reopening under a limited or no vaccine coverage. Additional epidemic waves can be avoided by appropriate screening and isolation plans. 
背景:严重急性呼吸系统综合征冠状病毒2型疫情正在全球范围内以更大的强度传播。公共卫生干预措施和流行病浪潮的同步性表明了对强调干预措施进行评估的重要性。方法:我们开发了一个数学模型来呈现严重急性呼吸系统综合征冠状病毒2型的传播动态,并分析隔离和筛查计划等关键非药物干预措施对美国新泽西州人民疾病结果的影响。流行病学和人口统计数据用于估计模型参数。对基线案例进行了进一步探讨,以展示几个关键和预测情景。结果和分析:模型模拟与2020年3月5日至2021年1月31日期间的感染数据非常一致。动态隔离和筛查计划被发现是可以改变疫情进程的潜在措施。隔离率增加7%可能会使疫情高峰减少31%,而筛查率增加3倍可能会使流行病高峰减少35%。该模型预测,新泽西州近9.7%至12%的总人口可能在2021年7月中旬感染,累计死亡24.6万至27.3万人。在广泛的可能情况下,存在第三波疫情的可能性结论:我们的研究结果可能对公共卫生界提供信息,以在有限或没有疫苗覆盖的情况下重新开放经济的情况下遏制疫情。通过适当的筛查和隔离计划可以避免额外的疫情浪潮。
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引用次数: 2
Cluster solutions in networks of weakly coupled oscillators on a 2D square torus 二维方形环面上弱耦合振子网络的簇解
Q4 MATHEMATICS, APPLIED Pub Date : 2021-09-19 DOI: 10.5206/mase/14147
J. Culp
We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von Neumann r-neighborhood. Using the phase model reduction technique, we study the existence of cluster solutions with constant phase differences (Ψh, Ψv) between adjacent oscillators along the horizontal and vertical directions in our network, where Ψh and Ψv are not necessarily to be identical. Applying the Kronecker production representation and the circulant matrix theory, we develop a novel approach to analyze the stability of cluster solutions with constant phase difference (i.e., Ψh,Ψv are equal). We begin our analysis by deriving the precise conditions for stability of such cluster solutions with von Neumann 1-neighborhood and 2 neighborhood couplings, and then we generalize our result to von Neumann r-neighborhood coupling for arbitrary neighborhood size r ≥ 1. This developed approach for the stability analysis indeed can be extended to an arbitrary coupling in our network. Finally, numerical simulations are used to validate the above analytical results for various values of N and r by considering an inhibitory network of Morris-Lecar neurons.
我们考虑具有周期边界条件的弱耦合神经振荡器的N×N晶格网络的模型(2D方环面),其中神经元之间的耦合被假设在大小为r的von Neumann邻域内,表示为von Neumann-r邻域。使用相位模型约简技术,我们研究了在我们的网络中,沿水平和垂直方向的相邻振荡器之间存在具有恒定相位差(Ψh,Ψv)的簇解,其中Ψh和Ψv不一定相同。应用Kronecker乘积表示和循环矩阵理论,我们提出了一种新的方法来分析具有恒定相位差(即Ψh,Ψv相等)的簇解的稳定性。我们通过导出具有von Neumann 1-邻域和2邻域耦合的这类簇解的稳定性的精确条件来开始我们的分析,然后我们将我们的结果推广到任意邻域大小r≥1的von Neumann-r邻域耦合。这种发展的稳定性分析方法确实可以扩展到我们网络中的任意耦合。最后,通过考虑Morris Lecar神经元的抑制网络,使用数值模拟来验证N和r的不同值的上述分析结果。
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引用次数: 1
期刊
Mathematics in applied sciences and engineering
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