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Mathematical Modelling of Natural Phenomena最新文献

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Heat and mass diffusion to Williamson fluid streaming through a tube with multiple stenoses while subjected to periodic body acceleration 热量和质量扩散到威廉森流体流过多管狭窄,同时受到周期性的身体加速度
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-06-30 DOI: 10.1051/mmnp/2023021
Muhammad Fahim, M. Sajid, N. Ali, Muhammad Noveel Sadiq
This article examines a mathematical framework that describes the versatile behavior of heat and mass exchange in blood flowing through a narrowed vessel having multiple stenoses. The geometry of a channel having multiple stenoses with an asymmetrical axial axis and a symmetrical radial axis can be visualized by applying a suitable mathematical expression. The geometry of the chosen model considers the height and shape of stenoses. The modification in shape parameter is used to capture variations in the shape of the stenoses in the artery. The blood is supposed to be isochoric (incompressible), while its rheological behavior is characterized by Williamson’s fluid model. The transfer of momentum is analyzed using the equation of motion in cooperation with the continuity equation. In addition, the equations of heat conduction and diffusion are utilized, respectively, to illustrate the distributions of heat and mass. Simplified forms of momentum, mass, and heat transport equations are achieved by incorporating dimensionless quantities and moderate stenosis conditions. A well-known explicit finite difference approach is utilized to solve the emergent non-linear system of governing equations numerically. The influence of different evolving parameters on the flow field along with mass and heat distributions is illustrated through various plots.
本文研究了一个数学框架,该框架描述了在具有多个狭窄的狭窄血管中流动的血液中热交换和质量交换的多种行为。具有具有不对称轴向轴线和对称径向轴线的多个狭窄的通道的几何形状可以通过应用合适的数学表达式来可视化。所选模型的几何形状考虑了狭窄的高度和形状。形状参数的修改用于捕捉动脉中狭窄形状的变化。血液被认为是等容的(不可压缩的),而其流变行为由威廉姆森流体模型表征。动量的传递是使用运动方程和连续性方程来分析的。此外,还分别利用热传导方程和扩散方程来说明热量和质量的分布。通过引入无量纲量和中等狭窄条件,实现了动量、质量和热传输方程的简化形式。利用一种著名的显式有限差分方法对涌现的非线性控制方程组进行了数值求解。通过各种曲线图说明了不同演化参数对流场以及质量和热量分布的影响。
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引用次数: 0
MMNP - next generation MMNP -下一代
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-06-02 DOI: 10.1051/mmnp/2023017
V. Volpert
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引用次数: 0
A control strategy for the Sterile Insect Technique using exponentially decreasing releases to avoid the hair-trigger effect 利用指数递减释放避免毛触发效应的无菌昆虫技术的控制策略
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-06-02 DOI: 10.1051/mmnp/2023018
N. Nguyen, Alexis L'eculier
In this paper, we introduce a control strategy for applying the Sterile Insect Technique (SIT) to eliminate the population of Aedes mosquitoes which are vectors of various deadly diseases like dengue, zika, chikungunya... in a wide area. We use a system of reaction-diffusion equations to model the mosquito population and study the effect of releasing sterile males. Without any human intervention, and due to the so-called hair-trigger effect, the introduction of only a few individuals (eggs or fertilized females) can lead to the invasion of mosquitoes in the whole region after some time. To avoid this phenomenon, our strategy is to keep releasing a small number of sterile males in the treated zone and move this release forward with a negative forcing speed c to push back the invasive front of wild mosquitoes. By using traveling wave analysis, we show in the present paper that the strategy succeeds in repulsing the population while consuming a finite amount of mosquitoes in any finite time interval even though we treat a moving half-space. Moreover, we succeed in constructing a 'forced' traveling wave for our system moving at the same speed as the releases. We also provide some numerical illustrations for our results.
本文介绍了一种应用无菌昆虫技术(SIT)消灭伊蚊种群的控制策略,伊蚊是登革热、寨卡病毒、基孔肯雅病毒等各种致命疾病的媒介。。。在广阔的区域内。我们使用反应扩散方程组来模拟蚊子种群,并研究释放不育雄性的效果。在没有任何人为干预的情况下,由于所谓的毛发触发效应,只引入少数个体(卵子或受精雌性),一段时间后就会导致蚊子入侵整个地区。为了避免这种现象,我们的策略是在治疗区继续释放少量不育雄性蚊子,并以负的强迫速度c向前释放,以击退野生蚊子的入侵前沿。通过使用行波分析,我们在本文中表明,即使我们处理的是移动的半空间,该策略在任何有限的时间间隔内都能成功地击退种群,同时消耗有限数量的蚊子。此外,我们成功地构建了一个“强迫”行波,使我们的系统以与释放相同的速度移动。我们还为我们的结果提供了一些数值说明。
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引用次数: 0
Pressure boundary conditions for viscous flows in thin tube structures: Stokes equations with locally distributed Brinkman term 薄管结构中粘性流动的压力边界条件:局部分布Brinkman项的Stokes方程
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-05-19 DOI: 10.1051/mmnp/2023016
G. Panasenko, K. Pileckas
The steady state Stokes-Brinkman equations in a thin tube structure is considered. The Brinkman term differs from zero only in small balls near the ends of the tubes. The boundary conditions are: given pressure at the inflow and outflow of the tube structure and the no slip boundary condition on the lateral boundary. The complete asymptotic expansion of the problem is constructed. The error estimates are proved. The method of partial asymptotic dimension reduction is introduced for the Stokes-Brinkman equations and justified by an error estimate. This method approximates the main problem by a hybrid dimension problem for the Stokes-Brinkman equations in a reduced domain. Asymptotic analysis is applied to determine the permeability of a tissue with a roll of blood vessels.
研究了薄管结构中的稳态Stokes-Brinkman方程。布林克曼项只有在靠近管子末端的小球中才与零不同。边界条件为:管状结构流入和流出处给定压力,侧向边界处无滑移边界条件。构造了问题的完全渐近展开式。对误差估计进行了验证。介绍了Stokes-Brinkman方程的部分渐近降维方法,并用误差估计进行了验证。该方法将Stokes-Brinkman方程的主要问题近似为约简域上的混合维数问题。渐近分析用于确定具有血管卷的组织的渗透性。
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引用次数: 0
OUTPUT TRAJECTORY CONTROLLABILITY OF A DISCRETE-TIME SIR EPIDEMIC MODEL 离散时间Sir流行病模型的输出轨迹可控性
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-04-24 DOI: 10.1051/mmnp/2023015
Lahbib Benahmadi, M. Lhous, A. Tridane, M. Rachik
Abstract. Developing new approaches that help control the spread of infectious diseases is a critical issue for public health. Such approaches must consider the available resources and capacity of the healthcare system. In this paper, we present a new mathematical approach to controlling an epidemic model by investigating the optimal control that aims to bring the output of the epidemic to target a desired disease output yd = (yid)i∈{0,...,N}. First, we use the state-space technique to transfer the trajectory controllability to optimal control with constraints on the final state. Then, we use the fixed point theorems to determine the set of admissible controls and solve the output trajectory controllability problem. Finally, we apply our method to the model of a measles epidemic, and we give a numerical simulation to illustrate the findings of our approach.Mathematics Subject Classification. — Please, give AMS classification codes —.
摘要开发有助于控制传染病传播的新方法是公共卫生的一个关键问题。这种方法必须考虑到现有的资源和卫生保健系统的能力。本文通过研究最优控制问题,提出了一种新的控制流行病模型的数学方法,其目的是使流行病的输出达到目标期望的疾病输出yd = (yid)i∈{0,…,N}。首先,利用状态空间技术将轨迹可控性转化为具有最终状态约束的最优控制。然后,利用不动点定理确定可容许控制集,求解输出轨迹可控性问题。最后,我们将我们的方法应用于麻疹流行模型,并给出了数值模拟来说明我们的方法的发现。数学学科分类。-请给出AMS分类代码-。
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引用次数: 0
A NUMERICAL 3D FLUID-STRUCTURE INTERACTION MODEL FOR BLOODFLOW IN A MRI-BASED ATHEROSCLEROTIC ARTERY 基于mri的动脉粥样硬化血流的三维流固耦合模型
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-03-29 DOI: 10.1051/mmnp/2023014
Nader El Khatib, O. Kafi, D. Oliveira, A. Sequeira, J. Tiago
Atherosclerosis, as a result of an inflammatory process, is the thickening and loss of elasticity of the walls of arteries that is associated with the formation of atherosclerotic plaques within the arterial intima, which present a double threat. A piece of vulnerable plaque can break off and be carried by the bloodstream until it gets stuck; and plaque that narrows an artery may lead to a thrombus that sticks to the blood vessel's inner wall. The purpose of the present article is to compare effects across different atheromatous plaque material assumptions on hemodynamics and biomechanics within a partly patient-specific computational domain representing an atherosclerotic artery. A full scale 3D FSI numerical model is implemented and different material hyperelastic assumptions are considered for comparison purposes. The 3D realistic geometry is reconstructed from a medical image. This technique may be useful, specially with the recent advances in computer-aided design (CAD), medical imaging, and 3D printing technologies that have provided a rapid and cost efficient method to generate arterial stenotic biomodels, making in vitro studies a valuable and powerful tool. To understand our results, hemodynamic parameters and structural stress analysis were performed. The results are consistent with previous findings.
动脉粥样硬化是炎症过程的结果,是动脉壁增厚和弹性丧失,与动脉内膜内动脉粥样硬化斑块的形成有关,这具有双重威胁。一块脆弱的斑块可能会脱落,并被血液携带,直到它被卡住;而使动脉变窄的斑块可能会导致粘在血管内壁的血栓。本文的目的是比较不同的动脉粥样硬化斑块材料假设对血流动力学和生物力学的影响,在一个部分患者特异性的计算域内代表动脉粥样硬化动脉。实现了一个全尺寸的三维FSI数值模型,并考虑了不同的材料超弹性假设进行比较。从医学图像中重建三维真实几何体。这项技术可能是有用的,特别是随着计算机辅助设计(CAD)、医学成像和3D打印技术的最新进展,这些技术提供了一种快速、经济高效的方法来生成动脉狭窄的生物模型,使体外研究成为一种有价值和强大的工具。为了理解我们的结果,我们进行了血流动力学参数和结构应力分析。研究结果与之前的发现一致。
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引用次数: 0
A minimal model coupling communicable and non-communicable diseases 耦合传染性和非传染性疾病的最小模型
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-03-28 DOI: 10.1051/mmnp/2023026
M. Marvá, E. Venturino, Carmen Vera
This work presents a model combining the simplest communicable and non-communicable disease models. The latter is, by far, the leadingn cause of sickness and death in the World, and introduces basal heterogeneity in populations where communicable diseases evolve. The model can be interpreted as a risk-structured model, another way of accounting for population heterogeneity.Our results show that considering the non-communicable disease (in the end, heterogeneous populations) allows the communicable disease to become endemic even if the basic reproduction number is less than $1$. This feature is known as subcritical bifurcation. Furthermore, ignoring the non-communicable disease dynamics results in overestimating the reproduction number and, thus, giving wrong information about the actual number of infected individuals. We calculate sensitivity indices and derive interesting epidemic-control information.
这项工作提出了一个结合最简单的传染病和非传染性疾病模型的模型。到目前为止,后者是世界上疾病和死亡的主要原因,并在传染病发生的人群中造成了基本的异质性。该模型可以解释为风险结构模型,这是另一种解释人口异质性的方法。我们的研究结果表明,考虑到非传染性疾病(最终,异质性人群),即使基本繁殖数小于1美元,传染病也会成为地方病。这个特征被称为亚临界分岔。此外,忽视非传染性疾病的动态会导致对繁殖数量的高估,从而对实际感染人数给出错误的信息。我们计算了敏感性指数,得到了有趣的流行病控制信息。
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引用次数: 0
Analysis of dynamic evolution process of the $N$-player division of labor game model $N$-玩家分工博弈模型的动态演化过程分析
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-03-20 DOI: 10.1051/mmnp/2023013
Hairui Yuan, Xinzhu Meng
This paper investigates a three-strategy (cooperators, toxin producers, and cheaters) $N$-player division of labor game in bacterial populations. We construct the replicator equation to discuss the evolution of the frequency of the three strategies. Firstly, we prove that the interior equilibrium is always unstable, the three strategies cannot coexist. Secondly, according to Sotomayor's theorem, the system undergoes transcritical bifurcation. Furthermore, the sensitivity of the two-dimensional evolutionary state diagrams to the third parameter (toxin rate, absorption rate, toxin quantity, etc) is analyzed. In summary, high toxicity rates, high levels of toxins, and low levels of competition tend to promote cooperation. All players choose to perform the task, and the cheater disappears. When the absorption rate of cooperators is high enough, only cooperators exist in the population over time. When the absorption rate of the cooperator is low, and the absorption rate of the toxin producer is greater than the threshold, the cooperator and the toxin producer coexist. All players perform the task. Finally, the triangle diagrams and three-dimensional diagrams are presented, which show the initial conditions of the three strategies also affect the dynamic results. As the amount of toxin increases, the range of players who choose to perform tasks widens.
本文研究了细菌种群中的一个三策略(合作者、毒素制造者和骗子)N人分工博弈。我们构造了复制因子方程来讨论这三种策略的频率演变。首先,我们证明了内部均衡总是不稳定的,三种策略不能共存。其次,根据索托马约尔定理,系统发生了跨临界分岔。进一步分析了二维演化状态图对第三个参数(毒素率、吸收率、毒素量等)的敏感性。总之,高毒性率、高毒素水平和低竞争水平倾向于促进合作。所有玩家都选择执行任务,作弊者消失。当合作者的吸收率足够高时,随着时间的推移,种群中只存在合作者。当合作者的吸收率较低,而毒素产生者的吸收率大于阈值时,合作者与毒素产生者共存。所有玩家都要完成这个任务。最后给出了三角图和三维图,说明了三种策略的初始条件也会影响动态结果。随着毒素数量的增加,玩家选择执行任务的范围也会扩大。
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引用次数: 0
Interaction between crowding and growth in tumours with stem cells: conceptual mathematical modelling 肿瘤干细胞拥挤和生长之间的相互作用:概念数学模型
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-03-17 DOI: 10.1051/mmnp/2023011
L. Meacci, M. Primicerio
The paper proposes a conceptual modelling of growth of tumours in presence of immortal multipotent cancer stem cells (CSCs) and several lineages of differentiated tumour cells (CCs).The replication of CSCs is assumed symmetric or asymmetric with a prescribed mean ratio and mitosis and apoptosis are taken into account for the CCs aging. Replication can be hindered by the local crowding of the cells.The model is implemented in the framework of 3D cellular automata (CA) whose dynamics is governed by stochastic rules. Simulations are displayed showing the growth of a tumour and the fractions of different lineages and age classes of CCs.Then, an approach that considers the same dynamics of aging, replication, and apoptosis, but studying the time evolution of the fractions of the different lineages and age classes of cells averaged over the total volume is presented. The dynamics is governed by a system of ordinary differential equations (ODEs), hence by deterministic rules. Numerical simulations of the solution of this system show qualitative similarity with the CA results, although the crowding effect is no longer a local effect, but averaged over the total volume. The proof of the mathematical well-posedness of this model is provided.
本文提出了一种在存在永生多能癌症干细胞(CSCs)和几种分化肿瘤细胞(CC)谱系的情况下肿瘤生长的概念模型。假设CSCs的复制是对称或不对称的,具有规定的平均比例,并将有丝分裂和凋亡考虑到CC的老化。细胞的局部拥挤可能会阻碍复制。该模型是在三维细胞自动机(CA)的框架下实现的,其动力学由随机规则控制。模拟显示了肿瘤的生长以及不同谱系和年龄级别的CC的部分。然后,提出了一种方法,该方法考虑了衰老、复制和凋亡的相同动力学,但研究了不同谱系和时间级别的细胞部分在总体积上的平均时间演变。动力学由常微分方程组(ODEs)控制,因此由确定性规则控制。该系统解的数值模拟显示与CA结果在质量上相似,尽管拥挤效应不再是局部效应,而是在总体积上取平均值。证明了该模型的数学适定性。
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引用次数: 0
Qualitative analysis for a diffusive predator-prey model with hunting cooperation and Holling type textrm{III}  functional response 具有狩猎合作和Holling型功能反应的扩散捕食-被捕食模型的定性分析
IF 2.2 4区 数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY Pub Date : 2023-03-05 DOI: 10.1051/mmnp/2023010
I. Benamara, A. El abdllaoui, R. Yafia, H. Dutta
The Spatio-temporal pattern induced by self-diffusion of a predator-prey model with Holling type III functional response that incorporates the hunting cooperation between predators has been investigated in this paper. For the local model without structure, stability of non-negative equilibria with or without collaborative hunting in predators is studied. For the Spatio-temporal model, we analyze the effect of hunting cooperation term on diffusion-driven Turing instability of the homogeneous positive equilibria. To get an idea about patterns formation near the Turing bifurcation, we derive and give a detailed study of the amplitude equation using the multiple-scale analysis. Our result shows that hunting cooperation plays a crucial role in determining the stability and the Turing bifurcation of the model, which is in sharp contrast to the case without cooperation in hunting. Furthermore, some numerical simulations are illustrated to visualize the complex dynamic behavior of the model.
本文研究了一个具有Holling III型功能反应的捕食者-猎物模型的自扩散诱导的时空模式,该模型包含了捕食者之间的狩猎合作。对于没有结构的局部模型,研究了捕食者在有或没有协同狩猎的情况下非负平衡的稳定性。对于时空模型,我们分析了狩猎合作项对齐次正平衡的扩散驱动的图灵不稳定性的影响。为了了解图灵分岔附近的模式形成,我们使用多尺度分析推导并详细研究了振幅方程。我们的结果表明,狩猎合作在决定模型的稳定性和图灵分支方面起着至关重要的作用,这与狩猎中没有合作的情况形成了鲜明对比。此外,还对一些数值模拟进行了说明,以可视化模型的复杂动态行为。
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引用次数: 0
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Mathematical Modelling of Natural Phenomena
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