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Assessing the impact of host predation with Holling II response on the transmission of Chagas disease 评估宿主捕食与Holling II反应对恰加斯病传播的影响
Q3 Mathematics Pub Date : 2023-11-08 DOI: 10.5206/mase/16743
Jiahao Jiang, Daozhou Gao, Jiao Jiang, Xiaotian Wu
Chagas disease is a zoonosis caused by the protozoan parasite Trypanosoma cruzi and transmitted by a broad range of blood-sucking triatomine species. Recently, it is recognized that the parasite can also be transmitted by host ingestion. In this paper, we propose a Chagas disease model incorporating two transmission routes of biting-defecation and host predation between vectors and hosts with Holling II functional response. The basic reproduction number R_v of triatomine population and basic reproduction numbers R_0 of disease population are derived analytically, and it is shown that they are insufficient to serve as threshold quantities to determine dynamics of the model. Our results have revealed the phenomenon of bistability, with backward and forward bifurcations. Specifically, if R_v>1, the dynamic is rather simple, namely, the disease-free equilibrium is globally asymptotically stable as R_0<1 and a unique endemic equilibrium is globally asymptotically stable as R_0>1. However, if R_v<1, there exists a backward bifurcation with one unstable and one stable positive vector equilibria, and bistability phenomenon occurs, revealing that different initial conditions may lead to disease extinction or persistence even if the corresponding R_0>1. In conclusion, predation transmission in general reduces the risk of Chagas disease, whilst it makes the complexity of Chagas disease transmission, requiring an integrated strategy for the prevention and control of Chagas disease.
恰加斯病是一种人畜共患病,由原生动物寄生虫克氏锥虫引起,并由广泛的吸血锥虫物种传播。最近,人们认识到寄生虫也可以通过宿主的摄食传播。本文提出了一种具有Holling II功能反应的恰加斯病模型,该模型包含媒介与宿主之间的叮咬-排便和宿主捕食两种传播途径。通过解析推导了三角蝽种群的基本繁殖数R_v和疾病种群的基本繁殖数R_0,表明它们不足以作为确定模型动力学的阈值。我们的结果揭示了双稳态现象,具有向后和向前分岔。具体来说,当R_v>1时,其动态非常简单,即无病平衡全局渐近稳定为R_0<1,唯一的地方性平衡全局渐近稳定为R_0>1。但当R_v<1时,存在一个不稳定和一个稳定正向量平衡的后向分岔,出现双稳态现象,说明即使对应的R_0>1,不同的初始条件也可能导致疾病灭绝或持续。总之,捕食传播总体上降低了恰加斯病的风险,同时使恰加斯病传播变得复杂,需要一项预防和控制恰加斯病的综合战略。
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引用次数: 0
Dynamical analysis of a COVID-19 model with human-to-human and environment-to-human transmissions and distributed delays 具有人传人、环境传人和分布式延迟的COVID-19模型动力学分析
Q3 Mathematics Pub Date : 2023-10-14 DOI: 10.5206/mase/16681
Jie Xu, Yayuan Lei, TARIQ ABDULLAH, Gang Huang
SARS-CoV-2 can survive in different environments and remain infectious for several days, which presents challenges to eliminating infectious diseases. It encourages researchers to study the effects of SARS CoV-2 on the environment. In this paper, we formulate an epidemic model for SARS-CoV-2, which focuses on the transmission of the virus under environmental conditions. Two distributed delays are introduced to describe the probability of the exposed and infected individuals in different infection periods based on the transmission of the virus in the environment. Th positivity and boundedness of solutions of model are derived. The basic reproduction number threshold theory is established and the results demonstrate that the persistence of COVID-19 depends on the basic reproduction number. Numerical simulations are presented to verify the theoretical results. Some measures are proposed to control and eliminate COVID-19 infectious diseases.
SARS-CoV-2可以在不同的环境中存活并保持数天的传染性,这给消除传染病带来了挑战。它鼓励研究人员研究SARS - CoV-2对环境的影响。本文建立了SARS-CoV-2的流行模型,该模型主要关注环境条件下病毒的传播。根据病毒在环境中的传播情况,引入两个分布式延迟来描述暴露个体和感染个体在不同感染时期的概率。导出了模型解的正性和有界性。建立了基本繁殖数阈值理论,结果表明COVID-19的持续依赖于基本繁殖数。通过数值模拟验证了理论结果。提出了控制和消除COVID-19传染病的措施。
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引用次数: 0
Steady-state dynamics in a two-patch population model with and without Allee effect 具有和不具有Allee效应的双斑块种群模型的稳态动力学
Q3 Mathematics Pub Date : 2023-09-22 DOI: 10.5206/mase/16474
Laurence Ketchemen Tchouaga, Frithjof Lutscher
Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.
大多数生物种群居住在由许多不同质量的不同斑块组成的景观中。不同的物种在运动行为、栖息地偏好和生长速度上存在差异。历史上,人口动态的数学模型做出了许多简化的假设,例如单一斑块或均匀景观。最近的模型已经开始实现景观异质性和个体运动特征,但其中许多是基于逻辑增长和零状态的线性分析。我们考虑一个具有更一般的生长函数的双补丁模型,可以包括Allee效应。证明了稳态的存在性,并对其定性行为进行了分类。在一些特殊情况下,我们显式地计算了它们的稳定性,并利用这些结果给出了系统呈现双稳定性的条件,即局部稳定状态的共存。我们还研究了与生境斑块大小有关的分岔,并给出了向前和向后分岔的条件。
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引用次数: 0
Application of multi-valued rough neutrosophic set and matrix in multi-criteria decision-making 多值粗糙中性集和矩阵在多准则决策中的应用
Q3 Mathematics Pub Date : 2023-09-22 DOI: 10.5206/mase/16636
Donbosco Jeni Seles Martina, Ganesan Deepa
Rough set concept is a methodology of information processing for relational databases. It is a unique uncertainty mathematics topic closely connected to fuzzy set theory. When the rough set is combined with neutrosophic set theory, an effective tool for working with indeterminacy arises. In this study, we defined a multi-valued rough neutrosophic set and a multi-valued rough neutrosophic matrix. Using separation measures, we introduced a new approach for a multi-valued neutrosophic with a rough structure. We consider the problem of determining the condition of dengue-affected patients in a specific hospital. Using this method, we create a multi-valued rough neutrosophic decision matrix that clearly displays the relationship between patient conditions and symptoms. We can determine which one has a serious condition by solving this problem and presenting it on the graph.
粗糙集概念是一种面向关系数据库的信息处理方法。它是与模糊集理论密切相关的一个独特的不确定性数学课题。当粗糙集与中性集理论相结合时,就产生了一种处理不确定性的有效工具。在本研究中,我们定义了一个多值粗糙嗜中性集合和一个多值粗糙嗜中性矩阵。采用分离方法,对具有粗糙结构的多值中性粒细胞提出了一种新的分离方法。我们考虑的问题是确定在某一医院中受登革热影响的病人的状况。使用这种方法,我们创建了一个多值粗略的中性粒细胞决策矩阵,该矩阵清楚地显示了患者病情和症状之间的关系。我们可以通过解决这个问题并将其呈现在图表上来确定哪个人的病情严重。
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引用次数: 0
Multiple-peak traveling waves of the Gray-Scott model Gray-Scott模型的多峰行波
Q3 Mathematics Pub Date : 2023-08-26 DOI: 10.5206/mase/16513
Xinfu Chen, Xin Lai, Cong Qin, Y. Qi, Yajing Zhang
We study a reaction-diffusion system which models the pre-mixed isothermal autocatalytic chemical reaction of order m  (m > 1) between two chemical species, a reactant A and an auto-catalyst B,   A + m B  --> (m+1) B, and a linear decay B -->C, where  C is an inert product. The special case of m = 2 is the much studied Gray-Scott model, but without feeding. We prove existence of multiple traveling waves which have distinctive number of local maximaor peaks. It shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different traveling pulses than related models in literature such as isothermal autocatalysis without decay, or a bio-reactor model with isothermal autocatalysis of order m + 1 with m-th order of decay.
我们研究了一个反应扩散系统,该系统模拟了两种化学物质,反应物a和自催化剂B, a + m B—> (m+1) B和线性衰变B—>C之间的m (m >)级预混合等温自催化化学反应,其中C是惰性产物。m = 2的特殊情况是研究得很多的Gray-Scott模型,但没有喂食。证明了具有不同数目的局部极大峰的多个行波的存在性。与文献中的无衰变等温自催化、m + 1阶等温自催化、m阶衰变的生物反应器模型相比,Gray-Scott型模型在产生丰富且结构不同的行脉冲方面表现出了一个新的非常鲜明的特点。
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引用次数: 0
Optimal actuator placement for control of vibrations induced by pedestrian-bridge interactions 控制行人-桥梁相互作用引起的振动的最佳驱动器位置
Q3 Mathematics Pub Date : 2023-08-20 DOI: 10.5206/mase/15949
Martin Arop, H. Kasumba, Juma Kasozi, F. Berntsson
In this paper, an optimal actuator placement problem, with a linear wave equation as the constraint, is considered. In particular, this work presents the framework for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on the shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical tests illustrate the theoretical results.
本文研究了以线性波动方程为约束的最优作动器布置问题。特别是,这项工作提出了根据给定初始条件找到执行器最佳位置的框架,并且对初始条件的依赖被平均掉。这个问题的动机是需要控制行人与桥梁相互作用引起的振动。采用基于形状优化技术的方法来解决这一问题。具体而言,使用平均伴随方法确定涉及成本函数的形状灵敏度。采用基于这些灵敏度的数值算法作为求解策略。数值试验验证了理论结果。
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引用次数: 0
Analysis of thermal stresses to 2D plane thermoelastic inhomogeneous strip 二维平面热弹性非均匀带材的热应力分析
Q3 Mathematics Pub Date : 2023-06-26 DOI: 10.5206/mase/16387
Abhijeet B. Adhe, K. Ghadle, U. Thool
This paper deals with study of the plane elasticity of thermoelastic problems for inhomogenous strip. Here, the original problems are reduced to set the governing equations in the volterra integral equations by making the use of direct integration method. Further using the iteration technique the numerical calculations has been performed. The stress distribution obtained and calculated numerically and shown graphically.
本文研究了非均匀带热弹性问题的平面弹性。本文利用直接积分法将原来的问题简化为volterra积分方程中的控制方程组。进一步使用迭代技术进行了数值计算。数值计算得到的应力分布,并以图形显示。
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引用次数: 0
On the weak solution of the Von Karman model with thermoelastic plates 热弹性板Von Karman模型的弱解
Q3 Mathematics Pub Date : 2023-06-09 DOI: 10.5206/mase/15658
M. Raissouli, J. Oudaani
The aim of this article is to study the dynamic Von-Karman model coupledwith thermoelastic equations without rotational terms, subject to a thermal dissipation. We establish the existence as well as the uniqueness of a weak solution related to the dynamic model. At the end, we apply the finite difference method for approximating the solution of our problem.
本文的目的是研究动力学冯-卡门模型与无旋转项的热弹性方程耦合,考虑热耗散。我们建立了与动态模型相关的一个弱解的存在性和唯一性。最后,应用有限差分法逼近问题的解。
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引用次数: 0
CONCEPTUAL MODEL OF MIXED-INTEGER LINEAR PROGRAMMING WATER DISTRIBUTION SYSTEM 混合整数线性规划配水系统概念模型
Q3 Mathematics Pub Date : 2023-05-22 DOI: 10.5206/mase/15591
Habiba Babangida Awwalu, N. Abdullahi, M. Hussaini
Water is a basic part of our daily lives, as such effective water supply is of paramount importance. Thus, as a result of the rise in population size and water shortage there is the need for proper, suitable and optimal utilization of water resources to efficiently be distributed among the populace. The proper allocation and distribution of water in the field of network planning need to be modelled through mathematical parameters for objective of water distribution system. This mathematical approach requires of solving an optimization problem based on multi-objective function subjected to certain constraints of mixed integer linear programming objective function which is proportional to the cost of the water distribution network. This study present a conceptual model of multi-objective optimization proposed for determination of design parameters of water distribution system by considering the significant number of constraints, decision variables, cost and reliability objective functions. The model was proposed to solve the reliability problem of water production and reduce the design and operational costs.
水是我们日常生活的基本组成部分,因此有效的供水至关重要。因此,由于人口规模的增加和水的短缺,需要适当、适当和最佳地利用水资源,以便在人口中有效地分配。在管网规划领域,用水的合理分配需要通过配水系统目标的数学参数进行建模。这种数学方法要求在混合整数线性规划目标函数与配水管网成本成正比的一定约束下,求解一个基于多目标函数的优化问题。本文提出了考虑大量约束条件、决策变量、成本和可靠性目标函数的配水系统设计参数确定的多目标优化概念模型。该模型的提出是为了解决出水可靠性问题,降低设计和运行成本。
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引用次数: 1
Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey 考虑捕食群体行为的θ逻辑捕食-被捕食模型的动力学研究
Q3 Mathematics Pub Date : 2023-05-01 DOI: 10.5206/mase/15648
P. Santra, G. Mahapatra
Relation between species and their livelihood environment in ecological systems is very complex. For that reason, in order to study predator-prey  relations, modeling is essential in biomathematics. The vital components of predator-prey models are prey species' growth function in the absence of apredator and the functional response. In this article, we proposed a predator-prey model with gregarious prey. In the existing literature, square-root functional response incorporates the gregarious behavior of prey. This study considers the generalized square root functional response and theta-logistic growth of prey in the absence of a predator. The effect of functional response parameters on stability, limit cycle, and Hopf bifurcation on the proposed model has been discussed. Numerical analysis is performed on the basis of some hypothetical parameter values to analyze the model numerically.
生态系统中物种与其生存环境的关系十分复杂。因此,为了研究捕食者-猎物关系,建模在生物数学中是必不可少的。捕食者-猎物模型的重要组成部分是在没有捕食者的情况下被捕食物种的生长功能和功能反应。在本文中,我们提出了一个具有群居性猎物的捕食者-猎物模型。在现有文献中,平方根功能反应包含了猎物的群居行为。本研究考虑了在没有捕食者的情况下,猎物的广义平方根功能反应和theta-logistic增长。讨论了函数响应参数对模型稳定性、极限环和Hopf分岔的影响。在一些假设参数值的基础上进行数值分析,对模型进行数值分析。
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引用次数: 0
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Mathematics in applied sciences and engineering
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