Letters in Biomathematics最新文献

英文中文

Examination of models for cholera: insights into model comparison methods 霍乱模型的检验:对模型比较方法的见解

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2016-01-01 DOI: 10.1080/23737867.2016.1211495

Olcay Akman, Marina Romadan Corby, Elsa Schaefer

This article provides an overview of the Akaike and Bayesian Information Criteria as applied to the setting of deterministic modelling, with the perspective that this may be a useful tool for biomathematics researchers whose primary interests lie in the analysis of compartmental models. We additionally examine a wide range mechanistic and parameter assumptions in the cholera literature through the unifying lens of model selection criteria. Five models for cholera are considered using multiple model selection formulations, and implications for cholera modelling and for model selection criteria are discussed.

本文概述了赤池和贝叶斯信息标准在确定性模型设置中的应用，并认为这可能是生物数学研究人员的一个有用工具，这些研究人员的主要兴趣在于分析区室模型。我们还通过模型选择标准的统一镜头检查了霍乱文献中广泛的机制和参数假设。使用多种模型选择公式考虑了五种霍乱模型，并讨论了对霍乱建模和模型选择标准的影响。

引用次数: 13

Canine distemper outbreak modeled in an animal shelter 在动物收容所模拟犬瘟热爆发

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2016-01-01 DOI: 10.1080/23737867.2016.1148644

Ashley Dantzler, M. Hujoel, V. Parkman, A. Wild, S. Lenhart, Benjamin Levy, R. Wilkes

Canine distemper virus (CDV) is a highly contagious virus that can cause outbreaks, specifically in crowding situations, such as an animal shelter, in which a large number of susceptible dogs are brought together. Introduction of this virus into a shelter can have devastating effects, potentially resulting in shelter canine depopulation. Motivated by recent outbreaks in Tennessee, a mathematical model was constructed to find relevant factors that could assist in preventing or reducing outbreaks. A system of ordinary differential equations was derived to represent the spread of CDV through susceptible, exposed, infected and recovered (S–E–I–R) classes as well as a vaccinated (V) class. Our model was adapted to represent a local Knoxville shelter. The effects of various control methods, both preventative and corrective, on disease spread were investigated.

犬瘟热病毒(CDV)是一种高度传染性的病毒，可引起疫情，特别是在拥挤的情况下，例如动物收容所，将大量易感狗聚集在一起。将这种病毒引入收容所会产生毁灭性的影响，可能导致收容所的犬类数量减少。受田纳西州最近暴发的影响，建立了一个数学模型，以寻找有助于预防或减少暴发的相关因素。推导了一个常微分方程系统来表示CDV在易感、暴露、感染和恢复(S-E-I-R)类以及接种(V)类中的传播。我们的模型被用来代表诺克斯维尔当地的一个避难所。研究了各种预防和纠正控制方法对疾病传播的影响。

引用次数: 3

The spruce budworm and forest: a qualitative comparison of ODE and Boolean models 云杉芽虫与森林:ODE模型与布尔模型的定性比较

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2016-01-01 DOI: 10.1080/23737867.2016.1197804

R. Robeva, D. Murrugarra

Boolean and polynomial models of biological systems have emerged recently as viable companions to differential equations models. It is not immediately clear however whether such models are capable of capturing the multi-stable behaviour of certain biological systems: this behaviour is often sensitive to changes in the values of the model parameters, while Boolean and polynomial models are qualitative in nature. In the past few years, Boolean models of gene regulatory systems have been shown to capture multi-stability at the molecular level, confirming that such models can be used to obtain information about the system’s qualitative dynamics when precise information regarding its parameters may not be available. In this paper, we examine Boolean approximations of a classical ODE model of budworm outbreaks in a forest and show that these models exhibit a qualitative behaviour consistent with that derived from the ODE models. In particular, we demonstrate that these models can capture the bistable nature of insect population outbreaks, thus showing that Boolean models can be successfully utilized beyond the molecular level.

生物系统的布尔模型和多项式模型最近作为微分方程模型的可行伙伴出现。然而，目前尚不清楚这些模型是否能够捕捉某些生物系统的多稳定行为:这种行为通常对模型参数值的变化很敏感，而布尔和多项式模型本质上是定性的。在过去的几年里，基因调控系统的布尔模型已经被证明可以在分子水平上捕获多稳定性，证实了这种模型可以用于在无法获得有关其参数的精确信息时获得有关系统定性动力学的信息。在本文中，我们研究了森林中budworm爆发的经典ODE模型的布尔近似，并表明这些模型表现出与ODE模型一致的定性行为。特别是，我们证明了这些模型可以捕捉昆虫种群爆发的双稳态性质，从而表明布尔模型可以成功地应用于分子水平之外。

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引用次数: 15

On the dynamics of dengue virus type 2 with residence times and vertical transmission 登革2型病毒停留时间和垂直传播动态研究

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2016-01-01 DOI: 10.1080/23737867.2016.1212678

Derdei Bichara, S. Holechek, J. Velázquez-Castro, Anarina L. Murillo, C. Castillo-Chavez

A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors’ vertical transmission and between patches human dispersal is introduced. Dispersal is modelled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts’ dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico.

介绍了登革热病毒2型(DENV-2)的双补丁数学模型，该模型考虑了媒介的垂直传播和补丁之间的人类传播。扩散是通过拉格朗日方法建模的。得出了宿主斑块停留时间乘以基本繁殖数，并确定了疾病灭绝或持续存在的条件。分析和数值结果强调了宿主的扩散在减轻或加剧疾病动态中的作用。该框架以2002年墨西哥科利马州的疫情为起点，用于探索登革热动态。

引用次数: 11

Bottom-up ecology: an agent-based model on the interactions between competition and predation 自下而上生态学:竞争与捕食相互作用的基于主体的模型

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2016-01-01 DOI: 10.1080/23737867.2016.1217756

I. Karsai, Emil Montano, T. Schmickl

Abstract We developed an agent-based computer model of an ecosystem to predict interactions of competition and predation. In our simulations of the model, the effects of the ‘Gause law’ emerged as the results of population fluctuations and a large number of stochastic events. Small biases in life history parameters produced strong effects through the interactions of positive feedback with the population fluctuations. In a low-production environment, the smaller and faster consumer outcompetes the larger and slower one, but in a high production environment the larger and slower consumer survives. Predation hastens the extinction of one of the consumers, but niche partitioning of the consumers increases both the coexistence of consumers and the number of predators. Predators with medium efficiency are able to coexist in the system longer and in larger numbers. Besides the ecological insights this model provides, we conclude that agent-based simulations are very effective tools to explore the interactions between predation and competition interactions.

本文建立了一个基于智能体的生态系统计算机模型来预测竞争和捕食的相互作用。在我们对该模型的模拟中，“高斯定律”的影响作为种群波动和大量随机事件的结果出现。生活史参数中的小偏差通过正反馈与种群波动的相互作用产生了强烈的影响。在低生产环境中，小而快的消费者会战胜大而慢的消费者，但在高生产环境中，大而慢的消费者会生存下来。捕食加速了一种消费者的灭绝，但消费者的生态位划分增加了消费者的共存和捕食者的数量。中等效率的捕食者能够在系统中共存更长时间，数量更多。除了该模型提供的生态学见解外，我们得出结论，基于主体的模拟是探索捕食和竞争相互作用之间相互作用的非常有效的工具。

引用次数: 12

Quantifying distribution in carbon uptake and environmental measurements with the Gini coefficient 用基尼系数量化碳吸收和环境测量的分布

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2016-01-01 DOI: 10.1080/23737867.2016.1144489

M. Safi, J. Zobitz

The Gini coefficient is a measure used in economics to evaluate the equitability of the distribution of a resource across a population. This project applied the Gini coefficient as a classification method for a decade-long data set consisting of environmental observations and carbon flux data for a coniferous forest in Finland. Our results show consistency in the Gini coefficient for environmental variables, even with interannual variation in the measurements during the carbon uptake period or when the ecosystem is absorbing carbon from the atmosphere. The Gini coefficient calculations showed this ecosystem has an inequitable distribution of carbon uptake and release within the carbon uptake period, which is comparable to the inequitable distribution of temperature and precipitation during the same time period. We also calculated the percentage of the carbon uptake period that has passed for different cumulative proportions of a measurement. Future applications of the Gini coefficient to other ecosystems will enhance knowledge of the distribution of environmental and flux measurements across the carbon uptake period.

基尼系数是经济学中用来评估一种资源在人口中分配的公平性的一种度量。该项目将基尼系数作为芬兰针叶林的环境观测和碳通量数据的十年数据集的分类方法。我们的研究结果表明，即使在碳吸收期或生态系统从大气中吸收碳时的测量值存在年际变化，环境变量的基尼系数也具有一致性。基尼系数计算表明，该生态系统在碳吸收周期内的碳吸收和碳释放分布不公平，与同一时间段内的温度和降水分布不公平相当。我们还计算了不同测量累积比例所经过的碳吸收期的百分比。未来将基尼系数应用于其他生态系统将增强对整个碳吸收期环境和通量测量分布的认识。

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引用次数: 2

Modelling and simulation: helping students acquire this skill using a Stock and Flow approach with MathBench 建模和仿真:帮助学生使用MathBench的库存和流量方法获得这一技能

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2015-01-01 DOI: 10.1080/23737867.2015.1035348

I. Karsai, Katerina V. Thompson, Kären C. Nelson

Computational and modelling skills are vital to most fields of biological research, yet traditional biology majors have no or little opportunity to develop these skills during their undergraduate education. We describe an approach, which can address this issue by a synergy of online resources called MathBench modules and Stock and Flow modelling. Using a step-by-step method starting with a MathBench ‘bootcamp’, we were able to achieve a significant gain in quantitative skills of students with no previous experience with model building. At the end of the course, the students were able to construct and analyse complex models and gained confidence in mathematical skills.

计算和建模技能对大多数生物研究领域至关重要，然而传统的生物学专业在本科教育中没有或很少有机会发展这些技能。我们描述了一种方法，它可以通过称为MathBench模块和库存和流量建模的在线资源的协同作用来解决这个问题。使用从MathBench“训练营”开始的一步一步的方法，我们能够在没有模型构建经验的学生的定量技能方面取得重大进展。在课程结束时，学生们能够构建和分析复杂的模型，并获得了对数学技能的信心。

引用次数: 6

Modelling the evolution and expected lifetime of a deme’s principal gene sequence 模拟deme主要基因序列的进化和预期寿命

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2015-01-01 DOI: 10.1080/23737867.2015.1040859

B. Clark

The principal gene sequence (PGS), defined as the most common gene sequence in a deme, is replaced over time because new gene sequences are created and compete with the current PGS, and a small fraction become PGSs. We have developed a set of coupled difference equations to represent an ensemble of demes, in which new gene sequences are introduced via chromosomal inversions. The set of equations used to calculate the expected lifetime of an existing PGS include inversion size and rate, recombination rate and deme size. Inversion rate and deme size effects are highlighted in this work. Our results compare favourably with a cellular automaton-based representation of a deme.

主基因序列(PGS)被定义为deme中最常见的基因序列，随着时间的推移，新的基因序列被创造出来并与当前的PGS竞争，一小部分成为PGS。我们已经开发了一组耦合差分方程来表示一个deme集合，其中新的基因序列是通过染色体倒位引入的。用于计算现有PGS预期寿命的一组方程包括反演尺寸和速率、重组速率和deme尺寸。在这项工作中强调了反转速率和deme尺寸的影响。我们的结果与基于元胞自动机的deme表示相比较有利。

引用次数: 1

The Evolution of Cooperation is Affected by the Persistence of Fitness Effects, the Neighborhood Size and their Interaction. 合作的进化受持续的健康效应、邻里规模及其相互作用的影响

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2015-01-01 Epub Date: 2015-10-22 DOI: 10.1080/23737867.2015.1090890

Eli Thompson, Jasmine Everett, Jonathan T Rowell, Jan Rychtář, Olav Rueppell

Evolutionary Game Theory and the Prisoner's Dilemma (PD) Game in particular have been used to study the evolution of cooperation. We consider a population of asexually reproducing, age-structured individuals in a two-dimensional square lattice structure. The individuals employ fixed cooperative or defecting strategies towards their neighbors in repeating interactions to accumulate reproductive fitness. We focus on the effects of the persistence of past interactions and interactive neighborhood size on the evolution of cooperation. We show that larger neighborhood sizes are generally detrimental to cooperation and that the persistence of fitness effects decreases the likelihood of the evolution of cooperation in small neighborhoods. However, for larger neighborhood sizes the persistence effect is reversed. Thus, our study corroborates earlier studies that population structure increases the evolutionary potential for cooperative behavior in a PD paradigm. This finding may explain the heterogeneity of previous results on the effect of neighborhood size and cautions that the persistence of fitness outcomes needs to be considered in analyses of the evolution of cooperative behavior. The persistence of fitness outcomes of pairwise interactions may vary dramatically in biological and social systems and could have profound effects on the evolution of cooperation in various contexts.

进化博弈论和囚徒困境（PD）博弈尤其被用来研究合作的进化。我们考虑的是一个二维方格结构中的无性繁殖、年龄结构个体群体。个体在重复的互动中对其邻居采取固定的合作或叛逃策略，以积累繁殖能力。我们重点研究了过去互动的持续性和互动邻域大小对合作演化的影响。我们的研究表明，较大的邻域规模通常不利于合作，而在较小的邻域中，持续的适存效应会降低合作进化的可能性。然而，邻域规模越大，持续效应就越大。因此，我们的研究证实了早先的研究，即种群结构增加了PD范式中合作行为的进化潜力。这一发现可能解释了之前关于邻域大小影响的不同结果，并提醒我们在分析合作行为的进化过程中需要考虑适合度结果的持续性。在生物和社会系统中，成对互动的适应性结果的持续性可能会有很大的不同，并可能对各种情况下的合作进化产生深远的影响。

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引用次数: 0

Crossing the Threshold: the role of density dependence and demographic stochasticity in the evolution of cooperation 跨越阈值:密度依赖和人口随机性在合作演化中的作用

Q3 Mathematics

Letters in Biomathematics

Pub Date : 2015-01-01 DOI: 10.1080/23737867.2015.1109481

T. Lofaro

We make two simplifications to a joint population model developed by M. Doebeli et al. of two populations whose growth rates depend on total population density and pay-offs governed by the Iterated Prisoner’s Dilemma. One population uses the ‘Always Defect’ strategy and the second uses the ‘Tit for Tat’ (TFT) strategy. In the deterministic model, there are two simple basins of attraction that lead to the extinction of one or the other population. In particular, a small TFT population cannot spread from rarity. We compute the boundary between these two regions. If, on the other hand, the growth rate of the TFT population is stochastic, then it is possible for the TFT population to become established if the growth rate at any given time is sufficiently large to allow the TFT population to cross the threshold computed in the deterministic model. We describe the factors that increase the likelihood of TFT establishment and explain why density dependence is an essential feature of the model. In particular, we show that if the relative advantage of defecting is small compared to the benefits of cooperating, then there is an increased likelihood that cooperation will evolve.

我们对M. Doebeli等人开发的两个种群的联合种群模型进行了两个简化，这两个种群的增长率取决于总种群密度和由迭代囚徒困境控制的收益。一个种群使用“永远缺陷”策略，另一个种群使用“以牙还牙”策略。在确定性模型中，有两个简单的吸引力盆地导致其中一个种群的灭绝。特别是，一个小的TFT人口不可能从稀有传播。我们计算这两个区域之间的边界。另一方面，如果TFT种群的增长率是随机的，那么如果在任何给定时间的增长率足够大，使TFT种群能够越过确定性模型中计算的阈值，则TFT种群就有可能建立起来。我们描述了增加TFT建立可能性的因素，并解释了为什么密度依赖是模型的基本特征。特别是，我们表明，如果背叛的相对优势比合作的优势小，那么合作进化的可能性就会增加。

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引用次数: 1

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Letters in Biomathematics

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