Mathematical Biosciences最新文献

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An ant territory formation model with chemotaxis and alarm pheromones 具有趋化性和报警信息素的蚂蚁领地形成模型

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-30 DOI: 10.1016/j.mbs.2025.109498

Paulo Amorim , Rodrigo de Lima , Bruno Telch

We present and analyze a PDE model of ant territory formation, consisting of a system of reaction–advection–diffusion PDEs of chemotaxis type in two space dimensions. Following existing literature on rival ant nest interactions, two ant populations are divided into peaceful and aggressive compartments. When encountering members of the other colony, peaceful ants can turn into aggressive ants, which produce an alarm pheromone. This pheromone attracts other aggressive ants, and also turns peaceful ants into aggressive ants. It is belived that these dynamics can help explain the formation of well segregated territories, which are observed in the field. We include these dynamics into a chemotaxis-type model, which we analyze and simulate. We prove that, under a small initial mass condition, weak solutions are globally bounded, and obtain a global well-posedness result (without any mass conditions) under a mild sublinear growth assumption on the pheromone deposition term. Besides the mathematical results, we show through simulations that well-defined, non-overlapping territories emerge from the dynamics, especially in the beginning of territory formation. Our analysis therefore supports the hypothesis that these interaction dynamics are an important part of the observed territorial patterns in ants.

我们提出并分析了一个蚂蚁领地形成的PDE模型，该模型由两个空间上趋化型的反应-平流-扩散PDE系统组成。根据现有的关于竞争蚁巢相互作用的文献，两个蚁群被分为和平和攻击性隔间。当遇到其他蚁群的成员时，和平的蚂蚁会变成具有攻击性的蚂蚁，这会产生一种警报信息素。这种信息素会吸引其他具有攻击性的蚂蚁，也会把平和的蚂蚁变成具有攻击性的蚂蚁。据信，这些动力学可以帮助解释在野外观察到的隔离良好的区域的形成。我们将这些动态纳入一个趋化型模型，并对其进行分析和模拟。我们证明了在小初始质量条件下，弱解是全局有界的，并在信息素沉积项的温和次线性增长假设下得到了一个全局适定性结果（没有任何质量条件）。除了数学结果外，我们还通过模拟表明，定义良好的非重叠区域从动力学中出现，特别是在区域形成的开始。因此，我们的分析支持了这样一个假设，即这些相互作用的动态是观察到的蚂蚁领土模式的重要组成部分。

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引用次数: 0

Flow-driven dynamics in a mussel-algae system with nonlinear boundary interactions 具有非线性边界相互作用的贻贝-藻类系统的流动驱动动力学

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-26 DOI: 10.1016/j.mbs.2025.109507

Chaochao Li , Hao Wang , Shangjiang Guo

We investigate a reaction–diffusion–advection mussel-algae model with nonlinear boundary conditions, motivated by population dynamics in flowing aquatic environments. The system exhibits complex threshold behavior governed by energy conversion efficiency, flow velocity, and boundary-mediated losses. We establish conditions for global existence, boundedness, and characterize semi-trivial and coexistence steady states. By employing techniques compatible with the maximum principle under the structural assumption (H1) on the nonlinear boundary flux, along with super- and sub-solution methods, we rigorously analyze the persistence and extinction regimes. Our analysis reveal critical thresholds and bifurcations that determine species survival, with advection and nonlinear boundaries interacting to shape system dynamics. These findings generalize classical constant-flux models and offer a new framework for studying stability and bifurcation phenomena in reaction–advection–diffusion systems with biologically motivated boundary interactions.

我们研究了一个具有非线性边界条件的反应-扩散-平流贻贝-藻类模型，该模型由流动水生环境中种群动态驱动。该系统表现出复杂的阈值行为，受能量转换效率、流速和边界介导损失的控制。我们建立了整体存在性、有界性的条件，并刻画了半平凡态和共存态。采用与非线性边界通量结构假设（H1）下的极大值原理相容的技术，结合超解和亚解方法，严格分析了持续和消光机制。我们的分析揭示了决定物种生存的临界阈值和分岔，平流和非线性边界相互作用形成系统动力学。这些发现推广了经典的常通量模型，为研究具有生物动力边界相互作用的反应-平流-扩散系统的稳定性和分岔现象提供了一个新的框架。

引用次数: 0

A stochastic model of prion dynamics with conversion and fragmentation 具有转换和碎裂的朊病毒动力学随机模型

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-24 DOI: 10.1016/j.mbs.2025.109505

Arpan Ghosh , Peter Olofsson , Suzanne S. Sindi

Prions are infectious proteins that, when misfolded, propagate their abnormal structure and cause degenerative diseases in humans and other mammals. The infectious units of prion diseases are aggregates of misfolded proteins, which grow by recruiting normal proteins (conversion) and break down into smaller aggregates (fragmentation).

We introduce a stochastic model describing the dynamics of a population of prion aggregates. The model is formulated as a continuous-time Markov chain that tracks both the number of aggregates and the total number of misfolded protein monomers within aggregates. We derive and solve a PDE for their joint probability generating function, establish results on population growth and mean aggregate size, and analyze how model parameters influence aggregate population dynamics.

朊病毒是一种传染性蛋白质，当错误折叠时，会传播其异常结构，并在人类和其他哺乳动物中引起退行性疾病。朊病毒疾病的传染单位是错误折叠蛋白质的聚集体，它们通过招募正常蛋白质（转化）而生长，并分解成更小的聚集体（破碎）。我们引入了一个随机模型来描述朊病毒聚集体的动态。该模型被表述为一个连续时间马尔可夫链，它可以跟踪聚集体的数量和聚集体内错误折叠的蛋白质单体的总数。我们推导并求解了它们的联合概率生成函数的偏微分方程，建立了种群增长和平均种群规模的结果，并分析了模型参数对种群动态的影响。

引用次数: 0

Optimal control of eggplant pest populations in a Predator–Prey–Parasitoid model with seasonal growth effects 具有季节生长效应的捕食者-被食性-寄生性模型对茄子害虫种群的最优控制

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-22 DOI: 10.1016/j.mbs.2025.109506

Mona Zevika, S. Khoirul Himmi

This study investigates the population dynamics of the eggplant fruit and shoot borer (EFSB), emphasizing the role of natural enemies — predators and parasitoids — in pest management. A mathematical model, comprising three variables representing each population, is constructed to analyze the interactions. The model exhibits six equilibrium points, with particular focus on the predator-free and coexistence equilibria. Crucially, the model incorporates the seasonal variability of the pest’s growth rate, reflecting the influence of environmental factors such as temperature changes. Optimal control strategies are explored, encompassing both chemical and biological approaches, including the use of parasitoids. For chemical control, Pontryagin’s Minimum Principle is employed to derive optimal strategies under varying seasonal growth conditions. The biological control strategy, centered on parasitoid release, is analyzed using State-Dependent Riccati Equations (SDRE) to determine optimal continuous and impulsive release methods. The findings highlight the importance of considering seasonal variations in pest growth and demonstrate the efficacy of impulsive parasitoid releases for pest management. This research provides valuable insights into sustainable pest management and offers a robust framework for applying mathematical modeling to complex agricultural systems.

本文研究了茄子果笋螟（EFSB）的种群动态，强调天敌和寄生蜂在茄子果笋螟防治中的作用。建立了一个数学模型，其中包含代表每个种群的三个变量，以分析相互作用。该模型具有6个平衡点，特别关注无捕食者平衡点和共存平衡点。至关重要的是，该模型纳入了害虫生长速度的季节性变化，反映了温度变化等环境因素的影响。探索了最优控制策略，包括化学和生物方法，包括使用拟寄生虫。在化学防治方面，采用庞特里亚金最小值原理推导出不同季节生长条件下的最优策略。以寄生虫释放为中心，利用状态相关Riccati方程（SDRE）对生物防治策略进行了分析，确定了最优的连续和脉冲释放方法。这些发现强调了考虑害虫生长季节变化的重要性，并证明了脉冲释放寄生蜂对害虫管理的有效性。这项研究为可持续虫害管理提供了有价值的见解，并为将数学建模应用于复杂的农业系统提供了一个强大的框架。

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引用次数: 0

Persistence index for harvested populations 收获种群的持久性指数。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-18 DOI: 10.1016/j.mbs.2025.109497

Jerzy A. Filar , Matthew H. Holden , Manuela Mendiolar , Sabrina H. Streipert

Fish stocks face both anthropogenic and environmental pressures, which can drastically reduce population sizes and threaten species’ survival. While some species can persist and recover from such disturbances, others require careful management to prevent collapse. We introduce a new, biologically intuitive, measure of persistence, the number of eggs produced by an individual fish over its lifetime (NEL) under a harvest policy. Additionally, we demonstrate the relationship between NEL and other candidate indices such as the inherent net reproductive rate, biomass, number of spawners, and dominant eigenvalue of the Jacobian. We show that, NEL inherits a desirable monotonicity property with respect to harvest survival probabilities. That is, NEL (persistence) is higher when survival is higher. If persistence were measured by the dominant eigenvalue of the Jacobian, we show that this property is violated. Hence, NEL offers a valuable and easily computable index for managers to assess persistence under alternative harvest policies.

鱼类资源面临着人为和环境的双重压力，这可能会大大减少种群规模，威胁到物种的生存。虽然有些物种可以从这种干扰中生存和恢复，但其他物种需要仔细管理以防止崩溃。我们引入了一种新的，生物学上直观的持久性测量方法，即在收获政策下，一条鱼在其一生中产生的卵数（NEL）。此外，我们还证明了NEL与其他候选指标（如固有净繁殖率、生物量、产卵数和雅可比矩阵的优势特征值）之间的关系。我们表明，NEL继承了关于收获生存概率的理想单调性。也就是说，存活率越高，NEL（持久性）越高。如果用雅可比矩阵的显性特征值来衡量持久性，我们证明了这个性质是违反的。因此，NEL为管理人员提供了一个有价值且易于计算的指标，以评估在不同收获策略下的持久性。

引用次数: 0

Pattern dynamics analysis and parameter identification of spatiotemporal infectious disease models on complex networks 复杂网络时空传染病模型的模式动力学分析与参数辨识

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-16 DOI: 10.1016/j.mbs.2025.109502

Tao Yang , Linhe Zhu , Shuling Shen , Le He

This paper primarily explores the dynamics of reaction–diffusion systems with advection effects on discrete networks and establishes a corresponding infectious disease transmission model incorporating delay effects. Initially, we consider the conditions for the existence of the equilibrium point and linearly approximate the time delay near this equilibrium point. Then we discuss the necessary conditions for Turing instability under various constraints based on the approximate system. We also introduce two types of lower-order network structures. In one of these lower-order networks, we discuss the directional movement of two different populations. To further analyze the dynamic behavior on different networks, we construct a special higher-order network based on another lower-order network. In addition, we use optimal control to solve the problem of parameter identification. We conduct extensive numerical simulations to study the impact of advection effects and higher-order networks on system dynamics, pattern parameter identification under unknown conditions, and model fitting and prediction based on actual data, which validate the model’s effectiveness and practical utility.

本文主要探讨了离散网络中具有平流效应的反应扩散系统的动力学问题，建立了相应的考虑延迟效应的传染病传播模型。首先考虑平衡点存在的条件，并对平衡点附近的时滞进行线性近似。然后讨论了基于近似系统的各种约束条件下图灵不稳定性的必要条件。我们还介绍了两种低阶网络结构。在其中一个低阶网络中，我们讨论了两个不同种群的定向运动。为了进一步分析不同网络上的动态行为，我们在另一个低阶网络的基础上构造了一个特殊的高阶网络。此外，我们使用最优控制来解决参数辨识问题。通过大量的数值模拟，研究了平流效应和高阶网络对系统动力学、未知条件下模式参数辨识、基于实际数据的模型拟合和预测的影响，验证了模型的有效性和实用性。

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引用次数: 0

On the design and stability of cancer adaptive therapy cycles: Deterministic and stochastic models 癌症适应性治疗周期的设计和稳定性：确定性和随机模型

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-15 DOI: 10.1016/j.mbs.2025.109504

Yuri G. Vilela , Artur C. Fassoni , Armando G.M. Neves

Adaptive therapy is a promising paradigm for cancer treatment exploiting competition between drug-sensitive and drug-resistant cells to delay evolution of drug resistance. Previous studies demonstrated that cyclic drug administration can restore tumor composition to its initial value in deterministic models. However, conditions and methods for designing such cycles deserve better investigation. We present biologically motivated conditions to construct such cycles in two well-known deterministic frameworks, Lotka–Volterra and adjusted replicator dynamics, and provide algorithms for building cycles using two drugs and a period with no drugs. Moreover, we analyze stability of these cycles, an essential consideration for their clinical applicability. We conjecture that a cycle is stable whenever the averaged treatment is stable, conversely it is unstable when the averaged treatment is also unstable. We further investigate stochastic counterparts of both models to account for the finite cell population and randomness inherent to real tumors. Our results reveal that the breakdown of cyclic behavior in stochastic settings, see Dua et al. (2021) and Park and Newton (2023), is not caused by stochasticity per se, but by instability of the corresponding deterministic cycles used as examples. In contrast, we demonstrate that stable deterministic cycles give rise to stable cyclic behavior despite stochastic fluctuations, highlighting the importance of stability in adaptive therapy. We illustrate how stable deterministic cycles avoid for large times the breakdown of cyclic treatments in stochastic models. These findings establish a coherent framework linking deterministic cycle stability to stochastic robustness, offering theoretical support for the design of clinically resilient adaptive cancer therapies.

适应性治疗是一种很有前途的癌症治疗模式，利用药物敏感细胞和耐药细胞之间的竞争来延缓耐药性的进化。先前的研究表明，在确定性模型中，循环给药可以使肿瘤成分恢复到初始值。然而，设计这种循环的条件和方法值得进一步研究。我们提出了在两个众所周知的确定性框架（Lotka-Volterra和调整复制因子动力学）中构建此类周期的生物学动机条件，并提供了使用两种药物和无药物时期构建周期的算法。此外，我们分析了这些周期的稳定性，这是其临床适用性的重要考虑因素。我们推测，只要平均处理是稳定的，循环就是稳定的，反之，当平均处理也是不稳定的，循环就是不稳定的。我们进一步研究了这两种模型的随机对应，以解释有限细胞群和真实肿瘤固有的随机性。我们的研究结果表明，随机环境中循环行为的破坏（参见Dua等人（2021）和Park和Newton(2023)）不是由随机性本身引起的，而是由作为示例的相应确定性周期的不稳定性引起的。相反，我们证明了稳定的确定性周期会产生稳定的循环行为，尽管随机波动，突出稳定性在适应性治疗中的重要性。我们说明了稳定的确定性循环如何在随机模型中避免大量的循环处理的破坏。这些发现建立了一个连贯的框架，将确定性周期稳定性与随机稳健性联系起来，为临床弹性适应性癌症治疗的设计提供了理论支持。

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引用次数: 0

Modelling the impact of organic molecules and phosphate ions on biosilica pattern formation in diatoms 模拟有机分子和磷酸盐离子对硅藻中生物二氧化硅图案形成的影响。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-11 DOI: 10.1016/j.mbs.2025.109484

Svetlana Petrenko, Karen M. Page

The rapid and complex patterning of biosilica in diatom frustules is of great interest in nanotechnology, although it remains incompletely understood. Specific organic molecules, including long-chain polyamines, silaffins and silacidins, are essential in this process. The molecular structure of synthesized polyamines significantly affects the quantity, size and shape of silica precipitates. Experimental findings show that silica precipitation occurs at specific phosphate ion concentrations. We focus on the hypothesis that pattern formation in diatom valve structures is driven by the phase separation of species-specific organic molecules. The resulting organic structures serve as templates for silica precipitation. We investigate the role of phosphate ions in the self-assembly of these organic molecules and analyse how the reaction between them affects the morphology of the organic template. Using mathematical and computational techniques, we gain an understanding of the range of patterns that can arise in a phase-separating system. By varying the rate of dissociation and the initial concentrations of the reacting components we demonstrate that the resulting geometric features are highly dependent on these factors. This approach provides insights into the parameters controlling patterning. Additionally, we consider the effects of prepatterns, mimicking silica ribs that preexist the pores, on the final patterns.

硅藻体中生物二氧化硅的快速和复杂的模式在纳米技术中引起了极大的兴趣，尽管它仍然没有完全被理解。特定的有机分子，包括长链多胺、硅烷和硅酸苷在这一过程中是必不可少的。合成的多胺的分子结构显著影响二氧化硅沉淀的数量、大小和形状。实验结果表明，在特定的磷酸盐离子浓度下，二氧化硅会发生沉淀。我们关注硅藻瓣结构的模式形成是由物种特异性有机分子的相分离驱动的假设。所得的有机结构可作为二氧化硅沉淀的模板。我们研究了磷酸盐离子在有机分子自组装中的作用，并分析了它们之间的反应如何影响有机模板的形态。利用数学和计算技术，我们了解了相分离系统中可能出现的模式范围。通过改变解离速率和反应组分的初始浓度，我们证明了所得到的几何特征高度依赖于这些因素。这种方法提供了对参数控制模式的深入了解。此外，我们考虑了预模式的影响，模拟存在于孔隙中的硅肋，对最终模式的影响。

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引用次数: 0

Advection-dominated models of atherosclerotic plaque composition: The impacts of cell death and cholesterol toxicity 动脉粥样硬化斑块组成的平流主导模型：细胞死亡和胆固醇毒性的影响。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-11 DOI: 10.1016/j.mbs.2025.109496

Ishraq U. Ahmed , Helen M. Byrne , Mary R. Myerscough

Advanced atherosclerotic plaques are characterised by a large necrotic core containing highly inflammatory lipids and debris from dead cells. In large plaques, newly recruited macrophages fail to penetrate this core, and instead push existing material deeper inside the plaque. In this paper, we consider two multiphase models for early atherosclerotic plaque growth, and we analyse their behaviour in the limiting regime where bulk advection drives mass transport of cells and lipids. In this regime, the dynamics of the deep plaque can be approximated by a system of advection–reaction equations. By applying the method of characteristics to these equations, we derive a set of ODEs that describes the evolution of individual segments of plaque tissue. We apply this approximation to a simple 1D three-phase model comprising macrophage foam cells, dead cells, and modified LDL, and we investigate how plaque tissue composition depends on the relative rates of cell death and efferocytosis (cell recycling). We also consider a six-phase model in which death rates depend on intracellular cholesterol content. We use this model to study the effects of cholesterol-induced toxicity, and the beneficial effects of high density lipoproteins (HDL), which can remove excess cholesterol from macrophages. We show that for both multiphase models, the advection–reaction approximations capture key structural features of the full model solutions, including the relative proportions of live and dead cells, and persistent spatial heterogeneities that arise from time-varying boundary influxes of LDL and HDL.

晚期动脉粥样硬化斑块的特征是含有高度炎症性脂质和死细胞碎片的大坏死核心。在大的斑块中，新招募的巨噬细胞不能穿透这个核心，而是将现有的物质推入斑块的更深处。在本文中，我们考虑了早期动脉粥样硬化斑块生长的两种多相模型，并分析了它们在大量平流驱动细胞和脂质大量运输的限制状态下的行为。在这种情况下，深斑块的动力学可以用平流-反应方程系统来近似。通过将特征方法应用于这些方程，我们推导出一组描述斑块组织单个片段演化的ode。我们将这一近似应用于一个由巨噬细胞泡沫细胞、死细胞和修饰LDL组成的简单1D三相模型，并研究斑块组织组成如何依赖于细胞死亡和efferocytosis（细胞再循环）的相对速率。我们还考虑了一个六阶段模型，其中死亡率取决于细胞内胆固醇含量。我们使用这个模型来研究胆固醇诱导的毒性作用，以及高密度脂蛋白（HDL）的有益作用，高密度脂蛋白可以从巨噬细胞中去除多余的胆固醇。研究表明，对于两种多相模型，平流反应近似捕捉了完整模型溶液的关键结构特征，包括活细胞和死细胞的相对比例，以及由LDL和HDL随时间变化的边界流入引起的持续空间异质性。

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引用次数: 0

Spatial pattern regulation strategy of bimolecular model with anomalous diffusion and nonlocal effects 具有异常扩散和非局部效应的双分子模型的空间格局调控策略

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-07-08 DOI: 10.1016/j.mbs.2025.109482

Yifeng Luan , Min Xiao , Jinling Liang , Zhen Wang , Yi Yao , Jinde Cao , Sergy Gorbachev

The mechanisms underlying the formation of spatial patterns in chemical reaction processes have been well established. However, there is still a lack of effective control methods for regulating the formation of spatial patterns and facilitating the transitions between different patterns. This article proposes a novel bimolecular model, incorporating nonlocal effects in reactions and molecular-level anomalous diffusion, within the two-dimensional reaction domain based on the previous framework. Linear stability analysis provides the necessary and sufficient conditions for inducing Turing instability. By utilizing the multiscale analysis, the amplitude equations pertinent to the new model are derived. After identifying the parameter ranges conducive to the formation of fundamental patterns, we introduce the proportional-derivative (PD) control strategy to manage spatial pattern formation and transitions. Simulation results validate the theoretical analysis and demonstrate the efficacy of the PD control strategy.

化学反应过程中空间模式形成的机制已经很好地确立了。然而，目前还缺乏有效的控制方法来调节空间格局的形成，促进不同格局之间的转换。本文在此基础上提出了一种新的双分子模型，该模型在二维反应域内结合了反应中的非局部效应和分子水平的异常扩散。线性稳定性分析为图灵不稳定性的产生提供了充分必要条件。利用多尺度分析，导出了与新模型相关的振幅方程。在确定了有利于基本模式形成的参数范围后，我们引入了比例导数（PD）控制策略来管理空间模式的形成和转变。仿真结果验证了理论分析，验证了PD控制策略的有效性。

引用次数: 0

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