Mathematical Biosciences最新文献_第4页

Integrating machine learning into the in silico clinical trial pipeline 将机器学习集成到计算机临床试验管道中。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-11-25 DOI: 10.1016/j.mbs.2025.109583

Rebecca A. Bekker , Renee Brady-Nicholls , Lisette de Pillis , Jana L. Gevertz , Harsh Vardhan Jain

In silico clinical trials offer a powerful tool for overcoming several limitations of traditional clinical trials. Conventional trials are time- and resource-intensive, typically designed to assess average effects across a population while being restricted to studying the impact of a fixed treatment protocol. In contrast, in silico trials are cost-effective, flexible in their design, and able to explore heterogeneity in treatment response. These trials generally rely on expert-developed and data-calibrated mechanistic mathematical models and the identification of model parameterizations that satisfy biological or clinical constraints. With the growing availability of multi-scale and high-resolution clinical data, it is the opportune time to thoughtfully consider how machine learning (ML) methods can enhance the feasibility, interpretability, and reliability of these in silico trials. In this perspective piece, we explore both the opportunities and the challenges of introducing ML tools at various stages of this process, from biomarker identification to interpreting the results of the trial. We argue that in the hands of an expert modeler, the thoughtful application of ML tools can result in more accurate and informative in silico clinical trials that may potentially accelerate drug development and find the right drug/protocol for the right patient.

计算机临床试验为克服传统临床试验的一些局限性提供了强有力的工具。传统的试验需要耗费大量的时间和资源，通常被设计用来评估整个人群的平均效果，而仅限于研究固定治疗方案的影响。相比之下，计算机试验具有成本效益，设计灵活，并且能够探索治疗反应的异质性。这些试验通常依赖于专家开发和数据校准的机械数学模型，以及满足生物学或临床限制的模型参数化的识别。随着越来越多的多尺度和高分辨率临床数据的可用性，现在是考虑机器学习（ML）方法如何增强这些计算机试验的可行性、可解释性和可靠性的时机。在这篇透视文章中，我们探讨了在这一过程的各个阶段引入机器学习工具的机遇和挑战，从生物标志物识别到解释试验结果。我们认为，在专家建模者的手中，机器学习工具的周到应用可以导致更准确和信息丰富的计算机临床试验，这可能会加速药物开发，并为合适的患者找到合适的药物/方案。

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引用次数: 0

Particle-based simulation of non-elementary bimolecular kinetics 基于粒子的非基本双分子动力学模拟

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-11-24 DOI: 10.1016/j.mbs.2025.109582

Taylor Kearney , Mark B. Flegg

Particle-based simulations are an essential tool for the study of biochemical systems for scales between molecular/Brownian dynamics and the reaction-diffusion master equation. These simulations utilise proximity-based reaction conditions and are typically limited to elementary (mass-action) kinetics. We present a novel framework for directly simulating non-elementary bimolecular kinetics in a particle-based framework. By mimicking the behaviour of a third implicit reactant, we adapt non-elementary reaction conditions, previously restricted to trimolecular chemical interactions, to biomolecular reactions for the first time. We implement our approach in an event-driven simulation, which we validate by reproducing Michaelis-Menten kinetics. We then demonstrate its utility by simulating the classical Goldbeter model of circadian oscillations completely at the level of individual molecules. This model features multiple non-elementary reactions and requires the incorporation of several existing simulation techniques. Our method accurately reproduces the target non-elementary kinetics, without simulating the implied underlying fast elementary reactions, thereby significantly reducing the computational cost. This work expands the class of reaction networks accessible to particle-based simulations and provides a practical alternative to explicitly simulating all elementary steps in systems where quasi-steady-state approximations are applicable.

基于粒子的模拟是研究生物化学系统在分子/布朗动力学和反应-扩散主方程之间尺度的重要工具。这些模拟利用基于接近的反应条件，通常限于基本（质量作用）动力学。我们提出了一个新的框架，直接模拟非基本双分子动力学在一个粒子为基础的框架。通过模拟第三种隐式反应物的行为，我们首次将非基本反应条件（以前仅限于三分子化学相互作用）应用于生物分子反应。我们在事件驱动的模拟中实现了我们的方法，我们通过再现Michaelis-Menten动力学来验证。然后，我们通过完全在单个分子水平上模拟昼夜节律振荡的经典goldbetter模型来证明其实用性。该模型具有多种非基本反应，需要结合几种现有的模拟技术。我们的方法准确地再现了目标非基本动力学，而不模拟隐含的潜在快速基本反应，从而大大降低了计算成本。这项工作扩展了可用于基于粒子的模拟的反应网络的类别，并提供了一种实用的替代方案，以显式模拟准稳态近似适用的系统中的所有基本步骤。

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引用次数: 0

Exploring the role of osteoblast-lineage cells in the evolutionary dynamics of acute myeloid leukemia through a stochastic differential equation model 通过随机微分方程模型探索成骨细胞谱系细胞在急性髓系白血病进化动力学中的作用

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-11-24 DOI: 10.1016/j.mbs.2025.109572

Shizhao Ma , Xiulan Lai

Acute myeloid leukemia (AML) is characterized by the uncontrolled proliferation of abnormal myeloid cells in the bone marrow and peripheral blood. In this study, we develop a stochastic differential equation model to capture the dynamic interactions among hematopoietic, osteoblastic, and leukemic cell populations within the bone marrow microenvironment. We calibrate model parameters using clinical data via an optimal control framework. Our study provides a mathematical framework to investigate how leukemic cells may remodel the heterogeneous bone marrow niche through dynamic interactions with osteoblastic lineages. This remodeling process disrupts both the quantity and functional capacity of hematopoietic populations, thereby offering insights into how leukemic-niche interactions may contribute to AML treatment failure. Furthermore, we evaluate the efficacy of combination therapies (traditional chemotherapy with targeted therapy) and compare their therapeutic outcomes. These findings offer a theoretical foundation for optimizing clinical strategies and advancing personalized treatment approaches for AML.

急性髓性白血病（AML）的特点是骨髓和外周血中异常髓细胞不受控制的增殖。在这项研究中，我们开发了一个随机微分方程模型来捕捉骨髓微环境中造血细胞、成骨细胞和白血病细胞群之间的动态相互作用。我们通过最优控制框架使用临床数据校准模型参数。我们的研究提供了一个数学框架来研究白血病细胞如何通过与成骨细胞谱系的动态相互作用来重塑异质骨髓生态位。这种重塑过程破坏了造血群体的数量和功能能力，从而为白血病-生态位相互作用如何导致AML治疗失败提供了见解。此外，我们评估了联合治疗（传统化疗与靶向治疗）的疗效，并比较了它们的治疗结果。这些发现为优化AML的临床策略和推进个性化治疗方法提供了理论基础。

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引用次数: 0

A phenotype-structured mathematical model for the influence of hypoxia on oncolytic virotherapy 缺氧对溶瘤病毒治疗影响的表型结构数学模型。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-11-19 DOI: 10.1016/j.mbs.2025.109570

David Morselli , Giulia Chiari , Federico Frascoli , Marcello Edoardo Delitala

The effectiveness of oncolytic virotherapy is significantly affected by several elements of the tumour microenvironment, which reduce the ability of the virus to infect cancer cells. In this work, we focus on the influence of hypoxia on this therapy and develop a novel continuous mathematical model that considers both the spatial and epigenetic heterogeneity of the tumour. We investigate how oxygen gradients within tumours affect the spatial distribution and replication of both the tumour and oncolytic viruses, focusing on regions of severe hypoxia versus normoxic areas. Additionally, we analyse the evolutionary dynamics of tumour cells under hypoxic conditions and their influence on susceptibility to viral infection. Our findings show that the reduced metabolic activity of hypoxic cells may significantly impact the virotherapy effectiveness; the knowledge of the tumour’s oxygenation could, therefore, suggest the most suitable type of virus to optimise the outcome. The combination of numerical simulations and theoretical results for the model equilibrium values allows us to elucidate the complex interplay between viruses, tumour evolution and oxygen dynamics, ultimately contributing to developing more effective and personalised cancer treatments.

溶瘤病毒治疗的有效性受到肿瘤微环境的几个因素的显著影响，这些因素降低了病毒感染癌细胞的能力。在这项工作中，我们关注缺氧对这种治疗的影响，并开发了一种新的连续数学模型，该模型考虑了肿瘤的空间和表观遗传异质性。我们研究了肿瘤内的氧梯度如何影响肿瘤和溶瘤病毒的空间分布和复制，重点研究了严重缺氧区与常氧区。此外，我们分析了肿瘤细胞在缺氧条件下的进化动力学及其对病毒感染易感性的影响。我们的研究结果表明，低氧细胞的代谢活性降低可能显著影响病毒治疗的效果；因此，对肿瘤氧合作用的了解可以建议最合适的病毒类型来优化结果。数值模拟和模型平衡值的理论结果相结合，使我们能够阐明病毒、肿瘤进化和氧动力学之间复杂的相互作用，最终有助于开发更有效和个性化的癌症治疗方法。

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引用次数: 0

Do “soft” interventions matter more than vaccination? Rabies as an example “软”干预比疫苗接种更重要吗？狂犬病就是一个例子。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-11-13 DOI: 10.1016/j.mbs.2025.109567

Nyuk Sian Chong , Thanisha Kaliapan , Can Chen , Kok Choon Cheah , Stacey R. Smith

Interventions such as vaccinations, treatment et cetera are usually the gold standard of disease control, as measured by reducing the reproduction number below unity. However, in practice, few diseases are reduced below this eradication threshold and instead persist despite active intervention campaigns. We propose an epidemic model of rabies with a saturated incidence rate that represents “soft” interventions such as public-awareness campaigns, animal curfews, fences etc. We prove local and global stability results based on the reproduction number. However, numerical simulations suggest that eradication is unlikely to occur using current practices. We thus investigate the effect of altering the saturated incidence term using “soft” interventions and show that near-eradication can be achieved even when the reproduction number exceeds unity. Soft interventions such as public-awareness campaigns, reducing contacts, animal curfews and fences can have a greater effect on eradicating rabies than current vaccination programs.

接种疫苗、治疗等干预措施通常是疾病控制的黄金标准，其衡量标准是将繁殖数量减少到1以下。然而，实际上，很少有疾病被减少到这一根除阈值以下，尽管开展了积极的干预运动，但这些疾病仍然存在。我们提出了一个具有饱和发病率的狂犬病流行模型，该模型代表了“软”干预措施，如公众意识运动、动物宵禁、围栏等。我们证明了基于复制数的局部和全局稳定性结果。然而，数值模拟表明，使用目前的做法不太可能根除这种疾病。因此，我们研究了使用“软”干预改变饱和发生率项的效果，并表明即使繁殖数超过1，也可以实现近根除。与目前的疫苗接种规划相比，公众意识运动、减少接触、动物宵禁和围栏等软干预措施可以在根除狂犬病方面发挥更大的作用。

引用次数: 0

Modeling covalently closed circular DNA dynamics in assessing chronic hepatitis B prognosis 评估慢性乙型肝炎预后的共价闭环DNA动力学建模。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-11-11 DOI: 10.1016/j.mbs.2025.109568

Qiulin Huang , Qiang Li , Zaitang Huang , Yuming Wang , Guangyu Huang , Kaifa Wang , Wendi Wang

The persistence of covalently closed circular DNA (cccDNA) in the nuclei of HBV-infected hepatocytes plays a critical role in the pathogenesis of chronic hepatitis B (CHB), and hepatitis B surface antigen (HBsAg) levels can be considered a surrogate marker for cccDNA quantification. In this paper, a mathematical model is proposed to mimic cccDNA kinetics in infected hepatocytes, and the basic reproduction rate of cccDNA is obtained. It is found that the backward bifurcation occurs. Importantly, the model predictions match well the clinical data from 96 newly treated CHB patients, collected at the authors’ hospitals. Specifically, 18 patients (23.96 %) achieved HBsAg serologic negative conversion (SNC), excluding 5 patients with serologic relapse. Ten patients were predicted to be uncertain, including two clinically confirmed patients with SNC. Excluding the uncertain patients, our model gives a concordance rate of 93.75 % (15/16). Our results suggest that the baseline HBsAg, HBV DNA and hepatitis e surface antigen statuses are the major factors related to the accuracy of the model for the prediction of negative conversion. Therefore, our model is helpful to design effective clinical withdrawal indicators.

共价闭合环状DNA （cccDNA）在hbv感染肝细胞细胞核中的持续存在在慢性乙型肝炎（CHB）的发病机制中起着关键作用，乙型肝炎表面抗原（HBsAg）水平可以被认为是cccDNA定量的替代标志物。本文提出了一个数学模型来模拟cccDNA在感染肝细胞中的动力学，并得到了cccDNA的基本繁殖率。结果表明，出现了后向分岔。重要的是，该模型预测与作者所在医院收集的96名新治疗的慢性乙型肝炎患者的临床数据非常吻合。其中18例（23.96%）患者实现HBsAg血清学阴性转化（SNC），排除5例血清学复发。10例患者预测不确定，包括2例临床确诊的SNC患者。排除不确定患者，我们的模型的一致性率为93.75%（15/16）。我们的研究结果表明，基线HBsAg、HBV DNA和e型肝炎表面抗原状态是与预测阴性转化模型准确性相关的主要因素。因此，我们的模型有助于设计有效的临床戒断指标。

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引用次数: 0

Impact of latent delay and environment infection on tuberculosis dynamics in a population 潜伏延迟和环境感染对人群结核病动态的影响。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-10-31 DOI: 10.1016/j.mbs.2025.109566

Hui Cao , Xianyi Zhao , Xingfu Zou

In this paper we explore the impact of latency delay and infection by Mycobacterium tuberculosis in the environment on the spread of tuberculosis in a population. We first derive a delay differential equation model with environmental indirect transmission. We address the well-posenedness and identify the basic reproduction number

R_{0}

of the model. We then discuss the equilibria and their stability in terms of the composite threshold parameter

R_{0}

which determine whether or not the tuberculosis will go extinct of persist in the popolaiton: the disease free equilibrium is globally stable if

R_{0} < 1

, and it becomes unstable if

R_{0} > 1

. In the latter case, there exists a unique endemic equilibrium, which is locally asymptotically stable when

τ

is sufficiently small; furthermore, we obtain the conditions for the existence of Hopf bifurcation around the endemic equilibrium. The condition implies that the interplay of the latency delay and infection of Mycobacterium tuberculosis in the environment may contribute not only to the TB’s persistence but also the way it persists: either as an constant pattern (endemic equilibrium) or as a periodic pattern (oscillation around the endemic equilibrium). We also discuss the epidemiological implication of the mathematical results.

在本文中，我们探讨了潜伏延迟和结核分枝杆菌感染的环境对结核病在人群中的传播的影响。首先推导了具有环境间接传输的时滞微分方程模型。我们处理了模型的完备性，并确定了模型的基本复制数R0。然后，我们用复合阈值参数R0讨论了平衡及其稳定性，该参数决定了结核病在种群中是灭绝还是持续存在：如果R00 bb0 1，则无病平衡是全局稳定的。在后一种情况下，存在唯一的地方性平衡，当τ足够小时，该平衡是局部渐近稳定的；进一步，我们得到了局部平衡点周围Hopf分岔存在的条件。这种情况意味着，环境中结核分枝杆菌的潜伏期延迟和感染的相互作用可能不仅有助于结核病的持续存在，而且还有助于其持续存在的方式：要么是一种恒定模式（地方性平衡），要么是一种周期性模式（围绕地方性平衡振荡）。我们还讨论了数学结果的流行病学含义。

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引用次数: 0

The impact of acid-base changes on the stochastic dynamics of phytoplankton growth under global warming 全球变暖条件下酸碱变化对浮游植物生长随机动力学的影响。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-10-30 DOI: 10.1016/j.mbs.2025.109565

Tiancai Liao, Honghui Yin

This paper deals with a stochastic nutrient-phytoplankton (NP) model with the impacts of

p H

and global warming, where the stochastic environmental disturbance is characterized by the logarithmic Ornstein-Uhlenbeck (LOU) process. In the deterministic NP model, we investigate the existence of possible equilibria and analyze their local and global stability. Additionally, by utilizing sensitivity analysis technique, it is shown that phytoplankton density and nutrient concentration are highly sensitive to global warming and

p H

. In the stochastic NP model, we derive the sufficient conditions of exponential extinction and persistence in the mean of phytoplankton, prove the existence of a stationary distribution, and give the specific expression of the probability density under some appropriate conditions. Ecologically, via numerical simulations, we find that the variation in global warming and

p H

can generate new influence mechanisms for the interactions between nutrient and phytoplankton within the deterministic and stochastic environments. One of the most interesting results is that an appropriate increase or decrease in

p H

value is beneficial for inhibiting the occurrence of phytoplankton blooms. This study may provide some new ideas for understanding the dynamic mechanisms of phytoplankton growth in natural aquatic environments.

本文研究了一个考虑pH和全球变暖影响的随机营养物-浮游植物（NP）模型，其中随机环境扰动以对数Ornstein-Uhlenbeck （LOU）过程为特征。在确定性NP模型中，我们研究了可能平衡点的存在性，并分析了它们的局部稳定性和全局稳定性。在随机NP模型中，我们推导了浮游植物平均指数灭绝和指数持续存在的充分条件，证明了其存在平稳分布，并给出了概率密度在适当条件下的具体表达式。生态学上，通过数值模拟，我们发现全球变暖和pH值的变化可以在确定性和随机环境中产生营养物与浮游植物相互作用的新的影响机制。其中一个最有趣的结果是，适当增加或减少pH值有利于抑制浮游植物华的发生。本研究为理解天然水生环境中浮游植物生长的动力学机制提供了新的思路。

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引用次数: 0

Rich dynamics in a delayed water borne pathogen model with overexposure 过度暴露延迟水传播病原体模型的丰富动力学。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-10-29 DOI: 10.1016/j.mbs.2025.109564

Jinhu Xu , Yanni Xiao , Xiaodan Sun

In this paper, we formulate a delayed water borne pathogen model incorporating overexposure, investigate threshold dynamics, and analyze the impact of overexposure and delay on disease transmission. Threshold dynamics are characterized by the basic reproduction number

R_{0}

. The model exhibits backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium for

R_{0}

values below 1, indicating that the disease may persist even when

R_{0} < 1

. Furthermore, we theoretically and numerically examined the existence of Hopf bifurcation in absence of time delay and the results reveal that the overexposure induces rich dynamics, including stability switches, endemic bubble and multiple limits cycles. For the delayed model, by regarding time delay as the bifurcation parameter, the local and global Hopf bifurcation have been carried out to show influence of time delay on model dynamics. Numerical simulations confirm that delay induces stability switches and coexistence of multiple periodic solutions. Our findings indicate that overexposure and time delay are responsible for the model’s complex dynamics, complicating disease control efforts.

本文建立了一个包含过度暴露的延迟水媒病原体模型，研究了阈值动力学，并分析了过度暴露和延迟对疾病传播的影响。阈值动力学的特征是基本繁殖数R0。模型呈现后向分岔，当R0值低于1时，稳定的无病平衡与稳定的地方性平衡共存，表明即使在R0时，疾病也可能持续存在

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引用次数: 0

Stability and bifurcation analysis of a predator–prey system with feedback-controlled odour and wind-driven decay 具有反馈控制气味和风驱动衰变的捕食-食饵系统的稳定性和分岔分析。

IF 1.8 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-10-28 DOI: 10.1016/j.mbs.2025.109561

Dipam Das , Debasish Bhattacharjee , Subarna Roy , Pankaj Kumar Tiwari

Chemical communication is a fundamental component of predator–prey interactions, significantly influencing prey vigilance and predator hunting efficiency. Despite its ecological importance, prevailing mathematical models commonly treat odour as a static or externally imposed parameter, thereby overlooking its inherently dynamic nature and the reciprocal feedback between chemical cues and population dynamics. In this study, we present a novel three-dimensional model incorporating odour concentration as a dynamic variable, directly influenced by predator density and species interactions. Our model captures odour production, its natural decay through environmental processes such as wind-mediated dissipation, and the resultant non-consumptive effects on prey, including stress-induced reductions and alterations in vigilance behaviour. We rigorously analyse the qualitative dynamics of the model. Specifically, we perform stability analyses of all biologically feasible equilibria and detect various bifurcation phenomena, such as transcritical and Hopf bifurcations. The dynamics of the system are also examined across various two-parametric spaces. Extensive numerical simulations corroborate our theoretical findings and facilitate a detailed investigation of parameter influences. Furthermore, we compute the normalized forward sensitivity index to quantify the relative impact of model parameters.

化学通讯是捕食者-猎物相互作用的基本组成部分，对猎物的警觉性和捕食效率有重要影响。尽管气味具有重要的生态意义，但主流数学模型通常将气味视为静态或外部强加的参数，从而忽略了其内在的动态性质以及化学线索与种群动态之间的相互反馈。在这项研究中，我们提出了一个新的三维模型，将气味浓度作为一个动态变量，直接受捕食者密度和物种相互作用的影响。我们的模型捕捉了气味的产生，其通过环境过程（如风介导的消散）的自然衰减，以及由此产生的对猎物的非消耗性影响，包括压力引起的减少和警惕行为的改变。我们严格地分析了模型的定性动力学。具体来说，我们进行了所有生物可行平衡的稳定性分析，并检测了各种分岔现象，如跨临界和Hopf分岔。系统的动力学也被检查跨各种双参数空间。广泛的数值模拟证实了我们的理论发现，并促进了参数影响的详细调查。此外，我们计算归一化前向灵敏度指数来量化模型参数的相对影响。

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引用次数: 0