Mathematics and Computers in Simulation最新文献_第3页

Fixed-time optimal bipartite containment fault-tolerant control for multi-agent systems under multiple faults and saturated actuation 多智能体系统在多故障饱和驱动下的固定时间最优二部容错控制

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-06 DOI: 10.1016/j.matcom.2026.01.001

Ning Xu , Li Tang , Abdullah A. Al-Barakati

This paper addresses the fixed-time optimal bipartite containment control problem for nonlinear multi-agent systems under multiple simultaneous faults — including concurrent actuator and sensor faults — and input saturation. A key contribution is a unified disturbance-observer–based reinforcement learning framework that integrates fault tolerance with optimal control objectives. By designing a novel performance index function, the traditional containment control problem is reformulated as an optimal control problem, enabling an explicit trade-off between control accuracy and energy consumption. To solve the corresponding Hamilton–Jacobi–Bellman equation without relying on accurate system dynamics, a neural reinforcement learning algorithm with an identifier–critic–actor architecture is developed. A disturbance observer is incorporated to actively estimate and compensate for external disturbances, while an auxiliary system is introduced to alleviate input saturation effects. The resulting fixed-time optimal controller ensures that all bipartite containment errors converge to a small neighborhood of the origin within a fixed time independent of initial conditions, while maintaining uniform boundedness of all closed-loop signals. Simulation results validate the effectiveness and superiority of the proposed method in achieving simultaneous fault tolerance, disturbance rejection, and optimal performance under saturated actuation conditions.

研究了非线性多智能体系统在多个同时故障（包括执行器和传感器同时故障）和输入饱和情况下的固定时间最优二部包容控制问题。一个关键的贡献是一个统一的基于干扰观测器的强化学习框架，它集成了容错和最优控制目标。通过设计新的性能指标函数，将传统的安全壳控制问题重新表述为最优控制问题，实现了控制精度与能耗之间的显式权衡。为了在不依赖精确系统动力学的情况下求解相应的Hamilton-Jacobi-Bellman方程，提出了一种具有辨识器-临界-行动者结构的神经强化学习算法。引入干扰观测器来主动估计和补偿外部干扰，同时引入辅助系统来缓解输入饱和效应。所得到的定时最优控制器保证所有的二部包容误差在不依赖于初始条件的固定时间内收敛到原点的一个小邻域内，同时保持所有闭环信号的一致有界性。仿真结果验证了该方法在饱和驱动条件下同时实现容错、抗干扰和最优性能的有效性和优越性。

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引用次数: 0

Multivalued extension of the Caristi-type theorem in semi-metric spaces and its numerical simulation 半度量空间中caristi型定理的多值推广及其数值模拟

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-22 DOI: 10.1016/j.matcom.2026.01.026

Pradip Debnath

We present a novel extension of the Caristi-type fixed point theorem recently established by Zubelevich (2025) for single-valued mappings on complete semi-metric spaces to the multivalued setting. Specifically, we prove that, in a complete semi-metric space

R

, if a set-valued mapping

F : R \to 2^{R}

satisfies a generalized Caristi-type inequality involving a family of lower semi-continuous, bounded-from-below functions and a semi-metric structure, then

F

admits a fixed point. Our approach constructs a suitable selection from the multivalued map and applies Zubelevich’s partial order method in conjunction with Zorn’s lemma to ensure the existence of a fixed point. Furthermore, we establish a multivalued counterpart to Zubelevich’s noncompactness theorem: if one of the associated potential functions fails to attain its minimum, then the fixed point set of

F

is necessarily noncompact. These results provide the first known multivalued Caristi-type fixed point framework for semi-metric spaces, unifying and generalizing prior work in both metric and topological vector space settings. The results are further validated by a numerical simulation showing convergence of iterates under deterministic selections.

本文将Zubelevich（2025）最近建立的关于完备半度量空间上单值映射的caristi型不动点定理推广到多值集。具体地，我们证明了在完备半度量空间R中，如果集值映射F:R→2R满足涉及下半连续、下有界函数和半度量结构的广义caristi型不等式，则F允许一个不动点。我们的方法从多值映射中构造一个合适的选择，并将Zubelevich的偏序方法与Zorn引理相结合来保证不动点的存在性。进一步，我们建立了非紧性定理的一个多值对应物：如果其中一个相关的势函数不能达到其极小值，则F的不动点集必然是非紧的。这些结果提供了已知的第一个半度量空间的多值caristi型不动点框架，统一和推广了度量和拓扑向量空间设置中的先前工作。数值模拟结果进一步验证了确定性选择下迭代的收敛性。

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引用次数: 0

A statistics-based simplification method to the Distribution Network Reconfiguration problem for large-scale networks 基于统计的大规模配电网重构问题简化方法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-12 DOI: 10.1016/j.matcom.2026.01.008

A. Graine , N. Karnib , J.-P. Gaubert , D. Larraillet

The Distribution Network Reconfiguration (DNR) consists of modifying the topology of a Distribution Network (DN) through the modification of the state of its switches, thus modifying the paths of power. It can be used to minimize losses or other physical quantities, while satisfying, among others, radial, electrical, and thermal constraints. It is an optimization problem of a type referred to as Mixed-Integer Programming (MIP). When the DNR is applied to large-scale DNs, which is the case for this paper since the aim is to optimize real networks for a French Distribution System Operator (DSO): this problem can be challenging to solve because the number of switches (and thus the number of binary variables) becomes very large, which can lead to a combinatorial explosion.

In this paper, a statistics-based simplification method is proposed to determine the most impactful switches for the DNR. The method can be fragmented into two phases: a training phase, then a deployment phase. Different strategies are tested and compared for the two phases. A simplified method is used for the training phase, during which the most impactful switches are identified. Then, these most impactful switches are used as decision variables in the deployment phase, while the non-impactful switches are considered as input parameters, hence greatly reducing the number of binary optimization variables. As a consequence, the computational time is decreased. The method’s performance is evaluated through simulations on a realistic 2 588-bus, 403-switch DN. Results show that the proposed method is able to speed up the computation.

DNR （Distribution Network Reconfiguration）是指通过改变配电网络交换机的状态来改变配电网络的拓扑结构，从而改变配电网络的供电路径。它可以用于最小化损耗或其他物理量，同时满足径向、电学和热约束。这是一种被称为混合整数规划（MIP）的优化问题。当DNR应用于大规模DNs时，这是本文的情况，因为目的是为法国配电系统运营商（DSO）优化真实网络：这个问题可能很难解决，因为开关的数量（以及二进制变量的数量）变得非常大，这可能导致组合爆炸。本文提出了一种基于统计的简化方法来确定最有效的DNR开关。该方法可以分成两个阶段：训练阶段，然后是部署阶段。对这两个阶段的不同策略进行了测试和比较。在训练阶段使用了一种简化的方法，在此期间识别最具影响力的开关。然后，将这些最具影响力的开关作为部署阶段的决策变量，而将不具影响力的开关作为输入参数，从而大大减少了二进制优化变量的数量。因此，计算时间减少了。通过在实际的2588总线、403交换机DN上的仿真，对该方法的性能进行了评价。结果表明，该方法能够提高计算速度。

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引用次数: 0

Modelling financial contagion and optimal policy design for bank runs and systemic risk 模拟金融传染和银行挤兑和系统性风险的最佳政策设计

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-03 DOI: 10.1016/j.matcom.2025.12.023

Samuel Asante Gyamerah , Emmanuel Afrifa , Perpetual Andam Boiquaye , Nelson Dzupire

Bank runs can destabilize individual institutions and, through financial networks, spread into general economic crises. The study explores the interconnection of systemic risk in the banking system, emphasizing interbank networks as the primary means of propagating financial contagion. We propose a compartmental system through which contagion is propagated. The system classifies the banks in the network into six compartments (undistressed, exposed, distressed, liquid, run, and failed states). We capture the dynamics of distress transmission through interbank interactions and depositor behaviours. We derive the basic reproduction number

R_{0}

to characterize the threshold conditions for systemic stability and identify both risk-free and risk-persistent equilibrium points. Through sensitivity experiments, we identify the parameters that exert the strongest influence on contagion dynamics—the contact rate between banks, the level of behavioural compliance, and transition intensities. Building on these insights, we formulate an optimal-control framework that incorporates three forms of intervention: deposit-insurance protection, policies aimed at calming depositors, and targeted liquidity intervention. Using Pontryagin’s Maximum Principle, we derive the time paths of these interventions that jointly reduce the spread of distress while keeping regulatory costs manageable. The numerical results highlight the importance of acting early: even a moderate level of deposit-insurance coverage, when implemented at the right moment, substantially dampens the transmission of shocks across the network. The study offers practical guidance for the design of policy tools intended to contain systemic risk in interconnected banking systems.

银行挤兑会破坏个别机构的稳定，并通过金融网络蔓延为普遍的经济危机。该研究探讨了银行体系中系统性风险的相互联系，强调银行间网络是传播金融传染的主要手段。我们提出了传染传播的分区系统。该系统将网络中的银行分为六个部分（未陷入困境的、暴露的、陷入困境的、流动的、运行的和失败的）。我们通过银行间相互作用和存款人行为捕捉到危机传播的动态。我们导出了基本再生数R0来表征系统稳定的阈值条件，并确定了无风险和风险持续的平衡点。通过敏感性实验，我们确定了对传染动态产生最大影响的参数——银行之间的接触率、行为依从性水平和过渡强度。在这些见解的基础上，我们制定了一个包含三种干预形式的最优控制框架：存款保险保护、旨在安抚储户的政策和有针对性的流动性干预。利用庞特里亚金的最大原则，我们得出了这些干预措施的时间路径，这些干预措施共同减少了危机的蔓延，同时保持了监管成本可控。数值结果强调了及早采取行动的重要性：即使是适度的存款保险覆盖范围，如果在适当的时机实施，也会大大抑制冲击在整个网络中的传播。该研究为旨在遏制相互关联的银行体系中的系统性风险的政策工具的设计提供了实用指导。

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引用次数: 0

Dynamic interplay of Allee effect and harvesting in a diseased amensalism model: Unraveling ecological complexity 在一个患病的仙人掌模型中，Allee效应和收获的动态相互作用：解开生态复杂性

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-19 DOI: 10.1016/j.matcom.2026.01.021

Sarita Bugalia , Sandeep Kumar , Jai Prakash Triapthi , Maia Martcheva

In this paper, we analyze the dynamics of an eco-epidemiological amensalism model involving three species, where the first species exhibits a weak Allee effect. In contrast, the second and third species are subjected to proportional harvesting. The proposed model assumes that the disease only affects the second species while the first species remains unaffected. We consider harvesting as a control parameter for both disease and amensalism dynamics. The amensalism functional response is modeled using the Holling type II response, while disease transmission follows a saturation incidence rate. Our primary mathematical objectives are to analyze the effects of the Allee parameter and harvesting on the system’s dynamics. By treating key parameters as bifurcation and threshold variables, the stability of all equilibria and the associated bifurcations are analyzed. The model exhibits a degenerate Bogdanov–Takens (BT), two saddle–node and three transcritical bifurcations. Conditions for both extinction and persistence are derived in terms of the harvesting rate. A critical threshold of harvesting is identified, beyond which the diseased species declines and the disease-free equilibrium becomes stable. Our findings reveal an upper limit of harvesting within which all species can coexist. However, the coexistence of all three species depends on initial conditions, leading to bistability. Notably, the Allee effect acts only on the first species, underlies the occurrence of a saddle–node bifurcation and eliminating equilibria for a certain parameter range, while leaving the other two species unaffected. These results provide quantitative insights into the interplay between the Allee effect and harvesting in shaping species coexistence and system dynamics.

本文分析了一个包含三种物种的生态流行病学模式的动态，其中第一种物种表现出弱的Allee效应。相比之下，第二种和第三种是按比例采伐的。提出的模型假设疾病只影响第二种物种，而第一种物种不受影响。我们认为收获是疾病和营养动力学的控制参数。amsalism功能反应使用Holling II型反应建模，而疾病传播遵循饱和发生率。我们的主要数学目标是分析Allee参数和收获对系统动力学的影响。通过将关键参数作为分岔变量和阈值变量，分析了所有平衡点的稳定性和相关的分岔。该模型具有一个简并Bogdanov-Takens （BT）、两个鞍节点和三个跨临界分叉。灭绝和持久的条件都是根据采伐率推导出来的。确定了收获的临界阈值，超过该阈值，患病物种减少，无病平衡变得稳定。我们的发现揭示了所有物种可以共存的采伐上限。然而，这三个物种的共存依赖于初始条件，导致双稳态。值得注意的是，Allee效应仅作用于第一个物种，这是鞍节点分岔和在一定参数范围内消除平衡的基础，而其他两个物种不受影响。这些结果提供了定量的见解，在形成物种共存和系统动力学的Allee效应和收获之间的相互作用。

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引用次数: 0

Percolation thresholds and epidemic spreading on small-world networks: Exact results and critical dynamics 小世界网络上的渗透阈值和流行病传播：精确结果和临界动力学

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-13 DOI: 10.1016/j.matcom.2026.01.011

Xiao-Long Peng , Shu-Yan Chang , Shanshan Chen , Gui-Quan Sun

Percolation theory provides a powerful framework for understanding the emergence of large-scale epidemic outbreaks on complex networks. Building on the seminal work of Moore and Newman (2000), we revisit and extend percolation-based models of disease spread on small-world networks that incorporate both local connections and long-range shortcuts. Specifically, we resolve two previously unresolved cases by deriving exact analytical expressions for the bond percolation threshold at local connectivity

K = 3

, and for the hybrid site-bond percolation threshold at

K = 2

. These results advance the theoretical foundations of epidemic modelling on structured networks. Complementing these theoretical results, we conduct extensive numerical simulations to characterize critical behaviour of both pure bond and hybrid site-bond percolation processes. We find that percolation thresholds are highly sensitive to shortcut density and local connectivity. Notably, the average size of finite percolating clusters exhibits a pronounced peak at criticality, offering a reliable early-warning signal for epidemic onset. Furthermore, we observe a clear transition in cluster size distributions — from exponential decay to heavy-tailed forms — as the system approaches the percolation threshold, culminating in the emergence of a giant component indicative of a large-scale epidemic. Temporal simulations further reveal abrupt epidemic transitions as control parameters cross critical thresholds, in agreement with our percolation-based predictions. Collectively, our results establish the percolation framework as a powerful tool for capturing both structural and dynamical features of epidemic spreading on small-world networks.

渗透理论为理解复杂网络中大规模流行病爆发的出现提供了一个强有力的框架。在Moore和Newman（2000）开创性工作的基础上，我们重新审视并扩展了疾病在小世界网络中传播的基于渗透的模型，该模型包含了本地连接和远程捷径。具体来说，我们通过推导局部连通性K=3时键渗透阈值和K=2时混合位点-键渗透阈值的精确解析表达式，解决了两个先前未解决的情况。这些结果为基于结构化网络的流行病建模提供了理论基础。为了补充这些理论结果，我们进行了广泛的数值模拟，以表征纯键和混合位点-键渗透过程的临界行为。我们发现渗透阈值对捷径密度和局部连通性高度敏感。值得注意的是，有限渗流簇的平均大小在临界时表现出明显的峰值，为流行病的发生提供了可靠的预警信号。此外，我们观察到集群大小分布的明显转变——从指数衰减到重尾形式——当系统接近渗透阈值时，最终出现一个表明大规模流行病的巨大组成部分。时间模拟进一步显示，当控制参数越过临界阈值时，流行病会突然转变，这与我们基于渗流的预测一致。总的来说，我们的结果建立了渗透框架作为捕获小世界网络中流行病传播的结构和动态特征的强大工具。

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引用次数: 0

A semi-adaptive discrete variable method for emulating dual space fractional convection–diffusion quenching problems 模拟对偶空间分数对流扩散猝灭问题的半自适应离散变量方法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-06-01 Epub Date: 2025-12-31 DOI: 10.1016/j.matcom.2025.12.019

Lin Zhu , Rumin Dong , Qin Sheng

This paper investigates the properties of discrete variable approximations for the quenching solutions of a nonlinear one-dimensional dual Riemann–Liouville fractional-order problem. The fractional-order spatial derivatives are discretized using a weighted average approach, combined with both the standard and shifted Grünwald formulas. The advection term is approximated via a direct Euler scheme, resulting in a semi-discretized system of nonlinear, constant-coefficient equations. The robustness of the proposed discrete variable method is demonstrated and validated through rigorous mathematical analysis and numerical experiments. The study systematically examines the effects of the critical length, convective terms, and the two fractional orders on the quenching phenomenon. Detailed computational results and analyses provide a deeper understanding of quenching behavior in nonlinear fractional-order problems.

研究了一类非线性一维对偶Riemann-Liouville分数阶问题猝灭解的离散变量近似的性质。分数阶空间导数采用加权平均方法，结合标准公式和移位的格恩瓦尔德公式进行离散化。平流项用直接欧拉格式近似，得到一个非线性常系数方程的半离散系统。通过严密的数学分析和数值实验，验证了离散变量方法的鲁棒性。该研究系统地考察了临界长度、对流项和两个分数阶对淬火现象的影响。详细的计算结果和分析使我们对非线性分数阶问题的猝灭行为有了更深的理解。

引用次数: 0

Diverse soliton solutions to the conformable Ivancevic option pricing model via the modified generalized Riccati equation mapping method 用改进的广义Riccati方程映射法求解符合Ivancevic期权定价模型的各种孤子解

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-06-01 Epub Date: 2026-01-03 DOI: 10.1016/j.matcom.2025.12.022

Muhammad Amin S. Murad , Usman Younas , Homan Emadifar , Mujahid Iqbal , Wael W. Mohammed , Karim K. Ahmed

In this paper, we employ the modified generalized Riccati equation approach to derive a variety of exact solutions for the Ivancevic option pricing model incorporating the conformable derivative. The Ivancevic option pricing equation is structured using an adaptive nonlinear Schrödinger equation, which describes the option-pricing wave function based on time and stock price. This equation captures the typical regulated Brownian motion seen in financial markets. The predictive nature of the model allows financial analysts to forecast option prices under varying market conditions. The model helps traders to price complex options with greater accuracy by considering nonlinear market dynamics. A variety of soliton solutions to the conformable Ivancevic model are derived, including dark, mixed dark–bright, singular, bell-shaped, and wave solutions. To provide deeper insights into their dynamical properties and physical significance, these solutions are visualized through three-dimensional plots, two-dimensional plots, and contour plots. The graphical representations underscore the intricate dynamics and potential financial applications of soliton solutions within the conformable framework, demonstrating their relevance in option pricing theory and nonlinear financial modeling.

本文利用改进的广义Riccati方程方法，导出了包含可调导数的Ivancevic期权定价模型的多种精确解。Ivancevic期权定价方程采用自适应非线性Schrödinger方程，描述了基于时间和股票价格的期权定价波动函数。这个方程反映了金融市场中典型的受监管的布朗运动。该模型的预测性质使金融分析师能够在不同的市场条件下预测期权价格。该模型通过考虑非线性市场动态，帮助交易者更准确地为复杂期权定价。导出了符合Ivancevic模型的各种孤子解，包括暗解、混合暗亮解、奇异解、钟形解和波解。为了更深入地了解它们的动力学特性和物理意义，我们通过三维图、二维图和等高线图对这些解进行了可视化。图形表示强调了在一致性框架内孤子解的复杂动态和潜在金融应用，展示了它们在期权定价理论和非线性金融建模中的相关性。

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引用次数: 0

A unified one-step joint optimization framework for sparse subspace clustering and self-constrained spectral clustering 稀疏子空间聚类与自约束谱聚类的统一一步联合优化框架

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-06-01 Epub Date: 2025-12-18 DOI: 10.1016/j.matcom.2025.12.011

Chengmao Wu, Yilong Zhu

Subspace clustering aims to explore multiple low-dimensional subspaces within data to more effectively represent the essential structure of high-dimensional datasets. Traditional subspace clustering methods typically employ a two-step strategy: first, constructing a similarity matrix based on the relevance between samples, and then performing spectral clustering on this matrix. Although these approaches achieve local optimality at each stage, they do not guarantee the global optimality of the clustering results. To address these issues, this study introduces an algorithm that integrates subspace clustering and spectral clustering, enabling the simultaneous optimization of the similarity matrix and the clustering indicator matrix in a low-dimensional space. In the subspace clustering module, an -

ℓ_{0, 2}

norm constraint is applied to the self-representation coefficient matrix to enhance the sparsity of the similarity matrix. For the spectral clustering component, we employ self-constrained spectral clustering to improve the graph-cut performance, resulting in higher-quality clustering indicator matrices. To integrate the two components, we develop a unified one-step joint optimization framework that addresses the clustering problem through a proximal alternating minimization approach with proven convergence. Its innovation lies in constructing a simultaneous optimization model for the similarity and cluster indicator matrices, effectively solved using the proximal alternating minimization (PAM) method to tackle the problem's inherent nonlinearity. The proposed algorithm has demonstrated strong performance across various datasets, outperforming eight representative comparison algorithms.

子空间聚类旨在探索数据内部的多个低维子空间，以更有效地表示高维数据集的本质结构。传统的子空间聚类方法通常采用两步策略：首先根据样本之间的相关性构造相似矩阵，然后对该矩阵进行谱聚类。虽然这些方法在每个阶段都实现了局部最优性，但它们不能保证聚类结果的全局最优性。针对这些问题，本研究引入了一种融合子空间聚类和谱聚类的算法，实现了在低维空间内相似性矩阵和聚类指标矩阵的同时优化。在子空间聚类模块中，对自表示系数矩阵施加- l0,2范数约束，增强相似性矩阵的稀疏性。对于谱聚类组件，我们采用自约束谱聚类来提高图切性能，从而获得更高质量的聚类指标矩阵。为了整合这两个组件，我们开发了一个统一的一步联合优化框架，该框架通过具有证明收敛性的近端交替最小化方法来解决聚类问题。该方法的创新之处在于构建了相似度和聚类指标矩阵的同时优化模型，利用最近邻交替极小化（PAM）方法有效地解决了该问题固有的非线性。该算法在各种数据集上表现出强大的性能，优于8种代表性的比较算法。

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引用次数: 0

Dynamic analysis and optimal control of a stochastic tumor-immune model 随机肿瘤免疫模型的动态分析与最优控制

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-06-01 Epub Date: 2025-12-18 DOI: 10.1016/j.matcom.2025.12.010

Xi Wang, Zijian Liu, Yuanshun Tan, Yu Mu

Competition between tumor cells and normal tissue cells due to limited resources is considered as a key dynamic in tumor development. Therefore, in this paper, we develop a stochastic model of the interaction between tumor cells, helper T cells, effector cells, and host cells. The existence and uniqueness of the global positive solutions, stochastic eventual boundedness, and stochastic persistence of the model are proved by establishing appropriate Lyapunov functions. Additionally, we derive the threshold condition for tumor cell extinction and investigate the system’s steady-state distribution. Furthermore, we obtain the optimal control strategy through stochastic control theory. The results and numerical simulations demonstrate that stochastic perturbations can inhibit tumor cell growth, the control strategy can accelerate tumor extinction while reducing damage to effector cells, and increasing the competition coefficient of normal tissue cells against tumor cells can accelerate tumor extinction.

由于资源有限，肿瘤细胞与正常组织细胞之间的竞争被认为是肿瘤发展的关键动力。因此，在本文中，我们建立了肿瘤细胞、辅助T细胞、效应细胞和宿主细胞之间相互作用的随机模型。通过建立适当的Lyapunov函数，证明了该模型整体正解的存在唯一性、最终有界性和随机持久性。此外，我们还推导了肿瘤细胞消失的阈值条件，并研究了系统的稳态分布。在此基础上，利用随机控制理论得到了最优控制策略。结果和数值模拟表明，随机扰动可以抑制肿瘤细胞的生长，控制策略可以在减少效应细胞损伤的同时加速肿瘤的消失，增加正常组织细胞对肿瘤细胞的竞争系数可以加速肿瘤的消失。

引用次数: 0