Journal of Theoretical Biology最新文献_第5页

Stiffness-sensitive gene regulation in human mesenchymal stem cells: Modelling mechanotransduction to predict mineralization and bone protein expression 人间充质干细胞的刚度敏感基因调控：模拟机械转导以预测矿化和骨蛋白表达。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-13 DOI: 10.1016/j.jtbi.2025.112284

Jean-Philippe Berteau , Abdennasser Chekroun , Laurent Pujo-Menjouet , Kevin Yueh-Hsun Yang

The goal of our study was to establish how a specific part of the bone Gene Regulatory Network (GRN) controls mineralization in response to stiffness. We hypothesized that a system of differential equations model stiffness-sensitive gene regulation in human mesenchymal stem cells through the epistatic genetic interactions between stiffness (e.g. WNT-β catenin pathway) and five of the main transcription factors and bone proteins (e.g. RUNX2, BSP, OSX, OC, and OPN). To test this hypothesis, we (i) performed in-vitro experiments culturing bone cells on different stiffness, (i) adapted our previously published model from being continuously time-dependent to continuously stiffness-sensitive, and (iii) simulated protein production in function of stiffness and other protein production from the best estimate of parameters coming from the experimental work. Our experimental findings reveal a non-parametric relationship between stiffness and RUNX2 production, with no discernible linear trends for other proteins. Modeling results demonstrate that continuous variations in stiffness enable simulation of bone GRN gene expression, fitting our novel experimental dataset. Specifically, our computational results indicate that OPN production peaks at low stiffness (8 kPa), while RUNX2, OSX, and OC achieve maximum production at higher stiffness levels (64 kPa). This alignment underscores the model’s capacity to replicate experimental data accurately. Additionally, our approach predicts that WNT-β-catenin activation serves as an enhancer for OPN and BSP production. The model also highlights a negative feedback-like interaction between OC and BSP production. Stiffness variations were shown to have a significant impact on OC and BSP production and a moderate effect on OPN production. By employing a stiffness-sensitive gene regulation model, we provide insights into one of the mineralization patterns through the prediction of bone protein expression dynamics.

我们研究的目的是确定骨基因调控网络（GRN）的特定部分如何控制矿化以响应刚度。我们假设一个微分方程系统通过刚度（如WNT-β catenin通路）与五种主要转录因子和骨蛋白（如RUNX2、BSP、OSX、OC和OPN）之间的上位性遗传相互作用来模拟人间充质干细胞中刚度敏感基因的调控。为了验证这一假设，我们(i)进行了体外实验，培养不同刚度的骨细胞，(i)调整了我们之前发表的模型，从连续的时间依赖到连续的刚度敏感，（iii）模拟了刚度和其他蛋白质产量的函数，从实验工作中得到的参数的最佳估计。我们的实验结果揭示了刚度和RUNX2产量之间的非参数关系，对其他蛋白质没有明显的线性趋势。建模结果表明，刚度的连续变化可以模拟骨GRN基因表达，符合我们新的实验数据集。具体来说，我们的计算结果表明，OPN产量在低刚度（8 kPa）时达到峰值，而RUNX2、OSX和OC在较高刚度水平（64 kPa）时达到最大产量。这种一致性强调了模型精确复制实验数据的能力。此外，我们的方法预测WNT-β-catenin的激活可以促进OPN和BSP的产生。该模型还强调了OC和BSP产量之间的负反馈式相互作用。刚度变化对OC和BSP产量有显著影响，对OPN产量影响不大。通过采用刚度敏感基因调控模型，我们通过预测骨蛋白表达动态来深入了解矿化模式之一。

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引用次数: 0

Mathematical modeling of tuberculosis with two strains, seasonality, and age heterogeneity 两株结核的数学模型、季节性和年龄异质性。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-13 DOI: 10.1016/j.jtbi.2025.112313

Yang Deng , Yi Zhao

Tuberculosis (TB) remains a significant global health threat, particularly in the regions with diverse age-specific transmission patterns and increasing drug resistance. To address these challenges, this study establishes a dual-strain model that incorporates both drug-resistant and drug-sensitive strains to investigate how these strains contribute to the dynamics of TB transmission. By integrating age heterogeneity, social interactions, and seasonal variations, the model offers a detailed depiction of TB transmission process, highlighting its inherent complexity across various population groups. We derive the basic reproduction number of the model as the maximum of the two reproduction numbers: one for the drug-resistant strain (

R_{0}^{r}

) and one for the drug-sensitive strain (

R_{0}^{s}

). It is found that the disease-free periodic equilibrium of the system is globally asymptotically stable when

R_{0} = \max (R_{0}^{r}, R_{0}^{s}) < 1

, in the absence of reinfection. We further explore the competitive dynamics of drug-resistant and drug-sensitive strains under

R_{0}^{r} > 1 > R_{0}^{s}

and

R_{0}^{s} > 1 > R_{0}^{r}

. Using a Markov Chain Monte Carlo (MCMC) algorithm, the model is calibrated with monthly TB infection data from mainland China, enabling the reconstruction of TB transmission dynamics across eight age-specific groups. The study reveals that drug-sensitive tuberculosis strains exhibit more prominent transmission characteristics compared to drug-resistant strains. Moreover, increased vaccination coverage significantly reduces TB prevalence, particularly in younger populations, while reducing contact intensity effectively suppresses TB across all age groups. These findings highlight the role of combining age-structured modeling, strain dynamics, and behavioral interventions, offering implications for the targeted TB control strategies.

结核病仍然是一个重大的全球健康威胁，特别是在具有不同年龄传播模式和耐药性日益增加的区域。为了应对这些挑战，本研究建立了一个包含耐药菌株和药敏菌株的双菌株模型，以调查这些菌株如何促进结核病传播的动态。通过整合年龄异质性、社会互动和季节变化，该模型提供了结核病传播过程的详细描述，突出了其在不同人群中的固有复杂性。我们推导出模型的基本复制数为耐药菌株（R0r）和药敏菌株（R0s）两个复制数的最大值。发现当R0=max(R0r,R0s)0r >> R0s和R0s >> R0r时，系统的无病周期平衡点是全局渐近稳定的。使用马尔可夫链蒙特卡罗（MCMC）算法，该模型使用来自中国大陆的每月结核病感染数据进行校准，从而能够重建8个特定年龄群体的结核病传播动态。该研究表明，与耐药菌株相比，药敏结核菌株表现出更突出的传播特征。此外，增加疫苗接种覆盖率可显著降低结核病患病率，特别是在年轻人群中，同时降低接触强度可有效抑制所有年龄组的结核病。这些发现突出了结合年龄结构建模、应变动力学和行为干预的作用，为有针对性的结核病控制策略提供了启示。

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引用次数: 0

Emergence of longitudinal queue behavior based on topological interaction and asynchronous dynamics 基于拓扑交互和异步动态的纵向队列行为的出现。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-12 DOI: 10.1016/j.jtbi.2025.112318

Decheng Kong, Kai Xue, Ping Wang, Zeyu Xu, Zhiqin Huang

Coordinated longitudinal queue behavior in biological groups, such as migratory bird flocks, remains underexplored in classical collective motion models that focus on metric-based interactions and synchronous dynamics. This study utilizes a modified self-propelled particle model incorporating topological interactions, gliding asynchrony, and limited view angle to investigate the mechanisms driving longitudinal queue formation. Simulations reveal that interacting with only two topological neighbors is critical for stable queue emergence, with an optimal view angle range of [200°, 270°] balancing frontward tracking and lateral collision avoidance. Gliding asynchrony enhances queue formation efficiency by reducing neighbor interaction frequency, leading to higher success rates and lower interaction complexity compared to synchronous or random update mechanisms. Topological interaction networks exhibit high connectivity and stability, fundamentally supporting queue maintenance, while metric-based or Voronoi interactions fail to produce linear order. The study highlights the interplay of limited sensory perception, low neighbor connectivity, and asynchronous dynamics in self-organized migration queues, providing a theoretical guidance for understanding animal collective behavior and guiding robotic swarm design.

生物群体（如候鸟群）的协调纵向队列行为，在经典的基于度量的相互作用和同步动力学的集体运动模型中仍未得到充分研究。本研究利用一个改进的自推进粒子模型，结合拓扑相互作用、滑行异步和有限视角来研究驱动纵向队列形成的机制。仿真结果表明，仅与两个拓扑邻居相互作用对于稳定的队列涌现至关重要，最佳视角范围为[200°，270°]，以平衡前向跟踪和侧避碰撞。与同步或随机更新机制相比，滑动异步通过降低邻居交互频率来提高队列形成效率，从而获得更高的成功率和更低的交互复杂性。拓扑交互网络表现出高度的连通性和稳定性，从根本上支持队列维护，而基于度量或Voronoi的交互不能产生线性秩序。该研究突出了自组织迁移队列中有限感官知觉、低邻居连通性和异步动力学的相互作用，为理解动物集体行为和指导机器人群体设计提供了理论指导。

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引用次数: 0

Fast approximate Bayesian inference of HIV indicators using PCA adaptive Gauss-Hermite quadrature 基于PCA自适应高斯-埃尔米特正交的HIV指标快速近似贝叶斯推断。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-11 DOI: 10.1016/j.jtbi.2025.112290

Adam Howes , Alex Stringer , Seth R. Flaxman , Jeffrey W. Imai–Eaton

Naomi is a spatial evidence synthesis model used to produce district-level HIV epidemic indicators in sub-Saharan Africa. Multiple outcomes of policy interest, including HIV prevalence, HIV incidence, and antiretroviral therapy treatment coverage are jointly modelled using both household survey data and routinely reported health system data. The model is provided as a tool for countries to input their data to and generate estimates with during a yearly process supported by UNAIDS. Previously, inference has been conducted using empirical Bayes and a Gaussian approximation, implemented via the TMB R package. We propose a new inference method based on an extension of adaptive Gauss-Hermite quadrature to deal with more than 20 hyperparameters. Using data from Malawi, our method improves the accuracy of inferences for model parameters, while being substantially faster to run than Hamiltonian Monte Carlo with the No-U-Turn sampler. Our implementation leverages the existing TMB C++ template for the model’s log-posterior, and is compatible with any model with such a template.

Naomi是一个空间证据综合模型，用于编制撒哈拉以南非洲地区一级的艾滋病毒流行指标。使用住户调查数据和常规报告的卫生系统数据，对包括艾滋病毒流行率、艾滋病毒发病率和抗逆转录病毒治疗覆盖在内的多种政策结果进行了联合建模。该模型是作为一种工具提供的，供各国在艾滋病规划署支助的年度进程中输入其数据并产生估计数。以前，推理是使用经验贝叶斯和高斯近似进行的，通过TMBR包实现。提出了一种基于自适应高斯-埃尔米特正交扩展的超参数推理方法。使用来自马拉维的数据，我们的方法提高了模型参数推断的准确性，同时比使用无u型转弯采样器的哈密顿蒙特卡罗运行速度快得多。我们的实现利用现有的TMBC++模板进行模型的对数后验，并且与具有这种模板的任何模型兼容。

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引用次数: 0

Treatment of methanol toxicity through ethanol and folinic acid: A mathematical study 乙醇和亚叶酸处理甲醇毒性的数学研究。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-10 DOI: 10.1016/j.jtbi.2025.112304

Sanju Sardar , Priti Kumar Roy , Sk Mosaraf Ahammed , Tushar Ghosh , David Greenhalgh

Methanol poisoning is an infrequent but immensely dangerous intoxication, causing severe metabolic disturbances, neurological dysfunction, and even death, if not treated timely and properly. In this article, we formulate a mathematical model based on the chemical kinetics reaction, to analyse the effect of co-administration of the antidote ethanol and folinic acid for the treatment of methanol toxicity. The maximum concentration level of formic acid has been identified, and through a one-dimensional impulsive system, we determined the maximum dosing interval of folinic acid. Under appropriate assumptions we have demonstrated the existence and stability of the equilibrium-like periodic orbit of our system with impulsive administration of folinic acid and ethanol. The dynamical changes of toxic metabolites are illustrated numerically for different doses and dosing intervals. We performed a sensitivity analysis to identify the key parameters affecting formic acid concentration during treatment. Model results were validated by comparing them with clinical and experimental data on methanol half-life during ethanol therapy and formic acid clearance under folinic acid treatment. Based on our detailed analytical and numerical analysis, we recommend an effective dosing regimen of folinic acid and ethanol to detoxify the human body and clearly identify the conditions beyond which hemodialysis becomes essential. We verified all of our analytical outcomes through numerical simulation.

甲醇中毒是一种不常见但非常危险的中毒，如果治疗不及时和适当，会引起严重的代谢紊乱、神经功能障碍，甚至死亡。本文建立了基于化学动力学反应的数学模型，分析了解毒剂乙醇与亚叶酸共给药治疗甲醇中毒的效果。确定了甲酸的最大浓度水平，并通过一维脉冲系统确定了亚叶酸的最大给药间隔。在适当的假设下，我们证明了该系统的类平衡周期轨道的存在性和稳定性。数值说明了不同剂量和给药间隔下毒性代谢物的动态变化。我们进行了敏感性分析，以确定治疗期间影响甲酸浓度的关键参数。通过将模型结果与乙醇治疗时甲醇半衰期和亚叶酸治疗时甲酸清除率的临床和实验数据进行比较，验证了模型结果。基于我们详细的分析和数值分析，我们推荐了一种有效的叶酸和乙醇的剂量方案来解毒人体，并清楚地确定了超过血液透析必须的条件。我们通过数值模拟验证了所有的分析结果。

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引用次数: 0

Rapid cell turnover to model adipocyte size distribution 快速细胞更新以模拟脂肪细胞大小分布。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-10 DOI: 10.1016/j.jtbi.2025.112311

Louis Fostier , Aloïs Dauger , Romain Yvinec , Magali Ribot , Chloe Audebert , Hedi Soula

White adipose tissue, composed of adipocyte cells, primarily stores energy as lipid droplets. The size of adipocytes varies significantly within the tissue according to the amount of stored lipids. A striking observation is that the adipocyte size distribution is bimodal, and thus, this tissue is lacking a characteristic size.

We propose a novel dynamical model, based on a partial differential equation, to represent the adipocyte size distribution. The model assumes continuous adipocyte growth, with a velocity dependent on cell radius and extracellular lipid availability, together with constant rates of cell recruitment and death.

We prove the existence and local stability of a unique stationary solution for a broad range of growth velocity functions. Choosing a parcimonious formulation, we show that only three parameters are enough to describe adipocyte size distributions measurements in rats. These parameters are robustly estimated through approximate Bayesian computation, and the model demonstrates excellent agreement with experimental data. This mechanistic, three-parameter framework offers a new and interpretable approach to characterizing adipocyte size distributions.

白色脂肪组织由脂肪细胞组成，主要以脂滴的形式储存能量。脂肪细胞的大小在组织内根据储存的脂质量有显著变化。一个引人注目的观察是，脂肪细胞的大小分布是双峰的，因此，该组织缺乏特征大小。我们提出了一个新的动态模型，基于偏微分方程，以表示脂肪细胞的大小分布。该模型假设脂肪细胞持续生长，其速度取决于细胞半径和细胞外脂质可用性，同时细胞招募和死亡的速率恒定。证明了一类大范围生长速度函数的唯一平稳解的存在性和局部稳定性。选择一个和谐的公式，我们表明只有三个参数足以描述脂肪细胞的大小分布测量在大鼠。通过近似贝叶斯计算对这些参数进行了稳健估计，模型与实验数据吻合良好。这种机制，三参数框架提供了一个新的和可解释的方法来表征脂肪细胞的大小分布。

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引用次数: 0

Mathematical modelling of tumor-immune interactions in breast cancer 乳腺癌中肿瘤-免疫相互作用的数学模型。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-08 DOI: 10.1016/j.jtbi.2025.112310

Haifeng Zhang , Chenghang Li

The dynamic interplay between tumors and immune system is pivotal to the progression of breast cancer. To systematically investigate how interactions between tumor cells and immune cells shape breast cancer evolution, we developed a mathematical model that incorporates tumor cells, dendritic cells (DCs), natural killer (NK) cells, regulatory T cells (Tregs) and CD8+ T cells. We first established analytical conditions for the local stability of the tumor-free equilibrium, identifying key constraints on tumor growth imposed by immune activity. The existence of a positive equilibrium solution further suggests the potential coexistence of tumor and immune cells. Numerical simulations demonstrate that effective tumor control is achieved under a high baseline level of CD8+ T cell precursors coupled with a low level of regulatory T cell precursors. These results highlight the important role of balancing immunostimulatory and immunosuppressive forces within the tumor microenvironment. Through bifurcation analysis, we identified regimes of bistability in which both high-tumor and low-tumor equilibria coexist with dynamic features that may underlie divergent clinical outcomes and present a critical challenge for clinical therapeutic intervention. Moreover, simulations of tumor-immune dynamics in virtual cohorts reveal that tumor control hinges on CD8+ T cell infiltration, whereas regulatory T cell abundance is a potent predictor of immune escape. Finally, we formulated an optimal control framework to design adaptive CD8+ T cell injection protocols. Numerical solutions demonstrate that such optimized strategies achieve superior tumor reduction compared with constant dosing, despite using the same total injection dose of CD8+ T cells and identical treatment intervals. Collectively, our findings provide a mechanistic understanding of breast cancer progression and establish a theoretical foundation for developing personalized therapeutic strategies to optimize clinical outcomes.

肿瘤与免疫系统之间的动态相互作用对乳腺癌的发展至关重要。为了系统地研究肿瘤细胞和免疫细胞之间的相互作用如何影响乳腺癌的进化，我们开发了一个包含肿瘤细胞、树突状细胞（dc）、自然杀伤细胞（NK）、调节性T细胞（Tregs）和CD8+ T细胞的数学模型。我们首先建立了无肿瘤平衡局部稳定性的分析条件，确定了免疫活性对肿瘤生长的关键限制。正平衡溶液的存在进一步表明肿瘤细胞和免疫细胞可能共存。数值模拟表明，在高基线水平的CD8+ T细胞前体加上低水平的调节性T细胞前体的情况下，可以实现有效的肿瘤控制。这些结果强调了在肿瘤微环境中平衡免疫刺激和免疫抑制力量的重要作用。通过分岔分析，我们确定了双稳定性机制，其中高肿瘤和低肿瘤平衡共存，动态特征可能是不同临床结果的基础，并为临床治疗干预提出了关键挑战。此外，虚拟队列中的肿瘤免疫动力学模拟显示，肿瘤控制取决于CD8+ T细胞浸润，而调节性T细胞丰度是免疫逃逸的有效预测因子。最后，我们制定了一个最优控制框架来设计自适应CD8+ T细胞注射方案。数值解表明，尽管使用相同的CD8+ T细胞总注射剂量和相同的治疗间隔，与恒定剂量相比，这种优化策略取得了更好的肿瘤减少效果。总的来说，我们的研究结果提供了对乳腺癌进展的机制理解，并为制定个性化治疗策略以优化临床结果奠定了理论基础。

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引用次数: 0

Direct reciprocity in multi-action repeated games 多动作重复游戏中的直接互惠性。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-07 DOI: 10.1016/j.jtbi.2025.112312

Feipeng Zhang , Lei Zhou , Guofeng Zhang , Long Wang

Direct reciprocity is a fundamental mechanism for sustaining cooperation in repeated interactions, where individuals adjust their behavior based on past experiences. Most previous models have focused on the prisoner’s dilemma, in which individuals face a strict choice between full cooperation and complete defection. However, this dichotomy oversimplifies the complexity of real-world reciprocal interactions. To address this, we introduce additional actions between these extremes, thereby increasing action diversity. Our analysis demonstrates that a broader range of available actions fosters cooperation more effectively than a binary choice. Through evolutionary analysis, we identify which types of intermediate actions promote cooperation. Moreover, equilibrium analysis establishes the theoretical conditions underlying this effect. While the increased computational complexity makes it infeasible to simulate scenarios with an arbitrarily large number of actions, our theoretical analysis remains applicable to settings with more actions, offering broader insights into the role of action diversity in promoting cooperation. These findings deepen our understanding of direct reciprocity and highlight the importance of action diversity in shaping cooperative behavior.

直接互惠是在重复互动中维持合作的基本机制，个体根据过去的经验调整自己的行为。大多数先前的模型关注的是囚犯困境，在这种困境中，个体面临着完全合作和完全背叛之间的严格选择。然而，这种二分法过分简化了现实世界中相互作用的复杂性。为了解决这个问题，我们在这两个极端之间引入了额外的行动，从而增加了行动的多样性。我们的分析表明，与二元选择相比，更广泛的行动范围能更有效地促进合作。通过演化分析，我们确定了哪种类型的中间行为促进了合作。此外，平衡分析建立了这种效应的理论条件。虽然计算复杂性的增加使得模拟具有任意大量动作的场景变得不可行，但我们的理论分析仍然适用于具有更多动作的设置，为行动多样性在促进合作中的作用提供了更广泛的见解。这些发现加深了我们对直接互惠的理解，并强调了行动多样性在塑造合作行为中的重要性。

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引用次数: 0

Network reciprocity turns cheap talk into a force for cooperation 网络互惠将廉价的谈话转化为合作的力量

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-07 DOI: 10.1016/j.jtbi.2025.112303

Zhao Song , Chen Shen , The Anh Han

Non-binding communication is common in daily life and crucial for fostering cooperation, even though it has no direct payoff consequences. However, despite robust empirical evidence, its evolutionary basis remains poorly understood. Here, we develop a game-theoretic model in which individuals can signal an intention to cooperate before playing a Donation game. Strategies differ in how they respond to these signals, ranging from unconditional to conditional types, with the latter incurring a cognitive cost for deliberation. Through evolutionary analysis, we show that non-binding communication alone cannot sustain cooperation in well-mixed, anonymous populations, consistent with empirical observations. In contrast, structured populations support the emergence of cooperation, with conditional cooperators acting as catalysts that protect unconditional cooperators through context-dependent patterns of cyclic dominance. These findings offer an evolutionary explanation for how non-binding communication promotes cooperation and provide a modelling framework for exploring its effects in diverse social settings.

非约束性沟通在日常生活中很常见，对促进合作至关重要，尽管它没有直接的回报结果。然而，尽管有强有力的经验证据，其进化基础仍然知之甚少。在这里，我们开发了一个博弈论模型，其中个人可以在玩捐赠游戏之前发出合作意愿的信号。策略的不同在于它们对这些信号的反应方式，从无条件的到有条件的，后者会产生考虑的认知成本。通过进化分析，我们表明，在混合良好的匿名群体中，仅靠非约束性交流无法维持合作，这与经验观察一致。相比之下，结构化种群支持合作的出现，有条件的合作者作为催化剂，通过环境依赖的循环优势模式保护无条件的合作者。这些发现为非约束性交流如何促进合作提供了一种进化解释，并为探索其在不同社会环境中的影响提供了一个建模框架。

引用次数: 0

Stability and threshold analysis of a class of epidemic models in a multi-patch environment 多斑块环境下一类流行病模型的稳定性和阈值分析。

IF 2 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2025-11-07 DOI: 10.1016/j.jtbi.2025.112285

Linhe Zhu , Le He , Haoyan Sha , Shuling Shen

Spatial heterogeneity and population migration may affect transmission threshold and the asymptotic behavior of epidemic transmission near the steady state. To investigate this issue, an epidemic transmission model with nonlinear natural growth mechanism and linear migration mechanism based on multi-patch structure is established. First, we study the findings related to the equilibrium state of the system and the transmission threshold, proving the uniqueness and the existence of epidemic-free equilibrium points, the existence of positive equilibrium points under certain conditions and the non-existence of mixed equilibrium points. Meanwhile, we discuss the asymptotic behavior of various types of equilibrium points and define the global basic reproduction number and the local basic reproduction number, demonstrating some of their unequal relationships. Further, we also consider the impact of the blocking mechanism on the patch model, illustrating that the epidemic disappears or persists in single patch under certain conditions. Finally, we carry out the numerical simulation analysis of our system. The results suggest that the epidemic may form a certain oscillatory pattern in space and there are multiple positive equilibrium points for the system. At the same time, the blocking mechanism may lead to different types of equilibrium states in different patches, but it is not effective in reducing the total number of infected individuals and the convergence time of the system.

空间异质性和人口迁移可能影响传播阈值和接近稳态的流行病传播渐近行为。为了研究这一问题，建立了基于多斑块结构的具有非线性自然生长机制和线性迁移机制的流行病传播模型。首先，我们研究了系统平衡状态和传播阈值的相关发现，证明了无流行病平衡点的唯一性和存在性，在一定条件下正平衡点的存在性和混合平衡点的不存在性。同时，我们讨论了各种类型平衡点的渐近性，定义了全局基本再生数和局部基本再生数，并证明了它们之间的一些不相等关系。此外，我们还考虑了阻断机制对斑块模型的影响，说明在一定条件下，流行病在单个斑块中消失或持续存在。最后，对系统进行了数值仿真分析。结果表明，疫情在空间上可能形成一定的振荡模式，系统存在多个正平衡点。同时，阻断机制可能在不同的斑块中导致不同类型的平衡状态，但在减少感染个体总数和系统收敛时间方面并不有效。

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引用次数: 0