Journal of Mathematical Biology最新文献

{"title":"Modelling the effects of biological intervention in a dynamical gene network.","authors":"Nicolas Champagnat, Rodolphe Loubaton, Laurent Vallat, Pierre Vallois","doi":"10.1007/s00285-026-02458-3","DOIUrl":"https://doi.org/10.1007/s00285-026-02458-3","url":null,"abstract":"<p><p>Cellular response to environmental and internal signals can be modeled by dynamical gene regulatory networks (GRN). In the literature, three main classes of gene network models can be distinguished: (1) non-quantitative (or data-based) models which do not describe the probability distribution of gene expressions; (2) quantitative models which fully describe the probability distribution of all genes co-expression; and (3) mechanistic models which allow for a causal interpretation of gene interactions. We propose two rigorous frameworks to model gene alteration in a dynamical GRN, depending on whether the network model is quantitative or mechanistic. We explain how these models can be used for design of experiment, or, if additional alteration data are available, for validation purposes or to improve the parameter estimation of the original model. We apply these methods to the Gaussian graphical model, which is quantitative but non-mechanistic, and to mechanistic models of Bayesian networks and penalized linear regression.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148876774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hybrid mathematical framework for morphogenesis and regeneration.","authors":"Yuriria Cortés-Poza","doi":"10.1007/s00285-026-02459-2","DOIUrl":"10.1007/s00285-026-02459-2","url":null,"abstract":"<p><p>We introduce a hybrid mathematical framework for morphogenesis and regeneration motivated by bioelectric phenomena documented in highly regenerative organisms, particularly planaria. The model couples four dynamical layers on a discrete cellular network: (i) a bistable bioelectric layer, in which each cell admits stable hyperpolarized and depolarized equilibria connected through gap-junction currents; (ii) a synthetic intracellular gene regulatory network (GRN) with proliferation, differentiation, positional-identity, and regenerative-response modules; (iii) adaptive gap-junction conductances that evolve in response to electrical state, regenerative activity, and tissue identity; and (iv) a slow tissue-memory variable representing persistent cellular commitment at an epigenetic timescale. Damage is represented by a propagating wound signal on the cellular graph. The central conceptual departure from classical models is that target morphology is not prescribed externally but emerges as an attractor of the coupled multiscale dynamics, in the spirit of distributed attractor-based memory. The framework is designed to capture anatomical homeostasis, regeneration after lesion, attractor switching induced by transient electrical perturbations, regenerative thresholds, and axial polarity. The paper establishes three analytical results for reduced subsystems: single-cell bistability, absence of a Turing instability in the reduced bioelectric-regulatory subsystem, and Lyapunov descent for the pure bioelectric layer. These are complemented by a set of open mathematical questions and numerical experiments that investigate pattern nucleation, regeneration robustness, polarity reversal, and adaptive energy-landscape reshaping in the full multiscale model.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13529881/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148867439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evolution of cooperation on graphs with degree-dependent inertia.","authors":"Nan Jiang, Xiaomeng Li, Qinghua Chen, Boyu Zhang","doi":"10.1007/s00285-026-02453-8","DOIUrl":"https://doi.org/10.1007/s00285-026-02453-8","url":null,"abstract":"<p><p>Cooperation is fundamental to biological and social systems, yet its evolutionary success depends critically on population structure. In reality, individuals often exhibit inertia, retaining current behaviors even when imitation is beneficial. The synergistic effects between heterogeneous inertia and network structure have been explored primarily through numerical simulations. In this work, we develop a mathematical framework incorporating degree-dependent inertia, wherein the tendency to maintain one's strategy is determined by node degree, and self-loops are permitted, and self-loops are permitted. Using a coalescent-theoretic approach, we derive the threshold benefit-to-cost ratio favoring cooperation in the donation game on arbitrary graphs in the weak-selection limit. Compared with the no-inertia, uniform-inertia, and inverse degree-dependent inertia cases, positive degree-dependent inertia markedly reduces this critical threshold in disassortative networks. An analytical expression for multi-star networks further reveals that, architectures with fewer hubs and more leaves promote cooperation most effectively. While prior studies emphasize that slower updating by high-degree nodes and faster updating by low-degree nodes can foster cooperation, we propose a refined perspective: cooperation is especially favored when high-degree nodes update slowly and their neighbors are predominantly low-degree individuals. This alignment of inertia and neighborhood composition provides a mechanistic explanation for the emergence of cooperation in structured populations.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148851888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large deviations of piecewise-deterministic Markov processes with application to stochastic calcium waves.","authors":"Gaetan Barbet, James MacLaurin, Moshe Silverstein, Pedro Vilanova","doi":"10.1007/s00285-026-02446-7","DOIUrl":"10.1007/s00285-026-02446-7","url":null,"abstract":"<p><p>We prove a large deviation principle for piecewise deterministic Markov processes (PDMPs). This is an asymptotic estimate for the probability of a trajectory in the large size limit. Explicit Euler-Lagrange equations are determined for computing optimal first-hitting-time trajectories. The results are applied to a model of stochastic calcium dynamics. It is widely conjectured that the mechanism of calcium puff generation is a multiscale process: with microscopic stochastic fluctuations in the opening and closing of individual channels generating cell-wide waves via the diffusion of calcium and other signaling molecules. We model this system as a PDMP, with <math><mrow><mi>N</mi> <mo>≫</mo> <mn>1</mn></mrow> </math> stochastic calcium channels that are coupled via the ambient calcium concentration. We employ the large deviations theory to estimate the probability of cell-wide calcium waves being produced through microscopic stochasticity.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13525034/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148851904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction to: Transient tumor-induced disruption of peristaltic flow: a magnetohydrodynamic modeling framework.","authors":"Ashvani Kumar, Dharmendra Tripathi, Anuj Mubayi, V K Narla","doi":"10.1007/s00285-026-02456-5","DOIUrl":"https://doi.org/10.1007/s00285-026-02456-5","url":null,"abstract":"","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148820063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the stability of discrete reaction-diffusion systems of networked dynamical systems.","authors":"Dinesh Kumar","doi":"10.1007/s00285-026-02454-7","DOIUrl":"https://doi.org/10.1007/s00285-026-02454-7","url":null,"abstract":"<p><p>We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly accommodates heterogeneous local dynamics-patches at different nodes governed by structurally distinct functional forms-a setting not covered by the classical bookkeeping reduction of J Jansen and Lloyd (2000), which requires identical patch dynamics, nor by the Master Stability Function of Pecora and Carroll (1998), which is restricted to identical nodes. The stability condition separates cleanly into two independent components: (i) a diagonal dominance criterion on the spatially averaged Jacobian of the local patch dynamics, verifiable directly from model parameters without computing eigenvalues of the full composite system; and (ii) a lower bound on the algebraic connectivity (Fiedler value) of the network Laplacian, capturing the role of network topology. The resulting sufficient condition holds for purely conservative dispersal (standard graph Laplacians with zero row sums) and does not require any dispersal loss or mortality during transit-a restrictive assumption appearing in the author's prior work (Kumar et al. 2021) and many classical multi-patch analyses. The theory is illustrated through metapopulation networks of predator-prey systems with heterogeneous functional responses, including a striking example in which individually unstable patches are stabilized entirely by dispersal connections.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Disease extinction in finite time for a continuous-time SIRS model.","authors":"Abderrahman Iggidr, Mohamed Ouzahra, Gauthier Sallet","doi":"10.1007/s00285-026-02457-4","DOIUrl":"https://doi.org/10.1007/s00285-026-02457-4","url":null,"abstract":"<p><p>This paper addresses the problem of controlling the spread of an epidemic through a multiplicatively controlled SIRS model, in which the control input modulates the infection rate in a bilinear manner. Classical approaches based on asymptotic stability only guarantee disease eradication as time tends to infinity, which may be inadequate for timely and effective intervention. To overcome this limitation, we investigate the finite-time behavior of the infected population, ensuring its convergence to zero either in finite time (FTS) or within a fixed time independent of the initial conditions (FxTS). Moreover, through an appropriate choice of the control gain, this convergence time can be arbitrarily prescribed, leading to prescribed-time stability (PrTS). We propose explicit feedback control laws under which the infected population vanishes in finite, fixed, or prescribed time, while the susceptible and recovered populations converge exponentially to their equilibrium values as time tends to infinity. Numerical simulations are provided to validate the theoretical results, illustrating rapid disease eradication and global system stability. These findings demonstrate the effectiveness of finite, fixed, and prescribed-time control strategies for controlled epidemic models and offer practical guidelines for the design of responsive and robust public health interventions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modeling for a primitive form of habituation in an amoeba.","authors":"Kota Nishi, Atsushi Tero, Yukinori Nishigami, Toshiyuki Nakagaki","doi":"10.1007/s00285-026-02438-7","DOIUrl":"https://doi.org/10.1007/s00285-026-02438-7","url":null,"abstract":"<p><p>Learning abilities, once thought to be unique to higher animals, have been reported to exist in their primitive form in single-celled organisms. This has triggered a growing interest in carefully examining the nature and mechanisms of the primitive versions of learning abilities, which would provide important clues for understanding the evolution of behavioral capabilities in organisms. In this study, we focused on previous experimental studies showing that the slime mold Physarum polycephalum, a model organism for studying protist behavior, exhibits the ability to adapt to chemical environments. We propose a possible dynamic mechanism underlying this habituation, reproducing reported experimental observations with accuracy. By refining a mathematical model that was as simple as possible and based on non-specific biochemical processes within cells, we clarified a plausible mechanistic framework. Based on these results, we examined the similarities and differences between this framework and previously proposed habituation models of single-cell movement and animal neural-circuit regulation. These findings are significant because they open new avenues for research into the generality and evolutionary origins of acclimation learning.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13481565/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148801026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Positive equilibria in mass action networks: geometry and bounds.","authors":"Murad Banaji, Elisenda Feliu","doi":"10.1007/s00285-026-02429-8","DOIUrl":"https://doi.org/10.1007/s00285-026-02429-8","url":null,"abstract":"<p><p>Any mass action network gives rise to a parameterised family of polynomial equations whose positive solutions are the positive equilibria of the network. Here, we consider alternative systems of equations, whose solutions are in smooth, one-to-one correspondence with positive equilibria of the network, and capture degeneracy or nondegeneracy of the corresponding equilibria. The construction leads us to consider partitions of networks in a natural sense, and we explore the implications of choosing different partitions. The alternative systems are in some situations simpler than the original mass action equations, which allows us to rapidly identify various algebraic and geometric properties of the positive equilibrium set. This includes the characterisation of toricity and local toricity, bounds on the number of positive nondegenerate equilibria on stoichiometric classes, semialgebraic descriptions of the parameter regions for multistationarity, and the study of bifurcations. After discussing the construction of the alternative systems, various consequences for particular classes of networks and numerous examples are presented. We also develop additional techniques specifically for quadratic networks, the most common class of networks in applications, and use these techniques to derive strengthened results for quadratic networks.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13481394/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The effect of treatment-induced resistance in a two-strain tuberculosis model with age structure and spatial diffusion.","authors":"Shengyu Huang, Hongyong Zhao","doi":"10.1007/s00285-026-02449-4","DOIUrl":"https://doi.org/10.1007/s00285-026-02449-4","url":null,"abstract":"<p><p>Tuberculosis (TB) is a highly contagious chronic infectious disease that, without timely intervention, can lead to severe health consequences or even death. Improper or incomplete treatment often induces the emergence of drug-resistant TB (DR-TB), which greatly complicates disease management and intensifies its public health burden. This paper develops and analyzes a two-strain TB transmission model incorporating age structure during latency, spatial diffusion, and a treatment-induced resistance pathway. Methodologically, we establish the global existence and non-negativity of model solutions and derive explicit expressions for the basic reproduction numbers of the sensitive and resistant strains, as well as for the reproduction number associated with treatment-induced resistance. This study then extends the persistence proof method for single-strain space-age structured models to examine the dynamics of competitive exclusion and persistence between the two strains. Subsequently, we characterize the local and global stability of equilibria using spectral analysis and Lyapunov function methods. Calibrating the model with WHO data for China, we estimate that the basic reproduction number for the sensitive strain exceeds one, and owing to the presence of a treatment-induced resistance pathway, the basic reproduction number for the resistant strain displays two distinct distributions, both of which remain below one. Despite this, theoretical and numerical results demonstrate that DR-TB can persist even when its basic reproduction number is less than one or even zero. Furthermore, our projections indicate that, given the current level of TB control, China is unlikely to achieve the WHO's 2035 incidence reduction target. Despite this, significant improvement in treatment efficacy and reduction of resistance induction risk could make the goal attainable. Moreover, under comparable conditions, the elimination target appears relatively easier to achieve for DR-TB. Our findings suggest that in the absence of treatment-induced resistance, the WHO's DR-TB elimination goal could be reached approximately 2 years earlier. Notably, early increases in DR-TB cases due to improved treatment should be anticipated, underscoring that TB control efforts must not only target existing DR-TB cases but also ensure standardized treatment for drug-sensitive TB (DS-TB) infections; otherwise, treatment-induced resistance in patients will further increase the TB burden.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148708364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}