Journal of Mathematical Biology最新文献

{"title":"Modeling parasite clearance and transmission delays in American Cutaneous Leishmaniasis transmission dynamics.","authors":"Sharmin Sultana, Gilberto Gonzalez-Parra, Luis Fernando Chaves","doi":"10.1007/s00285-026-02460-9","DOIUrl":"10.1007/s00285-026-02460-9","url":null,"abstract":"<p><p>American Cutaneous Leishmaniasis (ACL) is a multi-host vector-borne disease with complex transmission dynamics involving sand fly vectors, reservoirs, and incidental hosts. In this study, we develop and analyze two delay differential equation (DDE) models to explore the role of biological time delays in ACL transmission dynamics. The first model incorporates a delay in the parasite clearance term of the incidental host, reflecting the minimum parasite clearance time between infection and recovery. The second model introduces a delay that represents delays in skin lesion development following exposure to infective sand fly bites. For both models, we derived the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> and performed an elasticity analysis which revealed that vector-reservoir transmission and vector mortality are key drivers of outbreak potential. For both models we studied the stability of the disease-free and endemic equilibria. Using linearization, we identified critical delay thresholds that generate Hopf bifurcations. We show that time delays can destabilize the endemic equilibrium and induce periodic oscillations. Despite having the same <math><msub><mi>R</mi> <mn>0</mn></msub> </math> , the two models exhibit distinct qualitative behaviors due to differences in the delay structure. Simulations support the analytical findings, illustrating how increasing delays can lead to oscillations in transmission. These findings highlight the importance of incorporating biologically inspired delays when modeling ACL transmission.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13588845/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149002674","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":"An analytical stochastic stage-structured model for pest population dynamics: a case study on Cydia pomonella in Italy.","authors":"Berk Tan Perçin, Serena Baiocco, Federico Cavina, Gianfranco Pradolesi, Sara Pasquali","doi":"10.1007/s00285-026-02461-8","DOIUrl":"10.1007/s00285-026-02461-8","url":null,"abstract":"<p><p>In this work, we propose a novel phenological model to describe population dynamics based on a compound Poisson process driven development. The model offers an alternative to other well-established approaches founded on systems of ordinary or partial differential equations, in which, the stochasticity is driven by the Brownian motion. A key advantage of the proposed framework is that it prevents the age regression of individuals and allows for the analytical derivation of the number of individuals in each developmental stage into which the population is structured. The model is applied to Cydia pomonella, a major pest of pome fruit crops. The results obtained are highly promising and suggest that this approach constitutes a valuable alternative to traditional models based on partial differential equations for simulating the population dynamics.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13582155/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148983820","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":"A Fokker-Planck framework for control of epidemics.","authors":"Christian Parkinson, Souvik Roy","doi":"10.1007/s00285-026-02462-7","DOIUrl":"10.1007/s00285-026-02462-7","url":null,"abstract":"<p><p>We present a control framework for stochastic compartmental models in epidemiology. In this framework, rather than directly controlling the stochastic system, we perform optimal control of an associated Fokker-Planck equation, with the goal of steering the distribution of possible solutions of the stochastic system to some desirable state. In particular, this allows for robust control mechanism with uncertainty not only in the dynamics, but also in the initial data. We formulate and fully analyze a partial differential equation constrained optimization problem, including a proof of existence of optimal controls via analysis of the control-to-state map, and a characterization of optimal controls via the Pontryagin minimum principle. We describe the application of the sequential quadratic Hamiltonian method to our problem, which provides numerical approximations of optimal control maps. We demonstrate our method using a minimal stochastic susceptible-infected-recovered model with different choices of cost functionals that represent different policy-maker concerns.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13582153/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148983553","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":"To trace or not to trace: analytical insights from network-based contact-tracing models.","authors":"Giulia de Meijere, Andrea Pugliese, Gerardo Iñiguez, Péter L Simon, István Z Kiss","doi":"10.1007/s00285-026-02455-6","DOIUrl":"10.1007/s00285-026-02455-6","url":null,"abstract":"<p><p>Contact tracing is one of the most important control measures deployed during epidemics and pandemics, relying on the identification of contacts of known infected individuals. A network perspective is therefore essential for its accurate modelling. Pairwise models have been used extensively to study contact tracing, but their analysis typically depends on a decoupling assumption-most commonly that contact tracing operates on a much faster timescale than disease transmission. Furthermore, contact tracing models often assume that each infected individual becomes a contact tracing-triggering node, which is unrealistic given partial compliance to treatment in practice. In this paper, we relax both of these restrictive assumptions and provide a full analytical characterisation of the epidemic threshold in the pairwise mean-field model. Our analysis uses a fast-variables approach that captures the rapid early stabilisation of key network quantities. In addition, inspired by mechanisms from social adoption dynamics, we introduce triplewise contact tracing in which an infected individual can be traced not only through direct contact with a single tracing-triggering neighbor (pairwise tracing), but also indirectly when connected to two tracing-triggering nodes simultaneously. For pure pairwise and pure triplewise contact tracing, we derive analytical expressions for critical contact tracing thresholds and demonstrate that when many infected individuals bypass treatment, the epidemic can become uncontrollable. When both contact tracing mechanisms operate together, we map out their combined contribution and relative impact on epidemic control. This unified framework yields rigorous and tractable threshold conditions for contact tracing dynamics on networks, extending the applicability of pairwise models beyond the fast-tracing regime and providing new insight into the interplay between disease progression, partial treatment compliance, and higher-order tracing processes.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13547156/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148901433","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":"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":"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":"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":"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":"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}