Bulletin of Mathematical Biology最新文献

{"title":"Subtyping and Prediction of the Glucose Based on the Hybrid Modeling of Deep Learning and Dietary Stimulated Glucose Metabolism Dynamical Model.","authors":"Yuhao Zhou, Xianglong Liu, Shi Zhao, Yu Zhao","doi":"10.1007/s11538-026-01678-4","DOIUrl":"10.1007/s11538-026-01678-4","url":null,"abstract":"<p><p>Diabetes represents a significant global health challenge, underscoring the need for enhanced methodologies in glycemic monitoring and risk assessment. Static biomarkers, including fasting plasma glucose and glycated hemoglobin, may have limitations in capturing the temporal variations and individual heterogeneities inherent in glucose regulation. Continuous glucose monitoring (CGM) offers a high-resolution approach that may facilitate timely metabolic categorization. However, there is a notable scarcity of modeling frameworks that integrate CGM data while maintaining both interpretability and predictive accuracy. This study proposes an integrated analytical framework that amalgamates CGM data-driven classification of glucose response with a hybrid modeling approach that combines dynamical systems and deep learning methodologies for personalized glucose regulation assessments. A cohort of 44 adults was enrolled and followed up on an individual basis for 7 to 14 days, and typical daily glucose profiles were derived through dynamic time warping. K-shape clustering analysis was employed to identify significant glucose response subtypes, differentiating participants into three categories: health, prediabetes, and diabetes based on CGM-derived indicators. We subsequently developed an integrated hybrid model that synergizes a dietary stimulation glucose-insulin dynamical model with a long short-term memory residual network. This hybrid model demonstrated substantially improved accuracy, achieving a root mean square error (RMSE) of 6.61 and a coefficient of determination ( <math><msup><mi>R</mi> <mn>2</mn></msup> </math> ) of 0.91. The glucose-insulin dynamical model effectively elucidates the physiological mechanisms underlying postprandial glucose-insulin regulation. The findings of this study emphasize the utility of CGM-derived glucose phenotyping and hybrid predictive models as viable tools for individualized metabolic risk assessment. Additionally, they contribute to the early identification of dysglycemia and establish a practical framework for precision glycemic management.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148788479","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":"An Alternative Approach to Compute the Likelihood for the DAISIE (Dynamic Assembly of Island Biota Through Speciation, Immigration, and Extinction) Model.","authors":"Ornela N Dehayem, Bart Haegeman, Rampal S Etienne","doi":"10.1007/s11538-026-01714-3","DOIUrl":"10.1007/s11538-026-01714-3","url":null,"abstract":"<p><p>Understanding island biodiversity requires studying the processes driving its assembly and examining how these processes vary over time, across lineages, and across different islands. The DAISIE (Dynamic Assembly of Island biota through Speciation, Immigration, and Extinction) framework has been developed for this purpose, and has advanced our understanding of island community assembly by estimating, from phylogenetic data, the contribution of the processes of colonization, speciation and extinction to island community assembly. However, the model assumes uniform colonization and diversification rates across lineages, ignoring potential variation in these rates caused by, for example, lineage-specific traits. This assumption thus restricts the model's capacity to capture complex colonization and diversification dynamics, and may consequently bias inference of colonization and diversification dynamics on islands. An extension of the framework behind these more complex dynamics is therefore desired. However, for this state-dependent colonization and diversification extension, the current computation of the likelihood of the model given phylogenetic data is computationally prohibitive. In this study, we therefore propose an alternative approach to computing the DAISIE likelihood, under the assumption of diversity-independent colonization and diversification. Our novel approach is based on the pruning algorithm that has been used for computing the likelihood of SSE (State-dependent Speciation and Extinction) models, which traces lineage history backward in time from the present day to the root of the tree. We demonstrate that our alternative approach reproduces DAISIE's predictions under diversity-independent colonization and diversification. This provides an additional layer of support to DAISIE in diversity-independent settings, but in doing so also gives more confidence in the results under diversity-dependence. Furthermore, our alternative approach offers greater computational efficiency. Finally, it provides a flexible framework for incorporating state-dependent dynamics in colonization, speciation, and extinction processes.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13476295/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148758786","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 Dynamic Mechanism for Prevalence of Triangles in Competitive Networks.","authors":"M N Mooij, M Baudena, A S von der Heydt, L Miele, I Kryven","doi":"10.1007/s11538-026-01726-z","DOIUrl":"10.1007/s11538-026-01726-z","url":null,"abstract":"<p><p>Triangles are abundant in real-world networks but rare in standard null models for sparse graphs. Existing explanations typically rely on explicit triadic closure mechanisms or geometry-based connection rules. We propose an alternative hypothesis: the frequent appearance of triangles may arise naturally from the requirement of dynamic stability that maintains coexistence of species in Lotka-Volterra systems with equal competitive interactions. To evaluate this idea, we prove that, across all possible interaction graphs, coexistence is guaranteed whenever the coupling strength is below the reciprocal of the graph's maximum degree, and guaranteed not to occur when the coupling strength exceeds 1. This leaves a large gap that is unexplained by the graph degrees alone. We notice that the lower and upper bounds are achieved for star and complete graphs respectively and to investigate further what structural properties of the interaction graph control the critical coupling within the gap, we optimise networks algorithmically while keeping the degree sequence fixed. We find that networks supporting stronger interaction strengths consistently exhibit higher clustering coefficients in several network models. Moreover, in real-world grassland plant networks, we observe higher clustering and stronger stability than those expected from a configuration model with the same degree sequence. Our result suggests that triangles, and clustering in general, may emerge as a structural signature of stabilising competition.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13476320/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148764310","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":"Stochastic Chiral Pharmacokinetics: Dynamics with Dual Randomized Dosing Regimens.","authors":"Ze Wang, Dingding Yan, Xiaotian Wu, Jun Li","doi":"10.1007/s11538-026-01721-4","DOIUrl":"10.1007/s11538-026-01721-4","url":null,"abstract":"<p><p>Medication non-adherence is recognized as a critical determinant of therapeutic efficacy and safety. However, its specific impact on the concentration fluctuations of chiral drugs remains poorly understood. By incorporating dual stochasticity in dosing intervals and dosages, we developed a stochastic pharmacokinetic model for chiral drugs comprising bio-active and bio-inactive enantiomers under multiple intravenous bolus administrations. Utilizing characteristic functions and second-type Volterra integral equations, we derived explicit expressions for the expectation and variance of both the active moiety and total measured concentrations, as well as their discrepancy. Moreover, leveraging Kesten theorem and ergodic theory, the existence and the geometric ergodicity of the stationary probability distribution were mathematically demonstrated. Taking ibuprofen as a case study, we simulated various medication non-adherence scenarios to quantify the enantiomeric randomness. The results demonstrated that stochastic concentrations not only cause significant deviation from the ideal levels under perfect adherence, but also induce non-negligible discrepancy between the effective and total measured concentrations. These findings of the work provide a rigorous theoretical guidance for the characterization of two enantiomers variability of chiral drugs induced by medication non-adherence, offering new insights for enhancing therapeutic efficacy and safety.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148761579","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":"Correcting Structural Bias in Dynamical Models of Infectious Disease Using a Bayesian State-Space Framework.","authors":"Miracle Amadi, José Carlos García-Merino, Heikki Haario","doi":"10.1007/s11538-026-01730-3","DOIUrl":"10.1007/s11538-026-01730-3","url":null,"abstract":"<p><p>Deterministic dynamical models are widely used in infectious disease modelling, but they often become systematically biased when key drivers such as seasonality and random environmental variation are simplified or omitted. This paper proposes a practical way to account for structural bias while preserving the underlying mechanistic model. We model the observed time series as the sum of (i) a deterministic transmission component given by a reduced Ross malaria model and (ii) a latent stochastic seasonal component that captures unresolved seasonal forcing and other unmodelled variability. The seasonal component is defined as a mean-reverting stochastic differential equation with periodic forcing, which can be interpreted as a seasonally forced Ornstein-Uhlenbeck (OU) process and, at the same time, as a dynamically constrained model-discrepancy term. The combined model forms an additive Bayesian state-space system. A key challenge in additive decompositions is identifiability: many combinations of the deterministic and stochastic components can explain the same observations. We therefore use informative priors to stabilise this decomposition, together with a non-centred parameterisation (a reparameterisation that improves MCMC efficiency by sampling standardised noise terms instead of states directly) of the latent stochastic differential equation (SDE) states that enables efficient joint inference with Hamiltonian Monte Carlo (NUTS) in Stan. We validate the approach in three steps: (1) an OU example that contrasts parameter-only inference with latent state-space inference, (2) synthetic experiments that have a good agreement with the observed signal while highlighting the expected negative posterior dependence between components, and (3) an application to five years of monthly malaria case reports from Delta State, Nigeria. In the real-data analysis, the proposed additive ODE-SDE model produces a close fit with coherent uncertainty quantification and a flexible seasonal reconstruction, while keeping the mechanistic transmission model interpretable. Overall, the framework provides a flexible and transferable method for accounting for structural model discrepancy in misspecified dynamical models using a structured stochastic discrepancy.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13461677/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148705404","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":"Approaches for Assessing Parameter Identifiability in Mathematical Biology.","authors":"Matthew J Simpson, Ruth E Baker","doi":"10.1007/s11538-026-01725-0","DOIUrl":"10.1007/s11538-026-01725-0","url":null,"abstract":"","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148700652","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":"Dynamics of Two Species with Density-Dependent Interactions and Application to Mutualism.","authors":"Chloë Mian, Sylvain Billiard, Violaine Llaurens, Charline Smadi","doi":"10.1007/s11538-026-01724-1","DOIUrl":"10.1007/s11538-026-01724-1","url":null,"abstract":"<p><p>Ecological interactions shape the dynamics of natural populations in the wild. Density-dependent processes are widespread and may change the respective effects of populations on one another, for instance by shifting interactions from mutualistic to parasitic relationships. Here, we develop a general deterministic model of two interacting populations, assuming density-dependent costs and benefits for the interacting individuals within and between species. This framework aims at generalizing pre-existing population dynamics models involving competition, predation, mutualism and parasitism, by allowing ecological interactions to transition when the respective densities of interacting species change. Through ordinary differential equations and phase portrait analysis, we derive general principles governing these systems, identifying constraints on the organization of equilibria and sufficient conditions for the emergence of certain dynamic behaviors. In particular, we show that equilibrium indices alternate along isoclines under broad geometric assumptions, and that limit cycles can arise when interactions include mutualistic and parasitic phases, while they cannot be generated locally in strictly mutualistic regions where the relevant interaction signs remain fixed. This framework provides a general approach for characterizing the population dynamics of interacting species and highlights the effect of the density dependent transitions in ecological interactions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696962","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":"Coupled Information-Infection Dynamics Produce Information-Driven Shifts in Epidemic Regimes via Competing Vaccine Narratives.","authors":"Asma Azizi, Caner Kazanci, Xiaohui Guo","doi":"10.1007/s11538-026-01719-y","DOIUrl":"10.1007/s11538-026-01719-y","url":null,"abstract":"<p><p>Vaccine-related communication can be harnessed to curb infection; yet, in practice, it often undermines vaccine uptake and sustains transmission even when effective vaccines are available. Our goal is to understand how vaccine information dynamics may shape infection spread within a coupled information-infection modeling framework. We present a coupled information-infection modeling framework that links a standard SVIRS infection-spread model with an integrate-and-fire-inspired information-dissemination model. Vaccine-positive and vaccine-critical active groups disseminate competing information that shapes non-active/hesitant individuals' vaccine attitudes through direct peer influence, threshold-based acceptance, and persistence of engagement, while infection prevalence can feed back by amplifying caution. The evolving vaccine attitudes modulate vaccination uptake, and the model tracks the joint evolution of information dynamics and epidemic trajectories. Our analysis shows that, under the assumed coupling, information dynamics can shift the system among qualitatively distinct infection outcomes. In particular, reducing resistance to vaccine-positive information and sustaining vaccine-positive engagement can move the system toward lower-endemic regimes more reliably than changes focused only on weakening vaccine-critical engagement, for the parameter ranges considered here. These findings highlight the potential importance of information dynamics in epidemic modeling and suggest that sustained vaccine-positive engagement can be an important qualitative mechanism for reducing long-term infection burden.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696947","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 of HDV RNA, HBV DNA, and HBsAg Dynamics During Lonafarnib-Based Therapy: Insights from the LOWR HDV-1 Study.","authors":"Adquate Mhlanga, Louis Shekhtman, Rami Zakh, Sarah Duehren, Ashish Goyal, Alexander Churkin, Vladimir Reinharz, Danny Barash, Jeffrey Glenn, Ohad Etzion, Scott J Cotler, Cihan Yurdaydin, Harel Dahari","doi":"10.1007/s11538-026-01717-0","DOIUrl":"10.1007/s11538-026-01717-0","url":null,"abstract":"<p><p>Lonafarnib (LNF) is an investigational drug targeting hepatitis delta virus (HDV) but not hepatitis B virus (HBV), providing a unique opportunity to model HDV kinetics and how changes in HDV affect HBV. We performed a detailed kinetic analysis and developed a mathematical model to explain serum HBV DNA, HDV RNA and hepatitis B surface antigen (HBsAg) kinetics in 15 HBV/HDV coinfected patients receiving LNF-based treatment. After a delay of 0-2 days, patients experienced a rapid 1st-phase HDV-decline followed by either a viral plateau, 2nd slower-decline phase, or viral breakthrough (VB). LNF monotherapy led to a flat-partial-response (often followed by VB), while LNF combination therapy with ritonavir or pegylated interferon-α (PEG-IFN <math><mi>α</mi></math> ) was associated with a biphasic HDV decline (without VB). All treatments except LNF + PEG-IFN <math><mi>α</mi></math> had at least one patient experiencing an increase in HBV on-treatment. Our model successfully reproduced the observed HDV and HBV kinetics. We estimated an HDV RNA half-life of 1.26 days [95% confidence interval, CI 1.05-1.47] in serum and treatment efficacy of 94% in inhibiting HDV RNA production across all treatments [95% CI 89-97%], as reflected by the 1st phase HDV decline. The 2nd phase of HDV decline was explained by a time-dependent increase in efficacy, reaching a maximum of 98.9%. The model explained the increase in serum HBV DNA by a median four-fold [interquartile range, IQR: 1-28] increase in HBV DNA production rate when HDV declined below an inhibitory threshold. The stability of serum HBsAg was explained by a constant number of HBsAg-producing cells.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148677469","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":"Fisher Information Limits on Genetic Stability, Diversity, and Regulation.","authors":"J S Glasenapp, R A Gatenby","doi":"10.1007/s11538-026-01720-5","DOIUrl":"10.1007/s11538-026-01720-5","url":null,"abstract":"<p><p>Life and evolution require precise yet imperfect transmission of genetic information across generations. Accurate transmission maintains the genetic blueprint for phenotypes that succeed in current conditions, while some transmission error is necessary to generate heritable diversity that can further increase fitness and hedge against future environmental change. This background noise, however, risks excessive mutation accumulation that degrades fitness (\"Muller's ratchet\") or even destroys genetic information beyond recovery (\"error catastrophe\"). Across the history of life these competing pressures resolve into two regimes: during environmental fluctuation, a higher mutation rate aids survival; during prolonged stability, populations converge toward an evolutionarily stable state (ESS) in which mutations can only reduce fitness. We model this tension with a Fisher Information framework in which genetic inheritance is a noisy two-state channel. The nontrivial eigenvalue of the channel's symmetric circulant transition operator governs the decay of allelic contrast across generations; selection modifies this eigenvalue by suppressing the channel's switching (mutation) probability, acting as an anti-depolarizing force. We show this compensation is bounded: an instability boundary at <math><mrow><mi>p</mi> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>9</mn></mrow> </math> marks the point beyond which selection can no longer maintain informational stability - a boundary that coincides with the loss of quantum coherence in the formally equivalent depolarizing channel and with thermodynamic fine-graining failure, suggesting that genetic stability, regulatory fidelity, and structural order share a common information-geometric limit. We apply this framework to cancer, framing carcinogenesis as an informational transition: a shift from host-regulated, high-fidelity transmission that maintains tissue homeostasis to a regime in which cells retain only the genetic and epigenetic changes that maximize their own proliferation - including loss of functions that serve the host and gain of functions that improve competition for space and nutrients and evasion of the predator-like immune response. Because cancer cells operate farther from this information-geometric limit than the normal cells around them, we propose that they may pursue an informational \"niche construction\" strategy: producing a mutagenic, acidic, hypoxic microenvironment that pushes neighboring host cells past the same collapse boundary, driving loss of function (e.g., \"T cell exhaustion\") in infiltrating immune cells. We present empirical support for this framework together with specific, experimentally testable predictions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13442614/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148677442","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}