Bulletin of Mathematical Biology最新文献

{"title":"When Strain Meets Stress: Threshold Dynamics and Regime Shifts in Wolbachia-Based Mosquito Population Replacement.","authors":"Suddhyashil Sarkar, Ayan Paul, Joydeb Bhattacharyya","doi":"10.1007/s11538-026-01716-1","DOIUrl":"10.1007/s11538-026-01716-1","url":null,"abstract":"<p><p>Wolbachia-based mosquito population replacement is a promising biocontrol strategy to reduce arboviral disease transmission by introducing Wolbachia-infected mosquitoes into wild populations. The success of this approach depends on the strain-specific characteristics of the Wolbachia symbiont and the mosquito host. This study presents a mathematical modelling framework to evaluate how Wolbachia strains and mosquito hosts influence the success of population replacement. The model incorporates key biological factors, including incomplete cytoplasmic incompatibility (CI), imperfect maternal transmission (MT), fitness costs, immigration, and potential loss of Wolbachia from mosquitoes. Analytical and numerical simulations demonstrate that strain-specific differences significantly impact the establishment, spread, and long-term persistence of Wolbachia in mosquito populations. Results indicate that high CI and MT levels, combined with low fitness costs and minimal immigration, facilitate successful Wolbachia establishment. To account for environmental stress, the model is extended to a stochastic framework incorporating environmental noise. Analysis reveals that stochasticity can shift invasion thresholds, destabilize equilibria, and induce noise-driven transitions between coexistence states. Numerical simulations show that low noise levels allow deterministic thresholds to remain predictive, whereas stronger fluctuations can undermine replacement success despite favourable deterministic conditions. A stochastic optimal control formulation further indicates that higher and more prolonged releases are necessary in noisy environments to ensure replacement. Collectively, these findings highlight how both strain traits and environmental stress shape the deterministic and stochastic thresholds governing the success of Wolbachia-based mosquito population replacement.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148618151","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":"Assessing the Role of Model Complexity in Virtual Clinical Trial Outcomes.","authors":"Jana L Gevertz, Joanna R Wares","doi":"10.1007/s11538-026-01715-2","DOIUrl":"10.1007/s11538-026-01715-2","url":null,"abstract":"<p><p>Virtual clinical trials (VCTs) hold significant promise for improving the drug development process, yet their predictive reliability depends critically on design decisions that remain poorly understood. This study examines how model complexity influences VCT outcomes, as well as how the choice of prior parameter distributions and virtual patient inclusion criteria affects those outcomes. Using oncolytic virotherapy treatment of murine tumors as a case study, we compared a relative hierarchy of three mathematical models of increasing complexity under different parameter priors (uniform and normal distributions) and two inclusion methods (accept-or-reject and accept-or-perturb). Our results demonstrate that the simplest model produces a plausible population that inadequately spans the feasible trajectory space, potentially missing critical inter-patient heterogeneity. However, we found diminishing returns beyond intermediate model complexity, as both the intermediate and complex models captured similar ranges of patient responses across dosing protocols. Notably, the accept-or-reject method generated posterior parameter distributions that are more likely to resemble the chosen prior, possibly overly reducing inter-patient variability in treatment responses, particularly at high doses. In contrast, the accept-or-perturb inclusion criteria produced more robust results that were less sensitive to prior assumptions. These findings suggest that VCT design should prioritize models with sufficient biological detail to capture key mechanisms without unnecessary complexity, paired with inclusion criteria that avoid over-constraining plausible populations to match potentially unrealistic prior assumptions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148618065","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 Systemic Sclerosis and Its Treatment.","authors":"Teddy Lazebnik, Avner Friedman","doi":"10.1007/s11538-026-01700-9","DOIUrl":"10.1007/s11538-026-01700-9","url":null,"abstract":"<p><p>Systemic sclerosis (SSc) is an autoimmune disease marked by excessive extracellular matrix (ECM) deposited by myofibroblasts. The disease carries the risk of pathologically progressing to internal organs, particularly the lung. Since abnormally large densities of myofibroblasts are associated with SSc, clinical studies consider trials that reduce the density of myofibroblasts: imatinib treatment ( <math><mi>N</mi></math> ), which promotes apoptosis in myofibroblasts, and SSc by fresolimumab ( <math><mi>S</mi></math> ), which inhibits TGF- <math><mi>β</mi></math> , a key growth factor of myofibroblasts. In this paper, we develop a mathematical model of SSc by a system of partial differential equations, and use it to explore a range of treatment strategies with <math><mi>N</mi></math> and <math><mi>S</mi></math> . For example, we considered administering <math><mi>S</mi></math> in fractions three weeks apart. In this case, we determined the smallest amount of <math><mi>S</mi></math> such that <math><mrow><mi>ρ</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo></mrow> </math> , the density of the ECM at time <math><mi>t</mi></math> , will continuously and oscillatingly decrease from a disease level <math><mrow><mn>2</mn> <msup><mi>ρ</mi> <mn>0</mn></msup> </mrow> </math> , where <math><msup><mi>ρ</mi> <mn>0</mn></msup> </math> is the density <math><mi>ρ</mi></math> in health. Since SSc has no cure, <math><mrow><mi>ρ</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo></mrow> </math> cannot decrease below <math><msup><mi>ρ</mi> <mn>0</mn></msup> </math> . We found that with the smallest amount of <math><mi>S</mi></math> , <math><mrow><mi>ρ</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo></mrow> </math> decreases over a few months to <math><mrow><mn>1.19</mn> <msup><mi>ρ</mi> <mn>0</mn></msup> </mrow> </math> and remains nearly stable thereafter. The results of the paper could be useful in the design of future clinical trials aimed to decrease the excessive extracellular matrix in SSc patients.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13415493/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148599405","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":"Multiscale Analysis of a Kinetic Equation for Mechanotaxis.","authors":"Benoît Perthame, Francesco Salvarani, Shugo Yasuda","doi":"10.1007/s11538-026-01710-7","DOIUrl":"10.1007/s11538-026-01710-7","url":null,"abstract":"<p><p>We present a new kinetic equation for cell migration driven by mechanical interactions with the substrate, an effect not previously captured in kinetic models, and essential for explaining observed collective behaviors such as those in bacterial colonies. The model introduces an acceleration term that accounts for the dynamics of motile cells undergoing mechanotaxis, where extracellular signals modulate the forces arising from cell-substrate interactions. From this formulation, we derive a family of macroscopic limit equations and analyze their principal properties. In particular, we examine linear stability and pattern formation ability through theoretical analysis, supported by numerical simulations.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148577240","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 Graph-Theoretical Framework for Automated Computation of Reproduction Numbers in Deterministic Epidemiological Models.","authors":"Alexandre Simard, Jacques Bélair","doi":"10.1007/s11538-026-01705-4","DOIUrl":"10.1007/s11538-026-01705-4","url":null,"abstract":"<p><p>We introduce a graph-theoretical approach to epidemiological modeling that automates the derivation of the differential equations associated with a model and the computation of its base and real-time reproduction numbers. Our framework defines a novel structure called \"epidemiological hypergraphs\", graphs extended with epidemiological characteristics in order to automatize their analysis. The main focus of this article is to index a few individuals of interest and explicitly track their secondary infections, emulating the granularity of agent-based models. This structure also removes the need for model-specific analysis, improving reproducibility and enhancing accessibility for epidemiologists. We validate consistency with the next-generation matrix approach for the base reproduction number while demonstrating superior analytical accuracy over the classical estimate <math> <mrow><msub><mi>R</mi> <mi>t</mi></msub> <mo>=</mo> <mi>S</mi> <mo>/</mo> <mi>N</mi> <mo>·</mo> <msub><mi>R</mi> <mn>0</mn></msub> </mrow> </math> for the real-time reproduction number, especially in scenarios where parameters evolve in time or when variants are introduced. Our approach offers an adaptive mathematical framework for real-time epidemic tracking and intervention planning.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148577184","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 Modelling of the Mitochondrial Dicarboxylate Carrier (SLC25A10).","authors":"Ramin Nashebi, Yingying Lyu, Elías Vera-Sigüenza, Daniel A Tennant, Fabian Spill","doi":"10.1007/s11538-026-01709-0","DOIUrl":"10.1007/s11538-026-01709-0","url":null,"abstract":"<p><p>The mitochondrial dicarboxylate carrier SLC25A10 mediates reversible exchange among succinate, malate, and phosphate, contributing to mitochondrial metabolic regulation. Structural studies establish a ping-pong mechanism, but most mathematical models still assume sequential binding, lacking mechanistic justification and overlooking the alternation of a single binding site. Here, we present the first mechanistically derived and thermodynamically consistent model of SLC25A10 based on a ping-pong framework. The model incorporates competitive binding of succinate, malate, and phosphate, heteroexchange, reversibility, and electroneutrality, and is calibrated using experimental datasets from intact mitochondria and reconstituted proteoliposomes. To estimate kinetic parameters and quantify their uncertainty, we employed Bayesian inference, enabling statistically rigorous calibration to uptake and competition assays. The model introduces new terms that quantify which substrate and from which side of the membrane is most likely to start the transport cycle. Beyond reproducing experimentally observed exchange kinetics, the model resolves non-equilibrium transport dynamics that are difficult to access directly in classical uptake assays. In particular, the simulations reveal a two-phase response in which an initial phosphate-driven high-flux uptake regime for malate and succinate is followed by a slower redistribution phase in which the two dicarboxylates continue to readjust primarily against each other. The model also predicts that mitochondrial morphology modulates early transport behaviour, with matrix swelling increasing and matrix condensation decreasing the initial SLC25A10 flux magnitude. More broadly, the framework provides a quantitative basis for studying how substrate competition, thermodynamic driving forces, and compartment geometry shape SLC25A10-mediated exchange, and it offers a transferable modelling strategy for other carriers in the SLC25 family.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13395837/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148577189","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":"Who wins? Analysis and Simulation of a Batch Culture Model of Bacterial Competition in the Presence of Plasmids.","authors":"Ana C Mendez, Fawaz K Alalhareth, LeNaiya Kydd, Maryann E Hohn, Ami Radunskaya, Justyn Jaworski, Hristo V Kojouharov","doi":"10.1007/s11538-026-01708-1","DOIUrl":"10.1007/s11538-026-01708-1","url":null,"abstract":"<p><p>Bacteria are essential in research and commercial processes for producing DNA, proteins, and converting raw materials into high-value molecules, often using batch culture systems. These systems provide controlled conditions for bacterial growth, which is influenced by factors like temperature, oxygen, and nutrients. This study introduces a mathematical model of plasmid dynamics, including loss, uptake, and transfer by conjugation, within batch cultures. The model helps optimize E. coli cultures for product formation and predict plasmid-carrying bacteria levels, offering insights into plasmid dynamics in \"one-pot\" systems. Our findings show that plasmid retention is influenced by selection pressures which can be an important consideration in probiotic dosing regimens. The model aligns with experimental data and highlights the importance of understanding plasmid dynamics for controlling bacterial growth processes, with implications for research, commercial applications, and gut microbiome stability. Future work will explore temporal changes in plasmid dynamics, requiring advanced instrumentation for precise bacterial population quantification.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13391673/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148547922","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":"Spatial Establishment of Autotetraploid Populations Follows the Propagation of Bistable Waves of Advance.","authors":"Felipe Kauai","doi":"10.1007/s11538-026-01707-2","DOIUrl":"10.1007/s11538-026-01707-2","url":null,"abstract":"<p><p>The establishment of polyploid populations is constrained by minority cytotype exclusion, whereby newly formed polyploids are lost when rare in predominantly diploid populations. Here, we consider this problem through a continuous-time approximation of a discrete model of tetraploid establishment. The spatio-temporal dynamics of sexually reproducing mixed-ploidy populations is then formally investigated using a reaction-diffusion framework, which allows us to determine the conditions for spatial invasion of tetraploids. We first study the local dynamics of gamete frequencies in populations composed of diploid, triploid, and tetraploid cytotypes, where <math><mi>υ</mi></math> denotes the per-generation proportion of unreduced (diploid) gametes and <math><mi>ϕ</mi></math> denotes the relative viable-gamete contribution of triploid cytotypes. The conjugacy between models of cytotype and gamete frequency dynamics is formally established. Then, we show that the system admits a bistable structure and characterize its equilibria. In one spatial dimension, the continuous-time approximation yields a closed-form traveling-wave solution and a wave speed that scales with the standard deviation of distances between mother and offspring birth locations, <math><mi>σ</mi></math> . Extending the analysis to radially symmetric geometry, we show that successful establishment from a localized tetraploid patch requires a critical nucleus of radius <math><msub><mi>R</mi> <mi>c</mi></msub> </math> , for which we derive an asymptotic approximation <math> <mrow><msub><mi>R</mi> <mi>c</mi></msub> <mo>∼</mo> <msup><mi>υ</mi> <mrow><mo>-</mo> <mn>1</mn></mrow> </msup> <mi>σ</mi> <msqrt><mrow><mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>ϕ</mi> <mo>)</mo> <mo>/</mo> <mn>2</mn></mrow> </msqrt> </mrow> </math> for small <math><mi>υ</mi></math> . We confirm these analytical predictions through numerical simulations of the continuous-time model. Our analyses reveal that sufficiently large founding patches can nucleate expanding bistable waves without intrinsic tetraploid fitness advantages, or reproductive strategies that circumvent frequency-dependent selection in sexually reproducing populations.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148535363","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":"Stability and Robustness of a Generalized Pump-Leak Model for Epithelial Vesicles.","authors":"Kerry Tarrant, Alan R Kay, Zahra Aminzare","doi":"10.1007/s11538-026-01683-7","DOIUrl":"10.1007/s11538-026-01683-7","url":null,"abstract":"<p><p>Epithelial cells stabilize ion concentrations and volume through coordinated membrane pumps, ion channels, and paracellular pathways, which can be modeled by classical single-compartment pump-leak equations (PLEs). Many epithelial functions, however, depend on the interaction between a cell and an enclosed luminal space, a geometry that cannot be captured by classical PLEs. To address this, we develop a two-compartment model consisting of an intracellular compartment coupled to a luminal compartment through the apical membrane, with both compartments interfacing an infinite extracellular bath and connected to it through the basolateral membrane and a paracellular pathway. Building on the five-dimensional single-cell PLEs, we formulate a ten-dimensional PLE system for this geometry and derive analytical equilibria and steady-state formulas for both the passive system and the Na⁺/K⁺-ATPase (NKA) driven active system. We characterize how these states depend on physiologically relevant parameters, analyze local stability across wide parameter ranges, and apply global sensitivity and robustness methods to identify the principal determinants of ion and volume homeostasis. Our focus is on closed epithelial systems in which the lumen volume relaxes to a steady state, rather than on fluid-secreting epithelia with time-varying luminal volume. We quantify apical and basolateral membrane potentials at steady state; the basolateral potential varies widely across parameter regimes, whereas the apical potential remains comparatively small in magnitude. The model reveals fundamental differences between basolateral and apical placement of the NKA, including the onset of luminal volume expansion when apical potassium recycling is insufficient. More broadly, this framework provides a mathematically tractable and physiologically grounded foundation for studying epithelial transport and for predicting conditions under which pump localization and conductance changes lead to stable function or pathological lumen expansion.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13369021/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148434758","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":"Personalized Spatiotemporal Radiotherapy for GBM: A PDE-Constrained Optimization Study.","authors":"Chiu-Yen Kao, Seyyed Abbas Mohammadi, Mohsen Yousefnezhad","doi":"10.1007/s11538-026-01699-z","DOIUrl":"10.1007/s11538-026-01699-z","url":null,"abstract":"<p><p>We develop a personalized optimization framework for designing spatiotemporal radiotherapy strategies for Glioblastoma Multiforme (GBM). The tumor dynamics are described by a reaction diffusion model on patient-specific brain geometries, and the treatment objective is formulated as a PDE-constrained optimization problem in which the admissible targeting region is allowed to vary on each day of therapy. The resulting optimization requires repeated solutions of the state and adjoint equations, and we implement an adjoint-driven gradient algorithm with line search and projection to enforce clinical dose constraints. To improve robustness, the algorithm is first validated on a simplified surrogate model before being applied to full patient data. The proposed framework generates patient-specific targeting volumes informed by clinical and radiological parameters, producing a dynamic treatment region that adapts to tumor evolution rather than relying on standard fixed or population-based margins. Our results demonstrate that incorporating daily adaptability into the optimization process can lead to substantially different and potentially more effective treatment targets. This study highlights the potential of PDE-constrained optimization as a mathematical tool for personalized radiotherapy planning.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148434775","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}