Mathematical biosciences最新文献

{"title":"A Mechanistic Learning Framework for Breast Cancer Relapse Prediction.","authors":"Judith Pérez-Velázquez, Meltem Gölgeli, İbrahim Kulaç","doi":"10.1016/j.mbs.2026.109830","DOIUrl":"https://doi.org/10.1016/j.mbs.2026.109830","url":null,"abstract":"<p><p>Breast cancer recurrence is thought to arise, at least in part, from disseminated tumour cells (DTCs) that may seed distant organs prior to or during surgery, persist in a dormant state for years to decades, and eventually resume proliferation to form clinically detectable metastases. Standard survival models treat this process statistically, without reference to the underlying biological kinetics, and while artificial intelligence (AI) has improved predictive accuracy, its \"black-box\" nature limits clinical interpretability. Here we present a mechanistic learning approach that relates routine histopathological data to a mathematical model of tumour growth. Three modular buckets assign clinical observables to latent kinetic parameters: Seed (initial metastatic burden), Speed (effective proliferative rate), and Soil (permissiveness of the tumour microenvironment), guided by pathology expertise within the author team. In the METABRIC cohort (1,814 patients, 737 relapses) we implement Seed with tumour size and lymph node count, and Speed with histological grade and ER, HER2, and PR status. Soil is designed for stromal tumour-infiltrating lymphocyte scores and PD-L1 expression, which this cohort does not record. Feature-selection experiments on the same data examined tumour cellularity, age, and RNA-based immune proxies as candidate Soil variables, but the bucket is reserved for datasets that record these variables directly. The model estimates a patient-level initial DTC burden and covariate-associated deviations in proliferative rate, which enter an exponential growth model to yield a patient-specific predicted relapse time. Anchoring the model to a literature-based reference phenotype ensures parameter identifiability and fixes the absolute scale of these quantities. A saturating (logarithmic) link between lymph-node involvement and initial metastatic burden keeps the predicted relapse time positive for 99.8% of patients, and a bounded link, examined as a sensitivity analysis, does so for all. Fitted with a censoring-aware loss and evaluated by internal five-fold cross-validation on this cohort, the model attains a concordance index (a measure of how well predicted relapse times rank the observed survival times) of 0.654, comparable to a multivariate Cox proportional-hazards baseline, while each prediction decomposes into an initial tumour burden and a proliferative rate that trace back to routine histopathological measurements. This proof of concept provides a modular foundation for future multi-centre mathematical-oncology research.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109830"},"PeriodicalIF":1.8,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149217832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A degenerate Fokker-Planck stochastic modeling and simulation of the signaling pathways in esophageal cancer.","authors":"Asma Alghamdi, Souvik Roy","doi":"10.1016/j.mbs.2026.109826","DOIUrl":"https://doi.org/10.1016/j.mbs.2026.109826","url":null,"abstract":"<p><p>In this work, we present an innovative approach to model and control aberrant signaling pathways in esophageal cancer. The dynamics of the signaling process are described using an Itô stochastic process, leading to a degenerate Fokker-Planck partial differential equation that captures the random behavior of the system. To inform the model, we formulate a finite-dimensional constrained optimization problem that estimates key parameters directly from patient data. Building on this, we introduce a pharmacokinetic stochastic model tailored to reflect patient-specific dynamics. An optimal treatment strategy is then proposed through a non-smooth open-loop control approach, characterized via Pontryagin's minimum principle (PMP). The resulting optimal control problem is efficiently solved using the sequential quadratic Hamiltonian (SQH) method. Numerical experiments demonstrate the effectiveness of the proposed framework in personalizing treatment strategies and improving control over aberrant pathway activity.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109826"},"PeriodicalIF":1.8,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149217902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A modified predator-prey model involving dual time delays: Bifurcation mechanism and controller design.","authors":"Qinwen Deng, Changjin Xu, Jinting Lin, Yingyan Zhao","doi":"10.1016/j.mbs.2026.109829","DOIUrl":"https://doi.org/10.1016/j.mbs.2026.109829","url":null,"abstract":"<p><p>This study establishes a predator-prey model with dual time delays, aiming to rigorously investigate the mechanisms through which time delays influence system stability and periodic behaviors. The well-posedness of the solutions, including existence and uniqueness, non-negativity, and boundedness, is established by fixed-point theorem, inequality technique, and proper function creation. Furthermore, a rigorous analysis of delay-induced Hopf bifurcations is conducted across five distinct delay-combination scenarios. Utilizing the Routh-Hurwitz criterion in conjunction with stability theory and bifurcation principles, we derive explicit stability conditions and precise Hopf bifurcation thresholds. This systematically elucidates how variations in delays govern stability transitions and generate periodic solutions. Crucially, we calculate the critical time-delay length that triggers stability switching. Two innovative controllers (ordinary feedback controller and dislocated feedback controller) are designed to regulate bifurcation dynamics. These effectively modulate bifurcation behavior, significantly modify the stability region, and enable precise control over the time of Hopf bifurcation onset. Numerical simulations implemented via Matlab confirm the validity and efficacy of the theoretical results, providing fundamental theoretical insights and practical strategies for predicting ecosystem dynamics and regulating ecological equilibrium.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109829"},"PeriodicalIF":1.8,"publicationDate":"2026-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149217872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coherent dynamical analysis arising from a stage-structured predator-prey model in a chemostat.","authors":"Hui Zhou","doi":"10.1016/j.mbs.2026.109828","DOIUrl":"10.1016/j.mbs.2026.109828","url":null,"abstract":"<p><p>We study a stage-structured predator-prey chemostat model with egg-development and juvenile-maturation delays, incorporating juvenile mortality during maturation. Cohort consistency yields nonnegative stage densities, and an egg-inclusive balance functional proves global existence and dissipativity. We establish a sharp criterion for both positive coexistence and uniform persistence, with the extinction boundary defined using the recruitment history. The characteristic determinant at the positive equilibrium reduces to a stable factor and a two-delay characteristic function. Explicit derivatives include the dependence of the equilibrium and all linearization coefficients on the varying delays. We obtain conditional Hopf criteria and a stability-count theorem on the finite coexistence region. A characteristic-matrix normal-form calculation determines the direction of each nondegenerate periodic branch. For the parameter set considered numerically, the primary egg-delay Hopf bifurcation is supercritical when maturation is instantaneous and subcritical when the maturation delay is 1.8 days. Direct integrations exhibit attracting finite-amplitude oscillations in the latter case, which are distinguished from the local unstable Hopf branch. Parameter sensitivities quantify the displacement of the stability threshold.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109828"},"PeriodicalIF":1.8,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149198728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reaction-diffusion models of invasive tree pest spread: Quantifying the expansion of oak processionary moth in the UK.","authors":"Jamie P McKeown, Laura E Wadkin, Nick G Parker, Andrew Golightly, Andrew W Baggaley","doi":"10.1016/j.mbs.2026.109824","DOIUrl":"10.1016/j.mbs.2026.109824","url":null,"abstract":"<p><p>UK woodlands, forests, and urban treescapes are under threat from invasive species, exacerbated by climate change, trade, and transport. Invasive tree pests debilitate their host and disrupt forest ecosystems, thus it is imperative to quantitatively model and predict their spread. Addressing this, we model the spread of an invasive pest using a spatiotemporal reaction-diffusion equation, representing the spatial distribution as a population density field. We solve this intractable equation numerically and, from the solution, we determine first arrival times of the pest at locations in the field. The adopted model permits us to obtain the expansion rate of pest spread directly from the model parameters, which we infer in the Bayesian paradigm, using a Markov chain Monte Carlo scheme. We apply our framework to the ongoing spread of oak processionary moth in the UK, an outbreak which continues to grow despite management efforts. We demonstrate that our approach effectively captures the spread of the pest and that a model with a non-constant expansion rate is a better fit to the data than a constant-rate model. Finally, we discuss possible reasons for the apparent non-constant rate of expansion, arguing that this may be due to the impact of host species and environment heterogeneity, rather than a genuine change in the intrinsic expansion rate. The proposed framework is a powerful tool for quantitatively modelling the spread of an invasive tree pest and could underpin future prediction and management approaches.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109824"},"PeriodicalIF":1.8,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149187242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parkinson's disease, Gaucher disease, and bistability in the lysosomal degradation pathway.","authors":"Michael C Reed, Janet Best, Peter Lansbury, Craig Justman, H Frederik Nijhout","doi":"10.1016/j.mbs.2026.109827","DOIUrl":"10.1016/j.mbs.2026.109827","url":null,"abstract":"<p><p>Sphingolipids are intrinsic components of cell membranes that are transported to lysosomes for degradation into ceramide, which is used in the Golgi to synthesize new sphingolipids. Although sphingolipid metabolism is very complicated, the degradation pathway is relatively simple and converts the sphingolipids to ceramide and sphingosine. Polymorphisms in the genes for enzymes in this pathway are associated with various lysosomal storage disorders, and one of the enzymes, glucosylceramidase (GCase1), is associated with Parkinson's disease and Lewy-body dementia as well as Gaucher disease. We construct a mathematical model of the sphingolipid degradation pathway and show that over a wide range of V_max values of GCase1, the pathway exhibits bistability, two steady states with hysteresis between them. In addition, it is known that the formation of synuclein fibrils from monomers and oligomers is influenced by the degradation pathway and, in turn, inhibits GCase1. We show that there are two steady states, one with low fibril production and one with high fibril production, with hysteresis. The fact that there are two steady states with hysteresis presents both challenges and opportunities for drug discovery and dosing. Our work has implications for aging, since it is known that the expression level of the gene for GCase1 declines with age.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109827"},"PeriodicalIF":1.8,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149187258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics analysis of a delayed reaction-diffusion Filippov pest management model with double economic thresholds.","authors":"Zhenjie Zhang, Ruizhi Yang","doi":"10.1016/j.mbs.2026.109823","DOIUrl":"10.1016/j.mbs.2026.109823","url":null,"abstract":"<p><p>A delayed reaction-diffusion Filippov pest-natural enemy model with double thresholds is proposed to describe switching control in pest management. Compared with related Filippov pest models, the coupled effects of the double thresholds, diffusion, and delay are considered, allowing spatial pattern formation to be linked with nonsmooth dynamics. Sufficient conditions for the existence and stability of positive equilibria are established. Turing instability criteria and amplitude equations are derived, and Hopf bifurcation caused by reproductive delay is analyzed. Attracting sliding regions and pseudo-equilibria are determined, and boundary node and boundary focus bifurcations are investigated. Numerical simulations show that decreasing the pest diffusion coefficient changes the spatial pattern from spotted to mixed and then to striped. As the pest threshold approaches the equilibrium density, spatial heterogeneity is weakened and Turing patterns disappear through a boundary focus bifurcation. In addition, increasing the reproductive delay enlarges the sliding region and leads to touching, buckling, and crossing sliding bifurcations. These results reveal the interaction among spatial diffusion, delay, and threshold switching and provide useful insights for threshold selection and pest management.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109823"},"PeriodicalIF":1.8,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149187189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of fish-human transmission and different life stages of fish on Clonorchiasis: A novel mathematical model.","authors":"Wei Wang, Xiaohui Huang, Hao Wang","doi":"10.1016/j.mbs.2024.109209","DOIUrl":"10.1016/j.mbs.2024.109209","url":null,"abstract":"<p><p>Clonorchiasis is a zoonotic disease mainly caused by eating raw fish and shrimp, and there is no vaccine to prevent it. More than 30 million people are infected worldwide, of which China alone accounts for about half, and is one of the countries most seriously affected by Clonorchiasis. In this work, we formulate a novel Ordinary Differential Equation (ODE) model to discuss the biological attributes of fish within authentic ecosystems and the complex lifecycle of Clonorchis sinensis. This model includes larval fish, adult fish, infected fish, humans, and cercariae. We derive the basic reproduction number and perform a rigorous stability analysis of the proposed model. Numerically, we use data from 2016 to 2021 in Guangxi, China, to discuss outbreaks of Clonorchiasis and obtain the basic reproduction number R₀=1.4764. The fitted curve appropriately reflects the overall trend and replicates a low peak in the case number of Clonorchiasis. By reducing the release rate of cercariae in 2018, the fitted values of Clonorchiasis cases dropped rapidly and almost disappeared. If we decrease the transmission rate from infected fish to humans, Clonorchiasis can be controlled. Our studies also suggest that strengthening publicity education and cleaning water quality can effectively control the transmission of Clonorchiasis in Guangxi, China.</p>","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":" ","pages":"109209"},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140961248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modeling of brain metastases growth and response to therapies: A review.","authors":"B. Ocaña-Tienda, Víctor M. Pérez-García","doi":"10.1016/j.mbs.2024.109207","DOIUrl":"https://doi.org/10.1016/j.mbs.2024.109207","url":null,"abstract":"","PeriodicalId":94129,"journal":{"name":"Mathematical biosciences","volume":"54 5","pages":"109207"},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140975910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}