Journal of Mathematical Biology最新文献

{"title":"Modelling the effect of antibody depletion for dose-response behavior of common immunostaining protocols.","authors":"Dominik Tschimmel, Tim Hucho, Steffen Waldherr","doi":"10.1007/s00285-026-02394-2","DOIUrl":"10.1007/s00285-026-02394-2","url":null,"abstract":"<p><p>Antibody binding properties for immunostaining applications are often characterized by dose-response curves, which describe the amount of bound antibodies as a function of the initially applied antibody concentration. A common model for the dose-response curve is the Langmuir isotherm, which assumes an equilibrium between the binding and unbinding of antibodies. However, for common immunostaining protocols, the equilibrium assumption is violated, and the dose-response behavior is governed by an accumulation of permanently bound antibodies. Assuming a constant antibody concentration, the resulting accumulation model can easily be solved analytically. However, in many experimental setups the total amount of antibodies is fixed, such that antibody binding reduces the concentration of free antibodies. Solving the corresponding depletion accumulation model is more difficult and seems to be impossible for heterogeneous epitope landscapes. In this paper, we first solve the depletion accumulation model analytically for a homogeneous epitope landscape. From the obtained solution, we derive inequalities between the depletion accumulation model, the depletion-free accumulation model, and the Langmuir isotherm. This allows us to characterize the depletion effect for homogeneous epitope landscapes. Next, we generalize the problem to heterogeneous epitope landscapes, where we prove the existence and uniqueness of a solution that behaves as expected from the experimental setting. These natural properties define bounds for the depletion accumulation model. We conclude this paper by applying the bounds to characterize the depletion effect for heterogeneous epitope landscapes.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13233888/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148158959","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":"Transient tumor-induced disruption of peristaltic flow: a magnetohydrodynamic modeling framework.","authors":"Ashvani Kumar, Dharmendra Tripathi, Anuj Mubayi, V K Narla","doi":"10.1007/s00285-026-02417-y","DOIUrl":"10.1007/s00285-026-02417-y","url":null,"abstract":"<p><p>Tumor growth within physiological systems such as the gastrointestinal tract, ducts, or blood vessels can progressively obstruct fluid transport, impair organ function, and reduce the efficacy of therapeutic interventions like drug delivery and hyperthermia. In this study, a mathematical model is developed to investigate and characterize the mechanisms of peristaltic flow in a channel obstructed by transient tumor growth. The model incorporates fundamental conservation laws of mass and momentum, while a bump function is used to represent tumor-induced geometric deformation of the channel wall. In addition, a transverse magnetic field is introduced to account for magnetohydrodynamic effects relevant to biomedical applications such as magnetic hyperthermia. Tumor growth is modeled as a linear time-dependent process, and the flow is analyzed under low Reynolds number and lubrication theory assumptions, which are suitable for physiological flows. Analytical solutions are derived under simplified conditions to examine the influence of tumor growth rate and magnetic field strength on velocity distribution, pressure gradient, wall shear stress, streamline patterns and particle trajectories. The results suggest that early-stage tumor growth produces minimal flow disturbance, whereas progressive enlargement significantly obstructs flow, increases local pressure and skin friction and alters streamline patterns. An increase in Hartmann number enhances magnetic resistance, leading to a reduction in axial velocity and volumetric flow rate. Furthermore, parametric sensitivity analysis reveals that tumor geometric parameters play a dominant role in governing flow behavior compared with magnetic and peristaltic effects.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148151987","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":"Stochastic modelling and statistical inference for the time to extinction of a class of populations with sexual reproduction.","authors":"Ehyter M Martín-González, Santiago Abdiel González-Reyes","doi":"10.1007/s00285-026-02416-z","DOIUrl":"10.1007/s00285-026-02416-z","url":null,"abstract":"<p><p>We present a Bisexual Galton-Watson process to model the dynamics of populations with sexual reproduction, allowing overlaps in different generations. We study the time to extinction of this model, for which we provide a sufficient condition that ensures that extinction occurs with probability 1. This condition extends classical results from the literature of branching processes. Furthermore, we show that the time to extinction of our model can be approximated using standard tools from Extreme Value Theory, for which we make use of a methodology based on simulations of the time to extinction. This methodology is presented in full detail and is later applied to three numerical examples.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148152031","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 framework for jointly modeling the natural history of ductal carcinoma in situ and invasive breast cancer.","authors":"Evripidis Kapanidis, Keith Humphreys","doi":"10.1007/s00285-026-02418-x","DOIUrl":"10.1007/s00285-026-02418-x","url":null,"abstract":"<p><p>We present a new approach for jointly modelling the natural history of ductal carcinoma in situ (DCIS) and invasive breast cancer, based on a continuous tumor growth framework. We first describe the structure of a stable disease population, in which individuals traverse with rates invariant to calendar time through different health states. Based on the properties of this population we develop a likelihood model that jointly utilizes probability distributions describing sub-models for screening sensitivity, detection through symptoms, tumor growth rate and time for DCIS to become invasive. This model can incorporate any parametric forms for these sub-models, allowing for testing different assumptions for the occult biological progression of breast cancer. By using stable disease assumptions the model can be fitted to data from incident cancer cases and does not require specification of a sub-model for age at tumour onset. In the final part of the publication we perform simulations to verify the theoretical properties of the stable disease population and to show how our model can be used in a real setting to estimate characteristics of the involved latent processes.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13230285/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148151966","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 hybrid framework for compartmental models enabling simulation-based inference.","authors":"Domenic P J Germano, Alexander E Zarebski, Sophie Hautphenne, Robert Moss, Jennifer A Flegg, Mark B Flegg","doi":"10.1007/s00285-026-02409-y","DOIUrl":"10.1007/s00285-026-02409-y","url":null,"abstract":"<p><p>Multi-scale systems often exhibit a combination of stochastic and deterministic dynamics. In compartmental models, low occupancy compartments tend to exhibit stochastic dynamics while high occupancy compartments tend to follow deterministic dynamics. Representing both dynamics with existing methods is challenging. Failing to account for stochasticity in small populations can produce \"atto-foxes\", for example in the Lotka-Volterra ordinary differential equation (ODE) model. This limitation becomes problematic when studying the extinction of species or the clearance of infection, but it can be overcome by using discrete stochastic models, such as continuous-time Markov chains (CTMCs). Unfortunately, simulating CTMCs is impractical for many realistic models, where discrete events have very high frequencies. In this work, we develop a mathematical framework to couple continuous ODEs and discrete CTMCs: \"Jump-Switch-Flow\" (JSF). In this framework, compartments can reach extinct states (\"absorbing states\"), thereby resolving atto-fox-type problems. JSF has the desired behaviours of exact CTMC simulation, but is substantially computationally faster than existing alternatives, by at least one order of magnitude, and can even obtain constant scaling, irrespective of compartment occupancy. We demonstrate JSF's utility for simulation-based inference, particularly multi-scale problems, with several case-studies. In a simulation study, we demonstrate how JSF can enable a more nuanced analysis of the efficacy of public health interventions. We also carry out a novel analysis of longitudinal within-host data from SARS-CoV-2 infections to quantify the timing of viral clearance. In this work, we show how JSF offers a novel approach to compartmental model simulation.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13216187/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148037262","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":"Sustained oscillatory mosquito population suppression analysis based on a hybrid switching dynamical system model.","authors":"Yufeng Wang, Yining Chen, Jia Li, Jianshe Yu","doi":"10.1007/s00285-026-02407-0","DOIUrl":"10.1007/s00285-026-02407-0","url":null,"abstract":"<p><p>In this paper, we develop a hybrid dynamical system to model mosquito population suppression incorporating both time and state-dependent switching. The time-dependent switching arises from a mismatch between the sexual lifespan of sterile mosquitoes and the sampling period, while the state-dependent switching is governed by the relation between the state of wild mosquitoes at sampling instants and the epidemiological threshold. We investigate the long-term dynamics of the hybrid system with sampling period exceeding the sexual lifespan. The wild population is shown to converge to a pseudo-equilibrium when the epidemiological threshold exceeds this equilibrium value. For the other situation, we establish sufficient conditions for the existence of a unique (pseudo)-harmonic solution and analyze its stability. Using Poincaré mapping, we further derive explicit existence criteria for subharmonic solutions and rigorously prove their global asymptotic stability. Finally, some numerical examples are provided to illustrate our theoretical findings and to deliver practical insights for release strategy development.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148018533","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":"Threshold dynamics for a stage-structured model with non-local impulsive birth in a heterogeneous environment.","authors":"Yurong Zhang, Taishan Yi, Yanyu Xiao","doi":"10.1007/s00285-026-02412-3","DOIUrl":"10.1007/s00285-026-02412-3","url":null,"abstract":"<p><p>In this paper, we examine the effect of spatial heterogeneity on a stage-structured population model with non-local impulsive birth. We begin by introducing a non-local impulsive reaction-advection-diffusion model with spatial heterogeneity to describe the stage-structured population dynamics, accounting for two distinct life cycle phases. Next, we convert this model into a discrete-time recursive system defined by a discrete map. By utilizing the theory of the asymptotic spectral radius of linearized operators, and verifying fundamental qualitative properties of the discrete map, we establish results on threshold dynamics of the recursive system, including the non-existence, existence, and global attractivity of non-trivial fixed points. Finally, numerical simulations are presented to illustrate the theoretical results and to assess the influence of key parameters, such as drift rates, mortality and reproduction functions, and dispersal kernels on population extinction or dispersal patterns.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13194205/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147983966","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":"Dynamic analysis of an HIV stochastic time-delay differential equations incorporating two infection pathways and CTL immune response.","authors":"Yan Wang, Jingze Ma, Qiuyue Dong, Jane M Heffernan","doi":"10.1007/s00285-026-02411-4","DOIUrl":"10.1007/s00285-026-02411-4","url":null,"abstract":"<p><p>We propose a five-dimensional stochastic time-delay differential equation model that includes virus-to-cell infection, silent and active cell-cell transmissions and CTL immune response. Using mathematical methods, the non-degenerate five-dimensional stochastic delay differential equation model is transformed into a degenerate eight-dimensional stochastic differential equation model. The existence of a unique global positive solution is demonstrated. Then, by establishing a suitable Lyapunov function, we obtain the existence of a stationary Markov process when the stochastic CTL-activated reproduction number is greater than one. Additionally, we derive a critical condition for virus extinction using spectral radius analysis method and the law of large numbers theorem. Finally, through numerical simulations, we explore the impacts of random perturbations and cell-cell transmission on the dynamic behaviour of the model, and investigate the effect of time delays on T-cell count and viral load. Furthermore, ensemble simulations quantify viral clearance probabilities relative to the clinical detection limit, revealing that CTL-mediated immunity utilizes environmental stochasticity more efficiently than B-cell-mediated mechanisms to accelerate viral clearance.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147976929","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":"Consistent multiscale modelling of movement and habitat selection.","authors":"Paul G Blackwell","doi":"10.1007/s00285-026-02370-w","DOIUrl":"10.1007/s00285-026-02370-w","url":null,"abstract":"<p><p>In spatial ecology, the concept of resource selection expresses the idea that for many animals, the distribution of an individual's location is not uniform over the region available to them; instead, they spend time preferentially in some locations compared to others, in a way that can often be related to spatial covariates. The related concept of step selection describes the variation in an individual's tendency to move to particular locations in the short term, taking into account both spatial covariates and the constraints of their process of movement. Consistent modelling of resource selection and step selection is necessary to understand animals' distribution in space and to interpret movement, telemetry, and spatial survey data in a meaningful way. In this paper, I take advantage of recent developments in stochastic processes and statistical algorithms to develop a range of new stochastic models in which both the dynamics and the long-term behaviour are tractable and described parametrically, and which are flexible enough to represent a wide range of patterns of movement and space use encountered in reality. I extend the mathematical analogy between movement modelling and Markov chain Monte Carlo algorithms, first proposed by Michelot, Blackwell & Matthiopoulos (2019; Ecology 100, e02452), to a wide range of continuous-time stochastic processes, including both diffusion processes and velocity-jump models, that in different ways are motivated by the simple discrete-time step-and-turn models widely used in practice. Particular cases include a diffusion process where the dynamics are defined in terms of speed and direction of movement, and a velocity-jump process in d dimensions, generalizing the 'bouncy particle sampler' used in Bayesian inference, in which the distribution of velocity after a so-called 'bounce' event has support over a region which itself has dimension d. I also show how this mathematical approach can be extended to models incorporating distinct behavioural states and to higher dimensional models representing the joint movement of interacting individuals.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13190373/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147976903","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":"Numerical Analysis of BIMs for Stochastic SIR and SIS Models with Variable Contact Diffusion Rates.","authors":"Henri Schurz, Kursad Tosun","doi":"10.1007/s00285-026-02392-4","DOIUrl":"10.1007/s00285-026-02392-4","url":null,"abstract":"<p><p>Qualitative properties of adequate numerical methods for stochastic differential equations to simulate the stochastic counterparts of some known models with variable contact diffusion rates in mathematical epidemiology are investigated, especially SIS and SIR models with non-constant total population sizes on bounded domains. We show the convergence of numerical approximations based on Balanced Implicit Methods (BIMs) by proving several properties; including positivity, invariance, stability, mean and mean square consistency, local uniform boundedness, mean square Hölder continuity and mean square contractivity. We also present some simulation results for those models with realistic parameters.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13176071/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147943692","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}