Journal of Mathematical Biology最新文献_第2页

Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods. 集体细胞迁移中的表型结构：数学模型和方法教程。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-16 DOI: 10.1007/s00285-025-02223-y

Tommaso Lorenzi, Kevin J Painter, Chiara Villa

{"title":"Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods.","authors":"Tommaso Lorenzi, Kevin J Painter, Chiara Villa","doi":"10.1007/s00285-025-02223-y","DOIUrl":"10.1007/s00285-025-02223-y","url":null,"abstract":"Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc. Clearly, the phenotypic distribution - and how this changes over time and space - could be a major determinant of population-level dynamics. For instance, across a cancerous population, variations in movement, growth, and ability to evade death may determine its growth trajectory and response to therapy. In this review, we discuss how classical partial differential equation (PDE) approaches for modelling cellular systems and collective cell migration can be extended to include phenotypic structuring. The resulting non-local models - which we refer to as phenotype-structured partial differential equations (PS-PDEs) - form a sophisticated class of models with rich dynamics. We set the scene through a brief history of structured population modelling, and then review the extension of several classic movement models - including the Fisher-KPP and Keller-Segel equations - into a PS-PDE form. We proceed with a tutorial-style section on derivation, analysis, and simulation techniques. First, we show a method to formally derive these models from underlying agent-based models. Second, we recount travelling waves in PDE models of spatial spread dynamics and concentration phenomena in non-local PDE models of evolutionary dynamics, and combine the two to deduce phenotypic structuring across travelling waves in PS-PDE models. Third, we discuss numerical methods to simulate PS-PDEs, illustrating with a simple scheme based on the method of lines and noting the finer points of consideration. We conclude with a discussion of future modelling and mathematical challenges.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 6","pages":"61"},"PeriodicalIF":2.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12084280/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144081577","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}

引用次数: 0

Optimal adaptive therapeutic schedules for metastatic castrate-resistant prostate cancer based on bilevel optimization problem. 基于双水平优化问题的转移性去势抵抗性前列腺癌最优适应性治疗方案。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-16 DOI: 10.1007/s00285-025-02220-1

Dujuan Wang, Jinzhi Lei

{"title":"Optimal adaptive therapeutic schedules for metastatic castrate-resistant prostate cancer based on bilevel optimization problem.","authors":"Dujuan Wang, Jinzhi Lei","doi":"10.1007/s00285-025-02220-1","DOIUrl":"10.1007/s00285-025-02220-1","url":null,"abstract":"Abiraterone acetate has established itself as an effective treatment for metastatic castrate-resistant prostate cancer (mCRPC). However, disease progression remains inevitable with conventional long-term maximum tolerated dose (MTD) therapy due to the development of drug resistance. Adaptive therapy (AT), rooted in Darwinian evolutionary dynamics, offers a novel approach to combat drug resistance. By dynamically adjusting drug doses, AT aims to enhance treatment outcomes. Despite successful clinical trials and extensive theoretical studies on AT, significant challenges persist in determining optimal adaptive therapeutic schedules tailored to individual patients. This study presents a biochemically motivated mathematical model incorporating competition between drug-sensitive and drug-resistant cancer cells, incorporating mutated migration factors identified through prostate-specific antigen (PSA) data. Theoretical analyses, including the stability of equilibrium states and the existence of periodic solutions, validate the model's interpretability and support the feasibility of adapted periodic therapy. We propose an optimal adaptive periodic therapy framework, formulating a bilevel dynamic optimization problem with constraints to establish personalized adaptive therapeutic schedules for prostate cancer. Optimal solutions identify therapeutic switches and doses under adaptive therapy. We compare our proposed framework with other adaptive strategies regarding overall survival and total drug doses through numerical simulations and quantitative analysis, demonstrating superior performance. Our model presents a promising tool for integration into clinical research trials, offering individualized adaptive therapeutic schedules to enhance precision management of mCRPC.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 6","pages":"60"},"PeriodicalIF":2.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144081576","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}

引用次数: 0

Aggregation-diffusion in heterogeneous environments. 异质环境中的聚集-扩散。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-08 DOI: 10.1007/s00285-025-02222-z

Jonathan R Potts

{"title":"Aggregation-diffusion in heterogeneous environments.","authors":"Jonathan R Potts","doi":"10.1007/s00285-025-02222-z","DOIUrl":"10.1007/s00285-025-02222-z","url":null,"abstract":"Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical way. However, most existing studies do not account for the effect of the underlying environment on organism movement. In reality, the environment is often a key determinant of emergent space use patterns, albeit in combination with collective aspects of motion. This work studies aggregation-diffusion equations in a heterogeneous environment in one spatial dimension. Under certain assumptions, it is possible to find exact analytic expressions for the steady-state solutions when diffusion is quadratic. Minimising the associated energy functional across these solutions provides a rapid way of determining the likely emergent space use pattern, which can be verified via numerical simulations. This energy-minimisation procedure is applied to a simple test case, where the environment consists of a single clump of attractive resources. Here, self-attraction and resource-attraction combine to shape the emergent aggregation. Two counter-intuitive findings emerge from these analytic results: (a) a non-monotonic dependence of clump width on the aggregation width, (b) a positive correlation between self-attraction strength and aggregation width when the resource attraction is strong. These are verified through numerical simulations. Overall, the study shows rigorously how environment and collective behaviour combine to shape organism space use, sometimes in counter-intuitive ways.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 6","pages":"59"},"PeriodicalIF":2.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12062097/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144036145","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}

引用次数: 0

Analysis of neural activation in time-dependent membrane capacitance models. 时变膜电容模型中的神经激活分析。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-06 DOI: 10.1007/s00285-025-02218-9

Matías Courdurier, Leonel E Medina, Esteban Paduro

引用次数: 0

Reaction kinetics of membrane receptors: a spatial modeling approach. 膜受体的反应动力学：空间建模方法。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-06 DOI: 10.1007/s00285-025-02217-w

Anıl Cengiz, Sean D Lawley

引用次数: 0

Estimation of the lifetime distribution from fluctuations in Bellman-Harris processes. Bellman-Harris过程波动的寿命分布估计。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-06 DOI: 10.1007/s00285-025-02219-8

Jules Olayé, Hala Bouzidi, Andrey Aristov, Antoine Barizien, Salomé Gutiérrez Ramos, Charles Baroud, Vincent Bansaye

{"title":"Estimation of the lifetime distribution from fluctuations in Bellman-Harris processes.","authors":"Jules Olayé, Hala Bouzidi, Andrey Aristov, Antoine Barizien, Salomé Gutiérrez Ramos, Charles Baroud, Vincent Bansaye","doi":"10.1007/s00285-025-02219-8","DOIUrl":"10.1007/s00285-025-02219-8","url":null,"abstract":"The growth of populations without interactions can often be modeled by branching processes where each individual evolves independently and with the same law. In Bellman-Harris processes, each individual lives a random time and is then replaced by a random number of offspring. We are interested in the estimation of the parameters of this model. Our motivation comes from the estimation of cell division time and we focus on Gamma distribution for lifetime and binary reproduction. The mean of the lifetime is closely related to the growth rate of the population. Going farther and describing lifetime variability from fixed time observations is a challenging task, due to the complexity of the fluctuations of non-Markovian branching processes. Using fine results on these fluctuations, we describe two time-asymptotic regimes and explain how to discriminate between them and estimate the parameters. Then, we consider simulations and biological data to validate and discuss our method. It allows to determine single-cell parameters from time-resolved measurements of populations without the need to track each individual or to know the details of the initial condition. The results can be extended to more general branching processes.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 6","pages":"56"},"PeriodicalIF":2.2,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144041816","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}

引用次数: 0

Deformations of acid-mediated invasive tumors in a model with Allee effect. 具有Allee效应的酸介导的侵袭性肿瘤变形模型。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-05 DOI: 10.1007/s00285-025-02209-w

Paul Carter, Arjen Doelman, Peter van Heijster, Daniel Levy, Philip Maini, Erin Okey, Paige Yeung

引用次数: 0

Spreading dynamics for a time-periodic nonlocal dispersal epidemic model with delay and vaccination. 具有时滞和疫苗接种的时间周期非局部扩散流行病模型的传播动力学。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-03 DOI: 10.1007/s00285-025-02214-z

Xiao Zhang, Shi-Liang Wu, Lan Zou, Cheng-Hsiung Hsu

{"title":"Spreading dynamics for a time-periodic nonlocal dispersal epidemic model with delay and vaccination.","authors":"Xiao Zhang, Shi-Liang Wu, Lan Zou, Cheng-Hsiung Hsu","doi":"10.1007/s00285-025-02214-z","DOIUrl":"10.1007/s00285-025-02214-z","url":null,"abstract":"It is known that vaccination plays an important strategy in eliminating infectious diseases. In this paper, we investigate the spreading dynamics for a time-periodic nonlocal dispersal epidemic model with delay and vaccination. We first establish the spreading speed of the model and an abstract framework on the existence of time-periodic traveling waves, which will help us to derive the existence of the super-critical and critical time-periodic traveling waves. Then we show that the spreading speed coincides with the minimal waves speed of time-periodic traveling waves. Further, we consider the effects of delay, periodicity, nonlocality and vaccination on the spreading speed. In the absence of delay, we find a large class of the time-periodic systems that have the same spreading speed. When delay is introduced, some numerical simulations reveal that the spreading speed initially exhibits oscillatory behavior and ultimately converges to a constant as time-period increases. Moreover, we observe that both delay and efficacy of vaccination decrease the spreading speed; both diffusion rate and nonlocality of infectious individuals increase the spreading speed; while the diffusion rates, nonlocalities of susceptible and vaccinated individuals do not affect the spreading speed. In particular, it is worth mentioning that the spreading speed is highly sensitivity to the efficacy of vaccination than the rate of vaccination.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 5","pages":"54"},"PeriodicalIF":2.2,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144056793","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}

引用次数: 0

Evolution of pathogen tolerance and reproductive trade-off implications. 病原体耐受性的进化和生殖权衡的意义。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-04-30 DOI: 10.1007/s00285-025-02216-x

Sabrina H Streipert, David Swigon, Mark Q Wilber, Jason C Walsman

{"title":"Evolution of pathogen tolerance and reproductive trade-off implications.","authors":"Sabrina H Streipert, David Swigon, Mark Q Wilber, Jason C Walsman","doi":"10.1007/s00285-025-02216-x","DOIUrl":"10.1007/s00285-025-02216-x","url":null,"abstract":"We develop an epidemic model that accounts explicitly for the pathogen pool and incorporates population variations in host defense strategy, measured in disease tolerance that is assumed to be perfectly inherited by offspring. Although the proposed model is more general, it is motivated by the devastating Batrachochytrium dendrobatidis (Bd) fungus that is responsible for severe declines in amphibians. We show that the model's basic reproduction number consists of a weighted average of individual basic reproduction numbers associated to each tolerance class. If the individual basic reproduction number associated to the highest tolerance level is less than one, then any solution converges to a (non-unique) disease-free equilibrium. We show that in the absence of a trade-off, different host defense strategies can coexist as long as the disease will go extinct eventually. In contrast, if the disease persists, the set of pandemic equilibria consists of isolated vertex equilibria, implying the survival of an individual host defense strategy. The pandemic equilibrium corresponding to the highest tolerance, i.e., lowest disease-induced death rate is the only asymptotically stable pandemic equilibrium. Additionally, to investigate the impact of a trade-off, we incorporate a tolerance cost in reproduction, whereby a higher tolerance comes at the expense of a lower reproductive rate. Now, the coexistence of host defense strategies in the absence of the disease is no longer supported. However, the set of pandemic equilibria increases in richness to contain equilibria where different tolerance classes are present.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 5","pages":"53"},"PeriodicalIF":2.2,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144056788","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}

引用次数: 0

Lattice-based stochastic models motivate non-linear diffusion descriptions of memory-based dispersal. 基于格子的随机模型激发基于记忆的扩散的非线性扩散描述。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-04-24 DOI: 10.1007/s00285-025-02211-2

Yifei Li, Matthew J Simpson, Chuncheng Wang

{"title":"Lattice-based stochastic models motivate non-linear diffusion descriptions of memory-based dispersal.","authors":"Yifei Li, Matthew J Simpson, Chuncheng Wang","doi":"10.1007/s00285-025-02211-2","DOIUrl":"10.1007/s00285-025-02211-2","url":null,"abstract":"The role of memory and cognition in the movement of individuals (e.g. animals) within a population, is thought to play an important role in population dispersal. In response, there has been increasing interest in incorporating spatial memory effects into classical partial differential equation (PDE) models of animal dispersal. However, the specific detail of the transport terms, such as diffusion and advection terms, that ought to be incorporated into PDE models to accurately reflect the memory effect remains unclear. To bridge this gap, we propose a straightforward lattice-based model where the movement of individuals depends on both crowding effects and the historic distribution within the simulation. The advantage of working with the individual-based model is that it is straightforward to propose and implement memory effects within the simulation in a way that is more biologically intuitive than simply proposing heuristic extensions of classical PDE models. Through deriving the continuum limit description of our stochastic model, we obtain a novel nonlinear diffusion equation which encompasses memory-based diffusion terms. For the first time we reveal the relationship between memory-based diffusion and the individual-based movement mechanisms that depend upon memory effects. Through repeated stochastic simulation and numerical explorations of the mean-field PDE model, we show that the new PDE model accurately describes the expected behaviour of the stochastic model, and we also explore how memory effects impact population dispersal.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 5","pages":"52"},"PeriodicalIF":2.2,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144041160","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}

引用次数: 0