Journal of Mathematical Biology最新文献

{"title":"A model for mosquito-borne epidemic outbreaks with information-dependent protective behaviour.","authors":"Simone De Reggi, Andrea Pugliese, Mattia Sensi, Cinzia Soresina","doi":"10.1007/s00285-026-02472-5","DOIUrl":"10.1007/s00285-026-02472-5","url":null,"abstract":"<p><p>We investigate a model for a mosquito-borne epidemic in which human hosts may adopt protective behaviour against vector bites in response to information on both past and current disease prevalence. Assuming that mosquitoes can also feed on non-competent hosts (i.e. hosts that do not contribute to disease transmission), we first revisit existing results and show that behaviour-driven protection may either decrease or increase the basic reproduction number, depending on the interaction between behavioural response, host composition, and transmission parameters. Assuming that opinion dynamics evolves on a much faster time scale than disease transmission, we then apply Geometric Singular Perturbation Theory to effectively reduce the original two-group model to a model for a homogeneous host population. The reduced system enables a detailed investigation of the impact of information-induced behavioural changes on the transient dynamics of the epidemic, including scenarios in which protective measures lead to outbreaks with low attack rates. Our analysis shows that behavioural responses may either facilitate epidemic control or prolong disease persistence, potentially generating recurrent damped epidemic waves. Numerical simulations are provided to illustrate and support the analytical findings.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13675354/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208047","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":"Deciphering dengue fever transmission on higher-order networks.","authors":"Linhe Zhu, Bingxin Li, Shuling Shen","doi":"10.1007/s00285-026-02433-y","DOIUrl":"https://doi.org/10.1007/s00285-026-02433-y","url":null,"abstract":"<p><p>Dengue fever is a viral infection transmitted to humans through the bites of infected mosquitoes. Modeling dengue transmission is crucial for control, given its risk to half the world's population. This paper develops a host-to-host transmission model within hypergraphs constructed from simplicial complexes. Necessary conditions for the emergence of Turing instability in dengue dynamical systems naturally coupled on hypergraphs are derived. Furthermore, a multiplex network framework is constructed on hypergraphs by incorporating the influence of information on dengue transmission, and expressions for dengue outbreak thresholds are derived. Theoretical results are verified through numerical simulations. The Turing instability phenomenon in higher-order networks is investigated, while periodic diffusion effects are analyzed. Higher-order networks elevate the thresholds for dengue outbreaks within the multiplex network framework. Finally, to link theory with practice, we employ Physics-Informed Neural Networks (PINNs) to fit and predict dengue case data. By embedding the transmission model as physical constraints and constructing hypergraphs informed by geographical adjacency and tourism mobility, the PINNs achieves interpretable predictions and accurate parameter estimation. This study offers a feasible framework for understanding and predicting dengue transmission in complex real-world environments.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197343","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":"Towards the development of an efficient nonlinear controller for ART and cART against HIV infection.","authors":"Muhammad Arsalan, Muhammad Tariq Sadiq, Abubakar Rafique, Ahmad Almogren, Xiaojun Yu","doi":"10.1007/s00285-026-02471-6","DOIUrl":"https://doi.org/10.1007/s00285-026-02471-6","url":null,"abstract":"<p><p>The Human Immuno-deficiency Virus (HIV) is responsible for attacking the CD4+ T cells present in human blood and causes the human immune system to become vulnerable for numerous contagious and opportunistic diseases. It is hence pertinent to curb the spread of HIV infection using anti-HIV drugs. This study integrates sigmoid function with conventional sliding mode control and incorporate it within the framework of multi-objective optimal model predictive controller to reduce the impact of HIV infection through anti-retro-viral therapy. The proposed algorithm is designed using a deterministic HIV-human immune system model that also includes the dynamics of cytotoxic T-lymphocytes precursor and effector cells. The research work provides the detailed design of nonlinear sigmoid based SMC controller and its Lyapunov theory based stability analysis. This designed controller is then integrated within the framework of MPC. Simulation level dosage bounds derived from the considered reference values for anti-HIV drug dosage has been realized to explicate and understand the relationship between administered dosage and control inputs. To validate the superior performance of the proposed controller, the results are compared to that of recently proposed nonlinear backstepping, state-feedback and synergetic controllers. Lastly, the proposed control algorithm is also evaluated using a three-state, three-input HIV model to examine its applicability to combination anti-retro-viral therapy (cART). The simulations demonstrate that the proposed sigmoid SMC-MPC framework can regulate the modeled drug inputs while simultaneously improving the simulated CD4+ T-cell response and suppressing viral load. The results are intended to demonstrate the algorithmic performance of the proposed nonlinear control framework within the considered mathematical models. Importantly, this study is simulation-based and does not constitute a clinical treatment strategy or a recommendation for automated administration of anti-retro-viral drugs. The simulations are performed using MATLAB/Simulink. The observations and results presented in this study are also analyzed to substantiate the need of nonlinear feedback controllers to limit the amount of administered treatment burden to effectively and efficiently curb HIV advancement. Results showed that the proposed hybrid sigmoid SMC-MPC approach effectively lowered the initial drug dosage requirements by 30%. Whereas, the reduction in final steady state dosage has been reduced by upto 70% while reducing the convergence time of viral load by 14%. Similarly, the convergence time of healthy CD4+ T cell count, to the desired reference level, has been reduced by 26.8%. These results indicate favorable algorithmic performance within the considered simulation framework.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197353","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":"Expected value of the Sackin index under biased speciation models.","authors":"Daniel J Bauman, Noah A Rosenberg","doi":"10.1007/s00285-026-02465-4","DOIUrl":"10.1007/s00285-026-02465-4","url":null,"abstract":"<p><p>Models of random phylogenetic trees are important mathematical tools in phylogenetic data analysis; tree balance is a property of phylogenetic trees that helps describe and compare their shapes. Here, we investigate the Sackin index, one of the oldest and most widely used tree balance measures, under a variety of phylogenetic models beyond the standard Yule and Uniform models. The general biased speciation model is a biologically interpretable tree-generating model in which species branch into pairs of descendants according to an intrinsic branching rate, which is then split between the pair of descendants. The proportion of the branching rate of the parent that is assigned to a specific descendant, the split fraction, is a model parameter. Our main result is a formula for the expected value of the Sackin index under the general biased speciation model. Special cases of the general biased speciation model include a case that sets the split fraction to be a constant for each branching event, and two special cases inspired by the Aldous beta-splitting model: a random choice of split fraction is sampled independently at each branching event and drawn from a symmetric beta distribution in the Blum-François beta-splitting model or an asymmetric beta distribution in the Sainudiin-Véber beta-splitting model. As a corollary of our main result, we find formulas for the expected value of the Sackin index under these three cases of the general biased speciation model. We use the formulas to study how the balance of trees depends on the model parameters. Finally, because the Yule model is a special case of the Blum-François beta-splitting model, we find a new proof for the classical result describing the expected value of the Sackin index under the Yule model.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13669139/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149185686","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 2D fluid-based model for individual cell crawling.","authors":"Christèle Etchegaray, Nicolas Meunier, Raphaël Voituriez","doi":"10.1007/s00285-026-02468-1","DOIUrl":"https://doi.org/10.1007/s00285-026-02468-1","url":null,"abstract":"<p><p>This paper presents the analysis and numerical simulations of a two-dimensional model of single-cell crawling migration, focusing on intracellular dynamics. The fluid-based model relies on the interaction between the actin cytoskeleton and a generic molecular regulator of its activity. The model is formulated as a Poisson problem with Darcy's law, coupled with a nonlocal advection-diffusion equation for the molecular concentration, where the non-local term involves boundary values. Existence and uniqueness of resting and travelling stationary states are established in certain parameter domains, along with linear stability in the resting case. Numerical simulations illustrate both cell regimes. This demonstrates the model's ability to capture key features of cell migration.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149149799","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":"Geometry-induced pulse dynamics in a bulk-surface reaction-diffusion system for cell polarization.","authors":"Riku Watanabe","doi":"10.1007/s00285-026-02473-4","DOIUrl":"https://doi.org/10.1007/s00285-026-02473-4","url":null,"abstract":"<p><p>This paper studies a bulk-surface reaction-diffusion system for cell polarization in two-dimensional domains. The model describes the formation of localized patterns through the wave-pinning mechanism, while explicitly incorporating the effect of cell shape. Using singular perturbation methods, we formally derive reduced ordinary differential equations describing the wave-pinning dynamics on a fast time scale and the subsequent slow drift of pulse solutions induced by domain geometry. The resulting slow dynamics is a gradient flow of a potential function whose geometry-dependent part is expressed in terms of the Neumann Green's function. Moreover, we give a probabilistic interpretation of the potential function using the excursion Poisson kernel, which provides a more intuitive understanding of the pulse dynamics. We then analyze the reduced dynamics in several concrete geometries, including dumbbell-shaped domains and perforated disks. In these examples, we characterize stationary pulse positions, their stability, and the bifurcation structures arising from changes in geometric parameters. To evaluate the geometric terms appearing in the reduced dynamics, we use a conformal mapping method to compute the Neumann Green's function for these domains. Our analysis reveals geometry-induced phenomena such as nontrivial stationary pulse locations and both supercritical and subcritical pitchfork bifurcations. Finally, we perform numerical simulations to support the theoretical predictions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149129071","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":"State and parameter estimation for a neural model of local field potentials.","authors":"Daniele Avitabile, Gabriel J Lord, Khadija Meddouni","doi":"10.1007/s00285-026-02451-w","DOIUrl":"10.1007/s00285-026-02451-w","url":null,"abstract":"<p><p>The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying dynamics responsible for their emergence. We present an effort to capture certain features of the neural activity from the cortex of a mouse during natural sleep, obtained through local field potential measurements. Our approach relies on using a discretized Wilson-Cowan Amari neural field model for neural activity, along with a data assimilation method that allows the Bayesian joint estimation of the state and parameters. We demonstrate the feasibility of our approach on synthetic measurements before applying it to a dataset available in literature. Our findings suggest the potential of our approach to characterize the parameters of the external forcing in the neural activity model, while simultaneously inferring a state that aligns with the observed signal.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13634030/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149117763","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":"Multiplayer social dilemmas in completely mixed populations and networks of mixing communities.","authors":"Diogo L Pires, Mark Broom","doi":"10.1007/s00285-026-02464-5","DOIUrl":"10.1007/s00285-026-02464-5","url":null,"abstract":"<p><p>Human and non-human animals often form highly structured social systems in which individuals interact preferentially within specific groups, shaped by habitat structure, movement patterns, or social preferences. We consider a model that captures the interplay between social structure and emerging behaviour. Individuals are probabilistically distributed across the nodes of a spatial network representing interaction sites such as resource patches, territorial areas, or social hubs. Individuals present at the same node interact through a multiplayer game, so group structure is not imposed but instead emerges from movement under spatial constraints. As a benchmark, we analyse the completely mixed population, a null model in which individuals are indistinguishable, analogous to the classical well-mixed assumption, and further have no preference for particular network nodes. We derive exact expressions for fundamental properties of this population under arbitrary payoff functions, including the group size distribution, fitness functions, and fixation probabilities. We consider five multiplayer social dilemmas capturing the tension between individual and collective interests, such as those arising in public goods production, collective defence, and communal resource use. For these dilemmas, we derive analytical conditions for the evolution of cooperation in completely mixed populations. Using these as a reference, we reassess the effects of community structure. We show that asymptotically isolated communities expand the parameter range favouring cooperation, particularly under low population density. Finally, we explore intermediate regimes between completely mixed populations and isolated community structure, demonstrating that this expansion of the cooperative region remains robust even under higher levels of mixing between adjacent communities.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13630815/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149117723","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":"Spreading properties of a city-road reaction-diffusion model on one-dimensional lattice.","authors":"Grégory Faye, Jean-Michel Roquejoffre, Min Zhao","doi":"10.1007/s00285-026-02466-3","DOIUrl":"10.1007/s00285-026-02466-3","url":null,"abstract":"<p><p>We propose and study a new model to describe biological invasions constrained on infinite homogeneous one dimensional metric graphs. Our model consists of an infinite PDE-ODE system where, at each vertex of the one-dimensional lattice <math><mi>Z</mi></math> , we have a logistic equation, and connections between vertices are given by diffusion equations on the edges supplemented with Robin like boundary conditions at the vertices. We establish the main properties of the system and study the long time behavior of the solutions, especially by characterizing an asymptotic spreading speed for the system. In the fast diffusion regime, we derive a novel asymptotic model which exhibits similar propagation properties as the classical discrete Fisher-KPP on the one-dimensional lattice <math><mi>Z</mi></math> .</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149117734","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 vasomotion in supplying the nutrients in clogged blood vessels: an analytical approach.","authors":"Manoj Mahawar, Bharat Soni, Tithi Gupta, Ameeya Kumar Nayak","doi":"10.1007/s00285-026-02467-2","DOIUrl":"10.1007/s00285-026-02467-2","url":null,"abstract":"<p><p>This paper develops a theoretical model to examine the role of vasomotion and its effect on mass transfer processes. Vasomotion, consisting of periodic wave-like oscillations of blood vessel walls, is frequently observed in microcirculation and demonstrates distinct features in arterioles. The advection-diffusion equation governs the mass transport. This analysis can be used to model pathological conditions of blood flow, such as the formation of fatty cholesterol plaques and artery-clogging blood clots within the vessel lumen. These obstructions are modeled as a fictitious porous medium with permeability K. The fluid flow is described using the Darcy-Brinkman equation to quantify the effect of vasomotion. The novelty of the proposed framework is that it integrates the understanding of coupled vasomotion-driven flow and mass transfer in clogged arterioles using a lumped-parameter resistance approach. The developed model combines both blood flow and mass transfer resistances under pathological conditions and establishes their interaction via the Chilton-Colburn J-factor analogy. The present study employs the Frobenius method to solve the governing flow equations and obtain an expression for the velocity field. Furthermore, in the limiting case (absence of hematocrit and vasomotion), an approximate resistance formula for blood flow through a porous medium is derived and validated against previously obtained results. The mass transport equation is solved using the method of separation of variables, within the framework of a Sturm-Liouville problem. The governing equations are analyzed in a wave frame of reference moving in the positive axial direction with wave speed c to capture the effects of vasomotion. The influence of hematocrit level, Darcy number, Schmidt number, and power-law index is illustrated through three-dimensional surface plots and corresponding contour plots. The simulation results show that resistance increases with higher hematocrit levels and diffusivity effects, and decreases with increasing Darcy number. Compared with healthy conditions, fatty mass particles significantly increase resistance by altering viscosity and permeability.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149117776","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}