Journal of Mathematical Biology最新文献

{"title":"A multiscale theory for network advection- reaction-diffusion.","authors":"Hadrien Oliveri, Emilia Cozzolino, Alain Goriely","doi":"10.1007/s00285-026-02386-2","DOIUrl":"10.1007/s00285-026-02386-2","url":null,"abstract":"<p><p>Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), e.g. the spread of an infectious agent between different countries, or the transport and replication of toxic proteins across different brain regions in neurodegenerative diseases. In these models, transport is modelled at the macroscale through an operator, the so-called graph Laplacian, based on the edge properties and topology, capturing the fluxes between different nodes of the network. However, this phenomenological approach fails to take into account the physical processes taking place, at the microscale, within the edge. A fundamental problem is then to obtain a transport operator from mechanistic principles based on the underlying transport process. Using advection-reaction-diffusion as a generic mechanism for inter-nodal exchanges, we derive a multiscale network transport model and derive the corresponding linear transport operator at the macroscale from first principles. This effective graph Laplacian is fully determined by the transport mechanisms along the edges at the microscale. We show that this operator correctly captures the transport, and we study its scaling properties with respect to edge length.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13065590/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147640394","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 bifurcation analysis of turing and symmetry broken patterns of a PDE model for vegetation dynamics.","authors":"Konstantinos Spiliotis, Lucia Russo, Constantinos Siettos, Francesco Giannino","doi":"10.1007/s00285-026-02384-4","DOIUrl":"10.1007/s00285-026-02384-4","url":null,"abstract":"<p><p>We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water, and one ordinary differential equation (ODE) describing the dependence of the toxicity on the biomass. We perform a linear stability analysis in the one-dimensional finite space, we derive analytically the conditions for the appearance of Turing instability that gives rise to spatio-temporal patterns emanating from the homogeneous solution, and provide its dependence with respect to the size of the domain. Furthermore, we perform a numerical bifurcation analysis in order to study the pattern formation of the inhomogeneous solution, with respect to the precipitation rate, thus analyzing the stability and symmetry properties of the emanating patterns. Based on the numerical bifurcation analysis, we have found new patterns, which form due to the onset of secondary bifurcations from the primary Turing instability, thus giving rise to a multistability of asymmetric solutions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13065599/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147647244","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":"Reaction, diffusion, and nonlocal interaction in high-dimensional space.","authors":"Hiroshi Ishii, Yoshitaro Tanaka","doi":"10.1007/s00285-026-02391-5","DOIUrl":"10.1007/s00285-026-02391-5","url":null,"abstract":"<p><p>In this paper, we study the mathematical relationship between nonlocal interactions of convolution type and systems of multiple diffusive substances in high-dimensional spaces. Motivated by the observation that nonlocal evolution equations can reproduce similar patterns to those arising in reaction-diffusion systems, we approximate nonlocal interactions in evolution equations by solutions to appropriate reaction-diffusion systems with multiple components in Euclidean space of arbitrary dimension. The key idea of this approach is that any absolutely integrable radial kernel can be approximated by a linear combination of specific Green functions to elliptic partial differential equations. This enables us to demonstrate that a linear sum of auxiliary diffusive substances can approximate a broad class of nonlocal interactions of convolution type. Furthermore, for spatial dimensions up to three, we show that the parameters in the reaction-diffusion system can be explicitly determined depending on the kernel shape. Our results establish a connection between a broad class of nonlocal interactions and diffusive chemical reactions in dynamical systems.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147647273","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":"The role of multiscale and delayed dynamics in tuberculosis Transmission and control: a mathematical approach.","authors":"Wei Li, Yi Wang, Zhen Jin","doi":"10.1007/s00285-026-02385-3","DOIUrl":"10.1007/s00285-026-02385-3","url":null,"abstract":"<p><p>Transmission of tuberculosis (TB) among human population depends on an individual's infectiousness, which is further determined by the concentration of Mycobacterium tuberculosis (Mtb) in the body. Additionally, Mtb is resistant to dryness, cold, acidic, and alkaline environments and can survive in acidic and alkaline environments for 4-5 years. Mtb in the environment plays a significant role in TB transmission and should not be overlooked. To investigate the epidemiologic relationships among pathogens, hosts, and the environment, we first develop a multiscale TB model that includes multiple transmission routes (human-to-human and environment-to-human) and links Mtb-immune response interactions to TB transmission in population. We comprehensively analyze the dynamic properties of the fast system, slow system, and full system. Analysis results reveal that coupling bacterial processes within-host with transmission mechanisms between-host can trigger diverse complex behaviors, including both forward and backward bifurcation phenomena. This implies that thresholds routinely used to control TB infection or eliminate Mtb from an epidemiological or immunological perspective may fail under specific conditions; that is, even if the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> is less than 1, endemic equilibria may still exist in the system. Second, from a microtherapeutic point of view, we establish an impulsive time-delayed differential equation to characterize the actual medication regimen for TB. The basic reproduction number <math><msubsup><mi>R</mi> <mrow><mn>0</mn></mrow> <mo>'</mo></msubsup> </math> is defined as the spectral radius of a linear integral operator. Then, we show that <math><msubsup><mi>R</mi> <mrow><mn>0</mn></mrow> <mo>'</mo></msubsup> </math> is a critical parameter that determines the persistence of the model. More precisely, if <math> <mrow><msubsup><mi>R</mi> <mrow><mn>0</mn></mrow> <mo>'</mo></msubsup> <mo><</mo> <mn>1</mn></mrow> </math> , the disease-free periodic solution is globally attractive; if <math> <mrow><msubsup><mi>R</mi> <mrow><mn>0</mn></mrow> <mo>'</mo></msubsup> <mo>></mo> <mn>1</mn></mrow> </math> , the disease is uniformly persistent. Finally, we employ numerical methods to elucidate the interactions between population transmission dynamics and pathogen dynamics. Specifically, the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> of the full system increases rapidly with the rise in Mtb release rate, while its change is relatively slower with an increase in the immune rate. These results highlight the dominant role of chemotherapy, with immunotherapy playing only a supporting role.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147629143","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":"Age-structured mechanical models for tumor growth.","authors":"Doron Levy, Hyunah Lim, Antoine Mellet, Maeve Wildes","doi":"10.1007/s00285-026-02389-z","DOIUrl":"10.1007/s00285-026-02389-z","url":null,"abstract":"<p><p>In this paper, we introduce and analyze a mechanical model for tumor growth that takes into account the life cycle of a tumor cell. The underlying process for tumor growth is the same as in classical mechanical models: the spatial expansion of the tumor is driven by the proliferation of the cells (mitosis) which is only limited by the pressure inside the tissue. The natural incompressibility of the cells, which leads to a movement of the cells away from regions of high pressure, is taken into account via a nonlinear Darcy's law. Compared to similar models studied recently, we include an additional variable, which represents the age of the cells. The various phases of the life of a cell (growth, mitosis and death) are then dependent on this age variable. We prove the existence of weak solutions and investigate their behavior numerically, focusing on the age distribution of the cells inside the tumor, the convergence to traveling wave solutions and the existence of a threshold for the death rate for expansion/regression of the tumor.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13053348/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147629181","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":"Dynamics and suppression paradox of a stage-structured model for mosquito control.","authors":"Mugen Huang, Zixin Nie","doi":"10.1007/s00285-026-02387-1","DOIUrl":"10.1007/s00285-026-02387-1","url":null,"abstract":"<p><p>The widely used incompatible insect technique based on Wolbachia for the control of mosquito-borne diseases might be limited in field since high temperature has an adverse effect on some Wolbachia, which reduces its density in mosquitoes and induces incomplete cytoplasmic incompatibility (CI) when the larval habitats experience large temperature fluctuations. By analyzing a model of delay differential equations, we identify a threshold CI intensity, below which the infected male release would not reduce but instead increase the stable adult population level, a phenomenon called suppression paradox, which caused by the overcompensation effect of adult mosquitoes increasing when larval density decreases. For Aedes albopictus mosquitoes in Guangzhou, our simulations predict that paradox would occur if CI intensity is no more than 0.6094. Besides, to reduce at least <math><mrow><mn>80</mn> <mo>%</mo></mrow> </math> of the wild adult mosquitoes in the peak season within 8 weeks, we find that the CI intensity should be no less than 0.96, and the least release ratio is sensitive to the CI intensity.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147610244","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":"Insights into Dengue fever dynamics through advanced mathematical modeling and simulation.","authors":"Souad Bounouiga, Bilal Basti, Noureddine Benhamidouche","doi":"10.1007/s00285-026-02367-5","DOIUrl":"10.1007/s00285-026-02367-5","url":null,"abstract":"<p><p>This paper presents an innovative SITR(H)-SEI(M) model designed to analyze and understand the dynamics of dengue fever transmission. The model offers an accurate analysis of disease spread and is applied to recent health data from multiple countries, including Singapore, Costa Rica, Yemen, and India. We investigate the existence, uniqueness, and stability of solutions, and thoroughly examine the basic reproduction number, equilibrium points, and their stability effects. The results show that the disease-free equilibrium is stable when the basic reproduction number is below one, indicating control through preventive measures. Simulations demonstrate a direct relationship between transmission rates and the number of infected individuals, reinforcing the importance of swift action during outbreaks. Recommended preventive measures include insecticide spraying, distribution of treated nets, and implementation of effective treatment protocols. This study illustrates the value of continuously monitoring health data and updating the model parameters to maintain effectiveness and sustainability. These findings highlight the need for targeted interventions to reduce the basic reproduction number to below one, thereby controlling dengue transmission and ensuring community safety.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147575922","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":"Global dynamics in a reaction-diffusion competition model with edge behavior.","authors":"Kuiyue Liu, Shanshan Chen","doi":"10.1007/s00285-026-02379-1","DOIUrl":"10.1007/s00285-026-02379-1","url":null,"abstract":"<p><p>In this paper, we investigate a two-species competition model in a landscape consisting of a finite number of adjacent patches. For the two-patch scenario, by treating edge behavior at the interface as a strategy, it has been shown that there exists an ideal free distribution (IFD) strategy, which is a globally evolutionarily stable strategy. Specifically, when the resident species follows the IFD strategy and the mutant species does not, the mutant species is unable to invade the resident population. Building on this foundation, our work focuses on exploring the dynamics of the system when neither species can adopt the IFD strategy. We demonstrate that if the strategies of both species either exceed or fall below the IFD strategy, the mutant species can outcompete and eliminate the resident species, provided that its strategy is closer to the IFD strategy and its diffusion rates are equal to or slower than those of the resident species. Furthermore, if the strategies of the two species lie on opposite sides of the IFD strategy, the two species can coexist. This result is further extended to the case of an arbitrary but finite number of patches.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147576394","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":"Harmonic fields and the mechanical response of a cellular monolayer to ablation.","authors":"Oliver E Jensen, Christopher K Revell","doi":"10.1007/s00285-026-02374-6","DOIUrl":"10.1007/s00285-026-02374-6","url":null,"abstract":"<p><p>Multicellular tissues, such as the epithelium coating a developing embryo, often combine complex tissue shapes with heterogeneity in the spatial arrangement of individual cells. Discrete approximations, such as the cell vertex model, can accommodate these geometric features, but techniques for analysis of such models are underdeveloped. Here, we express differential operators defined on a network representing a monolayer of confluent cells in a framework inspired by discrete exterior calculus, considering scalar fields defined over cell vertices and centres and vector fields defined over cell edges. We achieve this by defining Hodge stars, wedge products and musical isomorphisms that are appropriate for a disordered monolayer for which cell edges and links between cell centres are not orthogonal, as is generic for epithelia. We use this framework to evaluate the harmonic vector field arising in an ablated planar monolayer, demonstrating an approximate 1/r scaling of the upper bound of the field's amplitude, where r is the distance from the ablation. Using a vertex model that incorporates osmotic effects, we then calculate the mechanical response of a monolayer in a jammed state to ablation. Perturbation displacements exhibit long-range coherence, monopolar and quadrupolar features, and an approximate 1/r near-hole upper-bound scaling, implicating the harmonic field. The upper bounds on perturbation stress amplitudes scale approximately like <math><mrow><mn>1</mn> <mo>/</mo> <msup><mi>r</mi> <mn>2</mn></msup> </mrow> </math> , a feature relevant to long-range mechanical signalling.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13033030/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147576476","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":"Reaction enhancement by flux-limited chemotaxis.","authors":"Jing An, Alexander Kiselev, Yao Yao","doi":"10.1007/s00285-026-02383-5","DOIUrl":"10.1007/s00285-026-02383-5","url":null,"abstract":"<p><p>Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines attracting monocytes to fight invading bacteria. Another example is reproduction, where eggs release pheromones that attract sperm. In this paper, we analyze a system of two reacting densities, one of which is chemotactic on another. Since the speed of any biological agents is limited, we employ flux limited chemotaxis model. Our main result is the rigorous derivation of the scaling laws showing how presence of chemotaxis affects the typical reaction time scale in two dimensions. This work builds on the results of Kiselev et al. J. Eur. Math. Soc., 25 (2023), no. 7, 2641-2696., which employed as a classical Keller-Segel chemotaxis term (not flux limited) - leading to the effect of possible over concentration and restricting the results to radial data. The model presented here is more reasonable biologically and covers broader parameter regimes.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147575880","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}