Journal of Mathematical Biology最新文献

{"title":"A predator-prey model with age-structured role reversal.","authors":"Luis Carlos Suarez, Maria K Cameron, William F Fagan, Doron Levy","doi":"10.1007/s00285-026-02402-5","DOIUrl":"10.1007/s00285-026-02402-5","url":null,"abstract":"<p><p>We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an \"ontogenetic niche shift,\" in which a species' functional role changes as it grows. This structure adds complexity to our model but increases its biological relevance. The time evolution of the age-structured predator population is motivated by the Kermack-McKendrick Renewal Equation (KMRE). Unlike KMRE, the predator population's birth and death rate functions depend on the prey population's size. We establish the existence, uniqueness, and positivity of the solutions to the proposed model's initial value problem. The dynamical properties of the proposed model are investigated via Latin Hypercube Sampling in the 15-dimensional space of its parameters. Our Linear Discriminant Analysis suggests that the most influential parameters are the maturation age of the predator and the rate of consumption of juvenile predators by the prey. We carry out a detailed study of the long-term behavior of the proposed model as a function of these two parameters. In addition, we reduce the proposed age-structured model to ordinary and delayed differential equation (ODE and DDE) models. The comparison of the long-term behavior of the ODE, DDE, and the age-structured models with matching parameter settings shows that the age structure promotes the instability of the Coexistence Equilibrium and the emergence of the Coexistence Periodic Attractor.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090279/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718839","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":"Evolution of a trait distributed over a large fragmented population: propagation of chaos meets adaptive dynamics.","authors":"Amaury Lambert, Hélène Leman, Hélène Morlon, Josué Tchouanti","doi":"10.1007/s00285-026-02371-9","DOIUrl":"10.1007/s00285-026-02371-9","url":null,"abstract":"<p><p>We consider a metapopulation made up of K demes, each containing N individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait values. Mutation and migration rates are tuned so that each deme receives a migrant or a mutant in the same slow timescale and is thus essentially monomorphic at all times for the trait value (adaptive dynamics). In the timescale of mutation/migration, the metapopulation can then be seen as a giant spatial Moran model with size K that we characterize. As <math><mrow><mi>K</mi> <mo>→</mo> <mi>∞</mi></mrow> </math> and physical space becomes continuous, the empirical distribution of the trait value (over the physical and trait spaces) evolves deterministically according to an integro-differential evolution equation. In this limit, the trait value of every migrant is drawn from this global distribution, so that conditional on its initial state, trait values from finitely many demes evolve independently (propagation of chaos). Under mean-field dispersal, the value <math><msub><mi>X</mi> <mi>t</mi></msub> </math> of the trait at time t and at any given location has a law denoted <math><msub><mi>μ</mi> <mi>t</mi></msub> </math> and a jump kernel with two terms: a mutation-fixation term and a migration-fixation term involving <math><msub><mi>μ</mi> <mrow><mi>t</mi> <mo>-</mo></mrow> </msub> </math> (McKean-Vlasov equation). In the limit where mutations have small effects and migration is further slowed down accordingly, we obtain the convergence of X, in the new migration timescale, to the solution of a stochastic differential equation which can be referred to as a new, canonical jump-diffusion of adaptive dynamics. This equation includes an advection term representing selection, a diffusive term due to genetic drift, and a jump term, representing the effect of migration, to a state distributed according to its own law.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090215/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718890","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":"Spatio-temporal pattern formation under varying functional response parametrizations.","authors":"Indrajyoti Gaine, Malay Banerjee","doi":"10.1007/s00285-026-02393-3","DOIUrl":"https://doi.org/10.1007/s00285-026-02393-3","url":null,"abstract":"<p><p>The limited availability of detailed ecological data introduces uncertainty in model predictions and constrains efforts to enhance the predictive power and robustness of nonlinear population dynamics models. While carefully chosen parameter values may yield a good fit to available datasets, alternative mathematical formulations of key component functions can sometimes provide an even better fit. The study of uncertainty in model predictions arising from such alternative formulations of component functions, such as those describing predation, is referred to as the study of structural sensitivity. In this work, we extend the concept of structural sensitivity to spatio-temporal ecological systems. We analytically derive parametric conditions that capture all possible cases for the number of homogeneous steady states, provide criteria for local bifurcations, and establish conditions for the existence or non-existence of spatially heterogeneous steady states, as well as for Turing instability, all expressed in terms of a generalized functional response. Numerical simulations using two ecologically well-established functional responses validate our analytical results and emphasize the importance of carefully selecting the mathematical formulation when modeling predator-prey interactions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718821","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":"Effects of host migration and travel loss on strain competition in a two-patch SIR model.","authors":"Bo-Sheng Chen, Chang-Hong Wu","doi":"10.1007/s00285-026-02397-z","DOIUrl":"10.1007/s00285-026-02397-z","url":null,"abstract":"<p><p>This paper investigates how host migration with travel loss affects competition between two pathogen strains in animal populations using a two-patch SIR model. We establish sufficient conditions involving migration rates and travel losses that ensure the global asymptotic stability of a single-strain endemic equilibrium or a coexistence equilibrium. Complemented by numerical simulations, our results provide insights into how competitive outcomes are shaped by the interplay among migration asymmetry, travel loss, and epidemiological traits.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090282/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718825","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":"Trajectory inference for a branching SDE model of cell differentiation via lineage tracing.","authors":"Elias Ventre, Aden Forrow, Nitya Gadhiwala, Parijat Chakraborty, Omer Angel, Geoffrey Schiebinger","doi":"10.1007/s00285-026-02375-5","DOIUrl":"10.1007/s00285-026-02375-5","url":null,"abstract":"<p><p>A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing trajectory inference methods cannot distinguish variability in net proliferation from cell differentiation dynamics, and hence require accurate prior knowledge of the proliferation rate. Building on Global Waddington-OT (gWOT), which performs trajectory inference with rigorous theoretical guarantees when birth and death can be neglected, we show how to use lineage trees available with recently developed CRISPR-based measurement technologies to disentangle proliferation and differentiation. In particular, when there is neither death nor subsampling of cells, we show that we extend gWOT to the case with proliferation with similar theoretical guarantees and computational cost, without requiring any prior information. In the case of death and/or subsampling, our method introduces a bias, that we describe explicitly and argue to be inherent to these lineage tracing data. We demonstrate in both cases the ability of this method to reliably reconstruct the landscape of a branching SDE from time-courses of simulated datasets with lineage tracing, outperforming even a benchmark using the experimentally unavailable true branching rates.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090286/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718819","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 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":2.3,"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":2.3,"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":"https://doi.org/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":2.3,"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":"https://doi.org/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":2.3,"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":2.3,"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}