Journal of Mathematical Biology最新文献

{"title":"Effects and biological consequences of the predator-mediated apparent competition I: ODE models.","authors":"Yuan Lou, Weirun Tao, Zhi-An Wang","doi":"10.1007/s00285-025-02286-x","DOIUrl":"10.1007/s00285-025-02286-x","url":null,"abstract":"<p><p>Predator-mediated apparent competition is an indirect negative interaction between two prey species mediated by a shared predator, which can lead to changes in population dynamics, competition outcomes and community structures. This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the other is invasive) and one predator model with Holling type I and II functional responses. Through the analytical results and case studies alongside numerical simulations, we find that the initial mass of the invasive prey species, capture rates of prey species, and the predator mortality rate are all important factors determining the success/failure of invasions and the species coexistence/extinction. The global dynamics can be completely classified for the Holling type I functional response, but can only be partially determined for the Holling type II functional response. For the Holling type I functional response, we find that whether the invasive prey species can successfully invade to induce the predator-mediated apparent competition is entirely determined by the capture rates of prey species. For the Holling type II functional response, the dynamics are more complicated. First, if two prey species have the same ecological characteristics, then the initial mass of the invasive prey species is the key factor determining the success/failure of the invasion and hence the effect of the predator-mediated apparent competition. Whereas if two prey species have different ecological characteristics, say different capture rates, then the success of the invasion no longer depends on the initial mass of the invasive prey species, but on the capture rates. In all cases, if the invasion succeeds, then the predator-mediated apparent competition's effectiveness essentially depends on the predator mortality rate. Precisely we show that the native prey species will die out (resp. persist) if the predator has a low (resp. moderate) mortality rate, while the predator will go extinct if it has a large mortality rate. Our study reveals that predator-mediated apparent competition is a complicated ecological process, and its effects and biological consequences depend upon many possible factors.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 5","pages":"47"},"PeriodicalIF":2.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12460439/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145132500","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":"Decoding the spatial spread of cyanobacterial blooms in an epilimnion.","authors":"Jacob Serpico, Kyung-Han Choi, B A Zambrano-Luna, Tian Xu Wang, Hao Wang","doi":"10.1007/s00285-025-02263-4","DOIUrl":"https://doi.org/10.1007/s00285-025-02263-4","url":null,"abstract":"<p><p>Cyanobacterial blooms (CBs) pose significant global challenges due to their harmful toxins and socio-economic impacts, with nutrient availability playing a key role in their growth, as described by ecological stoichiometry (ES). However, real-world ecosystems exhibit spatial heterogeneity, limiting the applicability of simpler, spatially uniform models. To address this, we develop a spatially explicit partial differential equation model based on ES to study cyanobacteria in the epilimnion of freshwater systems. We establish the well-posedness of the model and perform a stability analysis, showing that it admits two linearly stable steady states, leading to either extinction or a spatially uniform positive equilibrium where cyanobacterial biomass stabilizes at its carrying capacity. Further, we discuss the possibility of long-term spatially nonuniform solution with small diffusion and space-dependent parameters. We use the finite elements method (FEM) to numerically solve our system on a real lake domain derived from Geographic Information System (GIS) data and realistic wind conditions extrapolated from ERA5-Land. Additionally, we use a cyanobacteria estimation (CE) obtained from Sentinel-2 to set initial conditions, and we achieve strong model validation metrics. Our numerical results highlight the importance of lake shape and size in bloom monitoring, while global sensitivity analysis using Sobol Indices identifies light attenuation and intensity as primary drivers of bloom variation, with water movement influencing early bloom stages and nutrient input becoming critical over time. This model supports continuous water-quality monitoring, informing agricultural, recreational, economic, and public health strategies for mitigating CBs.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"44"},"PeriodicalIF":2.3,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145082265","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":"Mean Field Games and Ideal Free Distribution.","authors":"Robert Stephen Cantrell, Chris Cosner, King-Yeung Lam, Idriss Mazari-Fouquer","doi":"10.1007/s00285-025-02276-z","DOIUrl":"10.1007/s00285-025-02276-z","url":null,"abstract":"<p><p>The ideal free distribution in ecology was introduced by Fretwell and Lucas to model the habitat selection of animal populations. In this paper, we revisit the concept via a mean field game system with local coupling, which models a dynamic version of the habitat selection game in ecology. We establish the existence of classical solution of the ergodic mean field game system, including the case of heterogeneous diffusion when the underlying domain is one-dimensional and further show that the population density of agents converges to the ideal free distribution of the underlying habitat selection game, as the cost of control tends to zero. Our analysis provides a derivation of ideal free distribution in a dynamical context.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"46"},"PeriodicalIF":2.3,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12446418/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145082268","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":"Universality of the mean-field equations of networks of Hopfield-like neurons.","authors":"Olivier Faugeras, Etienne Tanré","doi":"10.1007/s00285-025-02271-4","DOIUrl":"https://doi.org/10.1007/s00285-025-02271-4","url":null,"abstract":"<p><p>We revisit the problem of characterising the mean-field limit of a network of Hopfield-like neurons. Building on the previous works of Ben Arous and Guionnet we establish for a large class of networks of Hopfield-like neurons, i.e. rate neurons, the mean-field equations on a time interval <math><mrow><mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace></mspace> <mi>T</mi> <mo>]</mo></mrow> </math> , <math><mrow><mi>T</mi> <mo>></mo> <mn>0</mn></mrow> </math> , of the thermodynamic limit of these networks, i.e. the limit when the number of neurons goes to infinity. Here, we do not assume that the synaptic weights describing the connections between the neurons are i.i.d. as zero-mean Gaussians. The limit equations are stochastic and very simply described in terms of two functions, a \"correlation\" function noted <math> <mrow><msub><mi>K</mi> <mi>Q</mi></msub> <mrow><mo>(</mo> <mi>t</mi> <mo>,</mo> <mspace></mspace> <mi>s</mi> <mo>)</mo></mrow> </mrow> </math> and a \"mean\" function noted <math> <mrow><msub><mi>m</mi> <mi>Q</mi></msub> <mrow><mo>(</mo> <mi>t</mi> <mo>)</mo></mrow> </mrow> </math> . The \"noise\" part of the equations is a linear function of the Brownian motion, which is obtained by solving a Volterra equation of the second kind whose resolving kernel is expressed as a function of <math><msub><mi>K</mi> <mi>Q</mi></msub> </math> . We give a constructive proof of the uniqueness of the limit equations. We use the corresponding algorithm for an effective computation of the functions <math><msub><mi>K</mi> <mi>Q</mi></msub> </math> and <math><msub><mi>m</mi> <mi>Q</mi></msub> </math> , given the weights distribution. Several numerical experiments are reported.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"45"},"PeriodicalIF":2.3,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145082335","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":"Derivation from kinetic theory and 2-D pattern analysis of chemotaxis models for Multiple Sclerosis.","authors":"M Bisi, M Groppi, G Martalò, R Travaglini","doi":"10.1007/s00285-025-02282-1","DOIUrl":"https://doi.org/10.1007/s00285-025-02282-1","url":null,"abstract":"<p><p>In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic interactions among cells. At the macroscopic level, we discuss the necessary conditions for Turing instability phenomena and the formation of two-dimensional patterns, whose shape and stability are investigated by means of a weakly nonlinear analysis. Some numerical simulations, confirming and extending theoretical results, are proposed for a specific scenario.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"43"},"PeriodicalIF":2.3,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145076440","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":"Modelling behavioural changes and vaccination in the transmission of respiratory viruses with co-infection.","authors":"Bruno Buonomo, Emanuela Penitente","doi":"10.1007/s00285-025-02280-3","DOIUrl":"10.1007/s00285-025-02280-3","url":null,"abstract":"<p><p>We consider a mathematical model to explore the effects of human behavioural changes on the transmission of two respiratory viruses, where co-infection is possible. The model includes an index to describe the human choices induced by information and rumours regarding the diseases. We first consider the case in which the public health authorities rely only on non-pharmaceutical containment measures and perform a qualitative analysis of the model through bifurcation theory, in order to analyse the existence and stability of both endemic and co-endemic equilibria. We also show the impact of the most relevant information-related parameters on the system dynamics. Then, we extend the model by assuming that a vaccine is available for each of the two viruses. We show how adherence to social distancing may be affected by information and rumours regarding the vaccination coverage in the community. Finally, we investigate the effects of seasonality by introducing a two-state switch function to represent a reduction in both vaccination and transmission rates during the summer season. We found that seasonality causes an increase in the prevalence peaks, suggesting that the detrimental effects due to the reduction of vaccination rates prevail over the beneficial ones due to the reduction of transmission.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"41"},"PeriodicalIF":2.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12441106/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145071065","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":"Global dynamics of a two-species competition patch model in a Y-shaped river network.","authors":"Weifang Yan, Shanshan Chen","doi":"10.1007/s00285-025-02284-z","DOIUrl":"https://doi.org/10.1007/s00285-025-02284-z","url":null,"abstract":"<p><p>In this paper, we investigate a two-species Lotka-Volterra competition patch model in a Y-shaped river network, where the two species are assumed to be identical except for their random and directed movements. We show that competitive exclusion can occur under certain conditions, i.e., one of the semi-trivial equilibria is globally asymptotically stable. Specifically, if the random dispersal rates of the two species are equal, the species with a smaller drift rate will drive the other species to extinction, which suggests that smaller drift rates are favored.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"42"},"PeriodicalIF":2.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145076427","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":"Petri nets in epidemiology.","authors":"Carlos Segovia","doi":"10.1007/s00285-025-02272-3","DOIUrl":"10.1007/s00285-025-02272-3","url":null,"abstract":"<p><p>This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe that any epidemiological model has the basic structures found in the SIR model of Kermack-McKendrick. This means that the basic reproduction number depends only on three substructures inside the Petri net, which are also given by three Petri nets inside, representing the susceptible population, the infection process, and the infected population. The five assumptions of the next-generation matrix method given by van den Driessche-Watmough can be described geometrically using Petri nets. Thus, the next-generation matrix results in a matrix of flows between the infection compartments with a dominant eigenvalue given by the basic reproduction number.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"40"},"PeriodicalIF":2.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12441085/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145071020","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":"Stability analysis of a non-cooperative system of reaction-diffusion equations modeling two sub-populations with mixed dispersal.","authors":"C Eleh, M Khachatryan, M A Onyido, R B Salako","doi":"10.1007/s00285-025-02281-2","DOIUrl":"10.1007/s00285-025-02281-2","url":null,"abstract":"<p><p>This study is concerned with the global stability of positive equilibrium (PE) solutions in a juvenile-adult structured diffusive model featuring a mixed dispersal mechanism. Under certain generic assumptions, we establish the uniqueness and global stability of the PE. Moreover, we show that these assumptions hold if either (i) the population disperses slowly, or (ii) the adults' reproduction rate is large. In particular, our findings demonstrate that a high adult reproduction rate always benefits species survival. Interestingly, with elevated juvenile maturity rates, the population can face extinction if the average death rate of adults surpasses their average reproduction rate. A key aspect of our analysis involves deriving the exact asymptotic limit of the principal spectrum point of some cooperative systems with mixed dispersals with respect to specific model parameters. In addition, we conducted numerical simulations to illustrate our theoretical results.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"39"},"PeriodicalIF":2.3,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145055980","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 replicator model with transport dynamics on networks for species evolution.","authors":"A Coclite, S F Pellegrino, T Politi, M Popolizio","doi":"10.1007/s00285-025-02279-w","DOIUrl":"10.1007/s00285-025-02279-w","url":null,"abstract":"<p><p>This paper proposes a network-based framework to model and analyze the evolution and dynamics of a marine ecosystem. The model involves two different length scales: the evolution of species in local reserves and the exchange of species between reserves. At the inter-reserve level, species evolution is ruled by the replicator equation, while a transport function accounts for the transport at the network level. This multi-scale approach allows for capturing both local dynamics within individual reserves and the broader connectivity and interactions across the network. We study how equilibria are modified due to the exchange between connected nodes and prove that evolutionarily stable states are asymptotically stable if the velocity transfer <math><mi>ν</mi></math> is contained within a condition involving the maximum degree of the network. A fourth-order P-(EC) <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mi>k</mi></mmultiscripts> </math> formulation of the Gauss-Legendre Runge Kutta scheme is adopted. This numerical procedure is challenged against a suitable numerical experiment involving three species on a single node for validating the robustness of the scheme in terms of accuracy for a large observation time. Several numerical experiments are provided for characterizing the abilities and limitations of the model. Three prototypical networks are considered for the case of two- and three-agent games with both linear and nonlinear transport terms. Moreover, the ability of the proposed model to reproduce synchronization phenomena on networks is discussed. This approach has been demonstrated to have the potential to uncover insights into the stability, resilience, and long-term behavior of these ecosystems, offering valuable tools for their conservation and management.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"38"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12431910/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145055864","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}