Journal of Mathematical Biology最新文献

{"title":"Global stability of an SIQR switched model with multiple two-threshold structures.","authors":"Haifeng Wang, Yanni Xiao, Xingfu Zou","doi":"10.1007/s00285-026-02432-z","DOIUrl":"10.1007/s00285-026-02432-z","url":null,"abstract":"<p><p>Prevention and control strategies play an essential role in reducing new infections of infectious diseases, while uniform and instantaneous responses to disease outbreaks are assumed in traditional epidemic models. To model the adaptive public health policies that account for hysteresis effects and heterogeneous control measures, we proposed an SIQR epidemic model with multiple two-threshold structures to describe the prevalence-dependent real-time control strategies. The formulated model incorporated the Preisach operator which effectively characterizes time-varying control strategies that depend on the historical evolution of a disease. We established the global stability of this steady-state set through an innovative analytical approach by constructing a series of Lyapunov functions corresponding to different branches of the hysteresis operator. Specifically, our results indicate that: (i) heterogeneity facilitates the convergence of system trajectories to a point within the continuum of steady-state, and (ii) greater heterogeneity leads to higher peaks of infected individuals during the evolution of an epidemic and more severe disease prevalence in the long term. Our findings reveal that the hysteresis phenomenon in control events may lead to existence of a continuum of endemic equilibria, significantly altering the effectiveness of disease suppression strategies. These results provide a theoretical foundation for designing adaptive control policies, emphasizing the importance of incorporating past intervention effects in epidemic modeling.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148498123","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":"Hyper-exponential growth in an epidemic model: some explicit solutions and their significance.","authors":"John M Halley","doi":"10.1007/s00285-026-02437-8","DOIUrl":"10.1007/s00285-026-02437-8","url":null,"abstract":"<p><p>The COVID-19 pandemic highlighted the ability of epidemics to evolve through the emergence of successive strains of greater infectiousness, which prompted the insight that hyper-exponential growth (HEG) can arise in the development of an epidemic. The phenomenon of HEG has intrigued many researchers, because of some radical differences from exponential growth such as the finite-time singularity. However, the actual mechanism of HEG was usually hidden or needed to be added phenomenologically. Thus, there was little insight into how constraints would be triggered. In this study, we explore an SIR model with evolving parameters leading to a discrete sequence of variants. This allows us to consider the HEG phenomenon in greater depth and with greater mathematical rigour. The model yields a mechanistic description of what happens at the collapse of HEG. The model also yields closed expressions for important features, such as the critical time to the singularity, in terms of basic demographic parameters. Our analysis flags a few important issues needing further research, such as the stochastic character of the emergence of variants. Greater understanding of the HEG process will yield dividends in other fields, since modern societies exhibit HEG at several levels, such as human population growth, economic indicators and technological innovation. For this reason, more research on HEG remains imperative, especially on HEG in the presence of limited resources.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13379400/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148473887","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 spatially heterogeneous diffusive two-strain epidemic model with varying total population.","authors":"J Kotounou, T J Doumatè, L Leadi, R B Salako","doi":"10.1007/s00285-026-02435-w","DOIUrl":"10.1007/s00285-026-02435-w","url":null,"abstract":"<p><p>This work investigates the dynamics of solutions to a diffusive two-strain epidemic model with varying total population size. First, assuming a spatially homogeneous environment, we show that the long-term dynamics of the diffusive model mirrors that of the corresponding system of ODE epidemic model. In this setting, we establish that the competitive-exclusion principle holds. However, when the environment is spatially heterogeneous, the global dynamics of the diffusive epidemic model is more challenging. Under some biologically meaningful assumptions, we establish results concerning the existence, uniqueness, and global stability of coexistence endemic equilibrium. Our findings highlight the complex interplay between population movement and spatial heterogeneity in shaping the dynamics of multi-strain infectious diseases.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148431032","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":"Exploring the evolution of maturation time via strong competition model with stage structure.","authors":"Jian Fang, Yifei Li, Ming Xu","doi":"10.1007/s00285-026-02426-x","DOIUrl":"10.1007/s00285-026-02426-x","url":null,"abstract":"<p><p>In evolutionary and ecological sciences, describing the adaptive dynamics of species affected by the phenotype of maturation time is challenging. In this work, considering the maturation time as a quantitative trait, we propose a stage-structured two-species competition model in a discrete environment. When competition leads to long-term bistable dynamics, we obtain the existence of pulsating waves of the population by appealing to monotone dynamical system theories. Furthermore, we numerically explore the relationship between the outcome of competition, characterised by the spreading direction of bistable pulsating waves, and the maturation time of species. When the maturation time has an inverse relationship with the competitiveness of the mature population, there may exist an optimal maturation time suggesting an evolutionarily stable strategy(ESS). Interestingly, the survival pressure from the increase of adult mortality or from spatial heterogeneity can lead to a decrease in the maturation time of ESS.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148425847","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 reaction telegraph model reveals synergy between motility strategies in Myxococcus xanthus predation.","authors":"Maxime Estavoyer","doi":"10.1007/s00285-026-02425-y","DOIUrl":"10.1007/s00285-026-02425-y","url":null,"abstract":"<p><p>The predatory bacterium Myxococcus xanthus can invade prey bacteria using two distinct motility apparatuses. It is commonly acknowledged that adventurous motility is used for isolated bacteria, while social motility corresponds to bacterial clusters. Inspired by recent biological findings, we propose a simple model of predatory invasion focusing on the co-occurrence of these two mechanisms and their possible synergistic effects. At microscopic scale, cell motion is persistent; therefore, we opt for a transport-reaction model, extending previous reaction-diffusion models. Another specificity is the structuration of the bacterial population into clusters with varying speeds and persistence times. In the linear regime, we find a transition from normal speed to anomalous speed, consistent with reaction-diffusion theory but with specificities due to the hyperbolic nature of the model. For the nonlinear regime, we numerically observe and study the existence of transitions between pulled and pushed fronts. Finally, we reproduced biological experiments with mutants lacking each of the motility apparatuses based on relevant modifications of the model. Moreover, we propose a rational basis for the reported synergistic effects. Our work paves the way for a better understanding of the complex waves of bacterial population advance, which are precursors to biofilm formation.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148425820","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":"Dynamical analysis of a stochastic dual-strain infectious model with hospital beds and logarithmic Ornstein-Uhlenbeck process.","authors":"Jiaxin Shang, Dan Li, Daihai He, Zhen Jin, Haitao Song","doi":"10.1007/s00285-026-02434-x","DOIUrl":"10.1007/s00285-026-02434-x","url":null,"abstract":"<p><p>Strain evolution poses a global threat, yet medical resources often fall short of meeting the demands of such public health emergencies. To examine how constrained medical resources and random factors influence disease transmission dynamics, this study incorporates the limited number of hospital beds into a stochastic infectious disease model that accounts for strain evolution and transmission rate affected by the logarithmic Ornstein-Uhlenbeck process. The primary contributions include deriving sufficient conditions that guarantee the existence, uniqueness and boundedness of the positive global solution for the stochastic model, identifying thresholds governing disease extinction and persistence and establishing sufficient conditions for the existence of a stationary distribution, based on which we compute the probability density function of the model to quantify the final size of the disease from a statistical perspective. Numerical simulations indicate that: (i) when strain 1 exhibits dominant transmissibility, it secures a dominant competitive position via its transmission advantage, while strain 2 sustains endemic transmission by exploiting recovered individuals, enabling the long-term coexistence of both strains. By contrast, when the two strains have comparable transmissibility, strain 1, which depends exclusively on susceptible individuals for transmission and survival, is eliminated via competitive exclusion by strain 2 (which can infect individuals recovered from strain 1), and is ultimately driven to extinction; (ii) for epidemic prevention and control, we should not only constrain the mean transmission rate of the disease below the epidemic threshold, but also reserve an adequate control safety margin against stochastic fluctuations in transmission rate; (iii) in the early stage of an epidemic when medical resources are scarce, it is necessary to rapidly expand hospital bed capacity. Once resource supply matches the epidemic demand, the focus of prevention and control should be shifted to optimizing the efficiency of resource scheduling. These results have certain significance for preventing and controlling diseases with such transmission patterns.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148425830","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":"Numerical modeling of fluid exchange between a collecting lymphatic vessel and the surrounding tissue.","authors":"Marina Furkes, Sanjoy Saha, N Keilany Lightsey, Donny Hanjaya-Putra, Martina Bukač","doi":"10.1007/s00285-026-02431-0","DOIUrl":"10.1007/s00285-026-02431-0","url":null,"abstract":"<p><p>Lymphatic vessel dysfunction is increasingly recognized in metabolic diseases, contributing to edema, dyslipidemia, and tissue lipid accumulation. Type 2 diabetes has been experimentally linked to lymphatic vascular defects characterized by enhanced permeability resulting from low nitric oxide (NO) bioavailability. To examine the effects of this dysfunction, we developed a mathematical model of fluid exchange between a collecting lymphatic vessel and the surrounding tissue. The lymph flow is modeled using the Stokes equations for an incompressible, viscous fluid, while the collecting vessel is represented by a thin Koiter shell model. The main novelty of our approach is that the interstitium is described as poroelastic, and modeled using the Biot equations, which capture both porous medium flow and the displacement. Lymph movement within the vessel is regulated by biological factors, specifically calcium ion ( <math><msup><mtext>Ca</mtext> <mrow><mn>2</mn> <mo>+</mo></mrow> </msup> </math> ) concentration and NO production, which are included to modulate the pumping mechanism. Using this model, we quantify lymph flow and fluid exchange for both wild-type (WT) and diabetic vessels. Our findings illustrate how variations in NO production rate, Young's modulus, and hydraulic conductivity impact leakage and pumping efficiency. The results demonstrate that reduced NO production in diabetic conditions leads to increased fluid leakage and altered pulsation frequency, while increased vessel stiffness further compromises lymphatic function.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13342411/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148399817","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 perception-memory PDE framework for seasonal migration dynamics.","authors":"Qi An, Xiunan Wang, Pinar Baydemir, William F Fagan, Peng Wu, Briana Abrahms, Hao Wang","doi":"10.1007/s00285-026-02423-0","DOIUrl":"10.1007/s00285-026-02423-0","url":null,"abstract":"<p><p>Seasonally migrating animals must navigate environments where resources shift predictably but are increasingly perturbed by climate change and human activities. Empirical work highlights the importance of cognition for these movements, yet the joint roles of perception and memory in sustaining stable seasonal migration remain poorly understood. We develop and analyze a novel PDE (partial differential equation) model that couples random dispersal with two taxis processes: perception-driven movement toward a nonlocally sensed, periodically shifting resource, and memory-driven movement guided by a spatiotemporal map of past foraging successes over seasonal time windows. We first establish global well-posedness of the system, proving existence, uniqueness, and uniform boundedness of classical solutions. Using Leray-Schauder degree theory, we then show that the model admits at least one time-periodic solution synchronized with the seasonal resource. By constructing a Lyapunov-Krasovskii functional, we further derive sufficient conditions under which this periodic migratory pattern is unique and globally asymptotically stable, revealing a key trade-off between perception- and memory-driven taxis strengths and diffusive spreading. Numerical simulations corroborate the analytical results and demonstrate how the balance of perception and memory, the precision of memory, and its match or mismatch with environmental periodicity jointly govern migration efficiency and persistence. Together, these results provide a rigorous theoretical framework linking individual-level cognitive processes to the emergence, stability, and breakdown of seasonal migration routes in changing environments.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148388363","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":"Spatiotemporal SEIQR Epidemic Modeling with Optimal Control for Vaccination, Treatment, and Social Measures.","authors":"Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi","doi":"10.1007/s00285-026-02430-1","DOIUrl":"10.1007/s00285-026-02430-1","url":null,"abstract":"<p><p>This paper introduces a spatiotemporal SEIQR epidemic model governed by a system of reaction-diffusion partial differential equations that incorporates optimal control strategies. The model captures the transmission dynamics of an infectious disease across space and time. The model incorporates the quarantined compartment Q as part of the epidemic structure. It also includes three time-dependent control variables representing vaccination, treatment of quarantined individuals, and non-pharmaceutical interventions that reduce transmission. The study has four main objectives: (i) to prove the existence, uniqueness, and positivity of global strong solutions using analytic semigroup theory, (ii) to demonstrate the existence of optimal control strategies through functional analysis techniques, (iii) to derive first-order necessary optimality conditions via convex perturbation methods and adjoint equations, and (iv) to perform numerical simulations to assess the effectiveness of different combinations of control interventions. The simulation results emphasize the advantages of combining pharmaceutical and non-pharmaceutical interventions to minimize disease prevalence and control-related expenses.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148377326","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":"Dynamic resource allocation in eukaryotic Resource Balance Analysis.","authors":"Saeed Sadeghi Arjmand","doi":"10.1007/s00285-026-02436-9","DOIUrl":"10.1007/s00285-026-02436-9","url":null,"abstract":"<p><p>Resource Balance Analysis (RBA) is a framework for predicting steady-state cellular growth under resource constraints. However, classical RBA formulations are static and do not capture the dynamic regulation of biosynthetic resources or macromolecular turnover, which is particularly important in eukaryotic cells. In this work, we propose a dynamic extension of eukaryotic RBA based on an optimal control formulation. Cellular growth is modeled as the result of a time-dependent allocation of translational capacity between metabolic enzymes and macromolecular machinery, aimed at maximizing biomass accumulation over a finite time horizon. Using Pontryagin's Maximum Principle, we characterize optimal allocation strategies and show that steady-state RBA solutions arise as limiting regimes of the dynamic problem.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148383212","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}