Journal of Mathematical Biology最新文献

{"title":"Disease extinction in finite time for a continuous-time SIRS model.","authors":"Abderrahman Iggidr, Mohamed Ouzahra, Gauthier Sallet","doi":"10.1007/s00285-026-02457-4","DOIUrl":"10.1007/s00285-026-02457-4","url":null,"abstract":"<p><p>This paper addresses the problem of controlling the spread of an epidemic through a multiplicatively controlled SIRS model, in which the control input modulates the infection rate in a bilinear manner. Classical approaches based on asymptotic stability only guarantee disease eradication as time tends to infinity, which may be inadequate for timely and effective intervention. To overcome this limitation, we investigate the finite-time behavior of the infected population, ensuring its convergence to zero either in finite time (FTS) or within a fixed time independent of the initial conditions (FxTS). Moreover, through an appropriate choice of the control gain, this convergence time can be arbitrarily prescribed, leading to prescribed-time stability (PrTS). We propose explicit feedback control laws under which the infected population vanishes in finite, fixed, or prescribed time, while the susceptible and recovered populations converge exponentially to their equilibrium values as time tends to infinity. Numerical simulations are provided to validate the theoretical results, illustrating rapid disease eradication and global system stability. These findings demonstrate the effectiveness of finite, fixed, and prescribed-time control strategies for controlled epidemic models and offer practical guidelines for the design of responsive and robust public health interventions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800953","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 for a primitive form of habituation in an amoeba.","authors":"Kota Nishi, Atsushi Tero, Yukinori Nishigami, Toshiyuki Nakagaki","doi":"10.1007/s00285-026-02438-7","DOIUrl":"10.1007/s00285-026-02438-7","url":null,"abstract":"<p><p>Learning abilities, once thought to be unique to higher animals, have been reported to exist in their primitive form in single-celled organisms. This has triggered a growing interest in carefully examining the nature and mechanisms of the primitive versions of learning abilities, which would provide important clues for understanding the evolution of behavioral capabilities in organisms. In this study, we focused on previous experimental studies showing that the slime mold Physarum polycephalum, a model organism for studying protist behavior, exhibits the ability to adapt to chemical environments. We propose a possible dynamic mechanism underlying this habituation, reproducing reported experimental observations with accuracy. By refining a mathematical model that was as simple as possible and based on non-specific biochemical processes within cells, we clarified a plausible mechanistic framework. Based on these results, we examined the similarities and differences between this framework and previously proposed habituation models of single-cell movement and animal neural-circuit regulation. These findings are significant because they open new avenues for research into the generality and evolutionary origins of acclimation learning.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13481565/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148801026","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":"Positive equilibria in mass action networks: geometry and bounds.","authors":"Murad Banaji, Elisenda Feliu","doi":"10.1007/s00285-026-02429-8","DOIUrl":"10.1007/s00285-026-02429-8","url":null,"abstract":"<p><p>Any mass action network gives rise to a parameterised family of polynomial equations whose positive solutions are the positive equilibria of the network. Here, we consider alternative systems of equations, whose solutions are in smooth, one-to-one correspondence with positive equilibria of the network, and capture degeneracy or nondegeneracy of the corresponding equilibria. The construction leads us to consider partitions of networks in a natural sense, and we explore the implications of choosing different partitions. The alternative systems are in some situations simpler than the original mass action equations, which allows us to rapidly identify various algebraic and geometric properties of the positive equilibrium set. This includes the characterisation of toricity and local toricity, bounds on the number of positive nondegenerate equilibria on stoichiometric classes, semialgebraic descriptions of the parameter regions for multistationarity, and the study of bifurcations. After discussing the construction of the alternative systems, various consequences for particular classes of networks and numerous examples are presented. We also develop additional techniques specifically for quadratic networks, the most common class of networks in applications, and use these techniques to derive strengthened results for quadratic networks.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13481394/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800364","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":"The effect of treatment-induced resistance in a two-strain tuberculosis model with age structure and spatial diffusion.","authors":"Shengyu Huang, Hongyong Zhao","doi":"10.1007/s00285-026-02449-4","DOIUrl":"10.1007/s00285-026-02449-4","url":null,"abstract":"<p><p>Tuberculosis (TB) is a highly contagious chronic infectious disease that, without timely intervention, can lead to severe health consequences or even death. Improper or incomplete treatment often induces the emergence of drug-resistant TB (DR-TB), which greatly complicates disease management and intensifies its public health burden. This paper develops and analyzes a two-strain TB transmission model incorporating age structure during latency, spatial diffusion, and a treatment-induced resistance pathway. Methodologically, we establish the global existence and non-negativity of model solutions and derive explicit expressions for the basic reproduction numbers of the sensitive and resistant strains, as well as for the reproduction number associated with treatment-induced resistance. This study then extends the persistence proof method for single-strain space-age structured models to examine the dynamics of competitive exclusion and persistence between the two strains. Subsequently, we characterize the local and global stability of equilibria using spectral analysis and Lyapunov function methods. Calibrating the model with WHO data for China, we estimate that the basic reproduction number for the sensitive strain exceeds one, and owing to the presence of a treatment-induced resistance pathway, the basic reproduction number for the resistant strain displays two distinct distributions, both of which remain below one. Despite this, theoretical and numerical results demonstrate that DR-TB can persist even when its basic reproduction number is less than one or even zero. Furthermore, our projections indicate that, given the current level of TB control, China is unlikely to achieve the WHO's 2035 incidence reduction target. Despite this, significant improvement in treatment efficacy and reduction of resistance induction risk could make the goal attainable. Moreover, under comparable conditions, the elimination target appears relatively easier to achieve for DR-TB. Our findings suggest that in the absence of treatment-induced resistance, the WHO's DR-TB elimination goal could be reached approximately 2 years earlier. Notably, early increases in DR-TB cases due to improved treatment should be anticipated, underscoring that TB control efforts must not only target existing DR-TB cases but also ensure standardized treatment for drug-sensitive TB (DS-TB) infections; otherwise, treatment-induced resistance in patients will further increase the TB burden.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148708364","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":"Unattainable regions in the space of genetic relationships.","authors":"Petter Mostad, Thore Egeland, Magnus Dehli Vigeland","doi":"10.1007/s00285-026-02452-9","DOIUrl":"10.1007/s00285-026-02452-9","url":null,"abstract":"<p><p>The relationship between two pedigree members may be summarized by their nine condensed identity coefficients <math><mrow><mo>(</mo> <msub><mi>Δ</mi> <mn>1</mn></msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub><mi>Δ</mi> <mn>9</mn></msub> <mo>)</mo></mrow> </math> , also known as Jacquard coefficients. These give the expected relative frequencies of the possible patterns of identity by descent between the alleles carried by the individuals at an autosomal locus. The collection J of all such vectors, taken over all pairs in all pedigrees, forms a subset of the probability simplex <math> <mrow><msup><mi>S</mi> <mn>8</mn></msup> <mo>⊂</mo> <msup><mrow><mi>R</mi></mrow> <mn>9</mn></msup> </mrow> </math> . Despite decades of constant use and recurring interest in the Jacquard coefficients, remarkably little is known about the geometry of J. For instance, a long-standing open question is whether J is dense in <math><msup><mi>S</mi> <mn>8</mn></msup> </math> , or, conversely, whether there exists full-dimensional unattainable regions not realizable by any pedigree. In the case of non-inbred individuals, this was famously resolved by Thompson, who identified the unattainable region bounded by a quadratic equation in the two-dimensional simplex of such relationships. In this paper we develop a general framework for constructing restrictions in the identity coefficients of any number of individuals. Applied to the pairwise case, we find several explicit quadratic inequalities in the nine Jacquard coefficients, each defining a full-dimensional unattainable region. One of these contains the known region unattainable by non-inbred relationships. To our knowledge, our results provide the first examples of full-dimensional holes in the space of pairwise relationships, arising purely from Mendelian constraints.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13447406/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148686654","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":"Site Frequency Spectrum in stationary branching populations.","authors":"Romain Abraham, Jean-François Delmas, Patrick Hoscheit","doi":"10.1007/s00285-026-02424-z","DOIUrl":"10.1007/s00285-026-02424-z","url":null,"abstract":"<p><p>This paper explores the Site Frequency Spectrum (SFS) in stationary branching populations. We derive estimates for the SFS associated with a sample from a continuous-state branching process conditioned to never go extinct, utilizing a quadratic branching mechanism. The genealogy of such processes is represented by a real tree with a semi-infinite branch, and we compute the expectation of the SFS under the infinitely-many-sites assumption as the sample size approaches infinity. Additionally, we present a continuum version of the SFS as a random point measure on the positive real line and compute the density of its expected measure explicitly. Finally, we derive estimates for the size of the clonal subpopulation carrying the same genotype as the most recent common ancestor of the whole population at a given time.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148686666","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":"Complex bifurcation dynamics of tumor-immune interactions incorporating combination therapies.","authors":"Yue Yang, Han Ma, Xiufen Zou","doi":"10.1007/s00285-026-02443-w","DOIUrl":"10.1007/s00285-026-02443-w","url":null,"abstract":"<p><p>The complex nonlinear dynamics of tumor-immune interactions drive tumor heterogeneity and complicate treatment strategies. While bifurcation and multistability analyses of mathematical models can uncover critical system dynamics, few studies have explored bifurcation-particularly cusp bifurcation-in high-dimensional tumor-immune systems, as most existing analyses are limited to simplified two-dimensional models. In this study, we extend the tumor-immune model proposed by Anderson et al. (2024a) to incorporate combination therapy with immune checkpoint inhibitors (ICIs) and C-C chemokine receptor type 2 (CCR2) antagonists. By combining linear algebra methods, Sotomayor's theorem, projection singularity analysis, numerical simulation, and continuation techniques, we explicitly identify transcritical and saddle-node bifurcations, conduct a systematic cusp bifurcation analysis as a classical two-parameter problem, and derive explicit quantitative conditions. Calibration against four independent murine datasets demonstrates the model's ability to reproduce tumor growth dynamics across multiple tumor datasets. Bifurcation analysis characterizes the multiplicity of tumorous equilibria, and reveals the emergence of monostable and bistable regimes. In particular, the saddle-node bifurcation curve partitions the two-parameter space under combination therapy into monostable and bistable regions. Notably, a dose-dependent inverse correlation between ICIs and CCR2 antagonists emerges along this bifurcation boundary. Our results demonstrate that effective tumor control depends not only on treatment intensity but also on the patient's initial tumor burden. The corresponding critical thresholds are determined by bifurcation structure and the stable manifold (or characteristic space) of the saddle point, respectively. These findings provide theoretical guidance for treatment design under different tumor states. Importantly, the identification of a stable low-tumor state-being clinically acceptable and controllable-highlights the potential for sustained tumor control as an alternative therapeutic objective to complete tumor eradication.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148686729","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":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">When reoxygenation fails: a dynamical model of HIF-1 <ns0:math><ns0:mi>α</ns0:mi></ns0:math> -mediated metabolic breakdown under hypoxia and SARS-CoV-2 infection.","authors":"Alexander Ryvkin, Yuri Kogan","doi":"10.1007/s00285-026-02441-y","DOIUrl":"10.1007/s00285-026-02441-y","url":null,"abstract":"<p><p>Cells normally combine glycolysis and oxidative phosphorylation (OXPHOS) to meet energy demands, but this balance shifts under pathological conditions. During SARS-CoV-2 infection, hypoxia, viral entry, and elevated tissue lactate alter cellular metabolism. To explore these effects, we propose a parsimonious mathematical model describing how oxygen levels, viral infiltration, and extracellular lactate jointly regulate metabolic balance through HIF-1 <math><mi>α</mi></math> protein, inside the cell, accounting for lactate's biphasic, non-monotonic influence on glycolysis. Model simulations reveal a single steady state whose position on the glycolysis-OXPHOS phase plane depends on environmental conditions, namely, oxygen concentration, infection, and extracellular lactate. We identify four metabolic regimes, determined by sufficiency of energy production and the driving process (OXPHOS or glycolysis). Decreasing the oxygen shifts cells from OXPHOS to glycolysis dominance in both infected and non-infected states, but infected cells may become energy-deficient even with sufficient oxygen due to virus-induced mitochondrial damage. Rising extracellular lactate initially promotes glycolysis but ultimately suppresses it at high levels, pushing cells into severe energy deficit with inhibited glycolysis. Simulations of reoxygenation exhibit hysteresis: cells pass through an energy-deficient zone during hypoxia onset but return through a safer trajectory when oxygen is restored; a vulnerability is higher in infected cells. Overall, the model clarifies metabolic trajectories during viral infection, suggesting that early hypoxia is particularly dangerous and that severe acidosis can further collapse energy production. Preventing or rapidly reversing hypoxia in respiratory infection may protect cells from energy failure and limit harmful lactate accumulation.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148686733","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":"Multiscale modelling of birth-death processes.","authors":"Tom Kimpson, Domenic P J Germano, Jennifer A Flegg, Mark B Flegg","doi":"10.1007/s00285-026-02448-5","DOIUrl":"10.1007/s00285-026-02448-5","url":null,"abstract":"<p><p>Many biological systems exhibit multiscale dynamics, where some species occur in high copy numbers while others remain rare. This heterogeneity necessitates hybrid modelling approaches: deterministic models are computationally efficient but inaccurate for low-count species, while fully stochastic simulations are accurate but prohibitively expensive. Threshold-based hybrid methods, such as the Jump-Switch-Flow (JSF) algorithm, address this by simulating low-count species stochastically and high-count species deterministically, switching at a user-chosen threshold <math><mi>Ω</mi></math> . In such methods, the choice of <math><mi>Ω</mi></math> controls the trade-off between computational cost and accuracy, but is typically made by trial-and-error: there is no principled way to choose <math><mi>Ω</mi></math> a priori for a given observable of interest. We close this gap for extinction probability. Our contribution is a computable, method-agnostic error bound that quantifies the discrepancy introduced by the threshold and yields an explicit rule for selecting <math><mi>Ω</mi></math> to meet a user-specified error tolerance. We formalise JSF as a piecewise-deterministic Markov process and derive backward equations for extinction under exact and hybrid dynamics. Near extinction boundaries, the complex nonlinear dynamics reduce to tractable time-inhomogeneous linear birth-death processes; this structure yields a rigorous error decomposition into early and late excursions, whose dominant term becomes a fast, actionable heuristic requiring only the solution of a scalar Riccati equation. Monte Carlo studies on a stochastic Lotka-Volterra model confirm that the heuristic reliably upper-bounds the empirical error in extinction probability across a wide parameter range. The framework depends only on the birth and death rates near extinction, not on the specific simulation method, and therefore applies beyond JSF to any threshold-based hybrid simulation scheme.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13433386/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664907","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":"Ideal free distribution in a system of multiple predator and prey species.","authors":"Robert Stephen Cantrell, Chris Cosner, King-Yeung Lam, Hua Zhang","doi":"10.1007/s00285-026-02428-9","DOIUrl":"10.1007/s00285-026-02428-9","url":null,"abstract":"<p><p>We study mechanisms and effects of ideal free distributions (IFDs) on an ecological community consisting of n prey and m predator species, for any positive integers n and m, by considering the corresponding diffusive Lotka-Volterra system with time-periodic coefficients. We define a notion of joint IFD in a time-periodic environment, and give necessary and sufficient conditions for it to be achieved by a subcollection of prey and predator species with suitable dispersal strategies. Next, we show, via construction of a Lyapunov functional, that such dispersal strategies are evolutionarily stable, in the sense that if a subcollection of prey and predator species adopts an ideal free dispersal strategy, then the total community must converge to an IFD for large time; if a unique combination of prey-predator species adopts an ideal free strategy, then it can drive all other species to extinction. Conversely, if a combination of prey-predator species adopts a non-ideal free dispersal strategy, then it can be invaded by some suitable mutant strategies. Our results provide insight into the evolution of spatial distribution of ecological communities with predator-prey interactions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148654981","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}