Journal of Mathematical Biology最新文献

{"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":"https://doi.org/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":"https://doi.org/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":"https://doi.org/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}

{"title":"Dynamics of pairwise-based SIS epidemic models on clustered networks with higher-order interactions.","authors":"Qingchu Wu, Zhaoyan Wu","doi":"10.1007/s00285-026-02439-6","DOIUrl":"10.1007/s00285-026-02439-6","url":null,"abstract":"<p><p>In clustered networks, the influence of higher-order interactions on disease dynamics has received limited attention. This paper investigates the susceptible-infected-susceptible epidemic model on clustered regular networks using the pair mean-field approach, where higher-order effects are explicitly considered in dynamic analysis. An auxiliary system is constructed to derive the analytical expression of the epidemic threshold. Through theoretical analysis and numerical simulations, we systematically explore the impacts of network clustering and higher-order interactions on epidemic invasion and persistence thresholds. The results reveal that stronger higher-order interactions reduce both invasion and persistence thresholds, while an increase in the network clustering coefficient raises the epidemic threshold. Furthermore, these phenomena cannot be fully captured by the conventional one-vertex mean-field approximation. This work highlights the vital roles of clustering structures and higher-order interactions in epidemic spreading and verifies the effectiveness of the pair mean-field method for analyzing higher-order network dynamics.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148632516","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":"Entrance saturation as a control point for recruitment robustness in social insect colonies.","authors":"Tao Feng, Xin Xu, Russell Milne, Zhiwei Zhu","doi":"10.1007/s00285-026-02440-z","DOIUrl":"10.1007/s00285-026-02440-z","url":null,"abstract":"<p><p>Nest entrance crowding and inhibitory feedback limit recruiter-worker encounters in social insects, yet explicit capacity constraints are rarely modeled. We introduce a minimal capacity-limited recruitment mechanism with worker-dependent saturation that represents entrance congestion and inhibitory signaling, and embed it in a four-compartment model together with an aggregate model. Analytically, we derive boundary replacement thresholds that separate maintenance from loss of alarm and recruiters, and a colony-level replacement ratio <math><msub><mi>R</mi> <mn>0</mn></msub> </math> for the aggregate model. The aggregate dynamics are globally convergent: every trajectory approaches an equilibrium, and periodic orbits are absent. Coexistence equilibria are determined by a cubic in available workers, so at most three occur. In the full model they are organized by a quartic, and up to four can occur under restricted regimes. The model yields testable predictions. Increasing saturation lowers <math><msub><mi>R</mi> <mn>0</mn></msub> </math> , renders it concave in colony size, attenuates the marginal effect of direct recruitment at high availability, and can reverse sensitivities to nest departure and return. Therefore, the stable interior equilibrium may occur at either low or high worker availability. In the full model, crowding reduces recruiter replacement thresholds but leaves the alarm threshold unchanged, which yields a permanence condition for coexistence. Numerical analyses map multistability windows and show that stronger saturation narrows multistability, suppresses or bounds periodic orbits, expands the basin of attraction of the worker-only state, and recovers bilinear behavior as saturation vanishes. These results link entrance design and flow control to colony-level robustness against over-recruitment and suggest interventions that ease entrance crowding, strengthen direct recruitment, or increase recruiter retention.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148622402","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":"An HIV-TB co-infection model: analysis and data-driven insights for China.","authors":"Chenglong Wang, Ling Xue, Yunfei Xia, Xuezhi Li, Jeffrey Shaman","doi":"10.1007/s00285-026-02444-9","DOIUrl":"10.1007/s00285-026-02444-9","url":null,"abstract":"<p><p>In this work, we propose an HIV-TB coinfection model that incorporates time since recovery from TB. We derive the basic reproduction numbers and the invasion reproduction numbers associated with the two infections, and investigate the existence as well as the local and global stability of the disease-free, HIV-only, and TB-only equilibria. Using data on new HIV and TB cases in China from 2005 to 2019, we estimate the optimal model parameters, and perform a sensitivity analysis of the invasion reproduction numbers. Theoretical analysis and numerical simulations reveal that coexistent equilibria arise in multiple regions of the parameter space. Moreover, bistability and limit cycles may arise under specific conditions. Our study finds that focusing TB control alone is insufficient to continuously reduce the disease burden; without concurrently suppressing HIV transmission, HIV invasibility may increase, reducing the effectiveness of TB control. Therefore, we emphasize that HIV prevention and TB treatment should be carried out simultaneously, and co-infected individuals should be isolated to effectively control the spread. These results support the implementation of integrated HIV-TB control strategies and provide scientific evidence to inform medium and long term planning, monitoring, and evaluation.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148622438","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":"Genome rearrangements as double coset Markov chains.","authors":"Mackenzie A Simper","doi":"10.1007/s00285-026-02450-x","DOIUrl":"10.1007/s00285-026-02450-x","url":null,"abstract":"<p><p>Permutation groups provide a natural framework for modeling genomes and their rearrangement events, which is crucial for understanding evolutionary relationships. Double cosets can be used to model objects arising from multiple symmetries, such as circular genomes with repeated genes. Suppose <math> <mrow><mrow><mi>λ</mi></mrow> <mo>=</mo> <mrow><mo>(</mo> <msub><mi>λ</mi> <mn>1</mn></msub> <mo>,</mo></mrow> <mrow><msub><mi>λ</mi> <mn>2</mn></msub> <mo>,</mo></mrow> <mrow><mo>⋯</mo> <mo>,</mo> <msub><mi>λ</mi> <mi>k</mi></msub> <mrow><mo>)</mo></mrow> </mrow> </mrow> </math> is a partition of <math><mrow><mi>n</mi></mrow> </math> which indicates the number of repeated regions or genes of different types ( <math> <mrow><msub><mi>λ</mi> <mi>i</mi></msub> </mrow> </math> of type <math><mrow><mi>i</mi></mrow> </math> with <math><mrow><mi>n</mi></mrow> </math> total regions). A circular genome with <math><mrow><mi>n</mi></mrow> </math> oriented regions determined by <math><mrow><mi>λ</mi></mrow> </math> can be identified with the double coset space <math> <mrow> <msub><mrow><mi>S</mi></mrow> <mrow><mi>λ</mi></mrow> </msub> <mrow><mo></mo></mrow> <msub><mrow><mi>B</mi></mrow> <mrow><mi>n</mi></mrow> </msub> <mo>/</mo> <msub><mrow><mi>D</mi></mrow> <mrow><mi>n</mi></mrow> </msub> </mrow> </math> , where <math> <mrow><msub><mi>B</mi> <mi>n</mi></msub> </mrow> </math> is the hyperoctahedral group, <math> <mrow><msub><mi>D</mi> <mi>n</mi></msub> </mrow> </math> the dihedral group extended to <math> <mrow><msub><mi>B</mi> <mi>n</mi></msub> </mrow> </math> , and <math> <mrow><msub><mi>S</mi> <mi>λ</mi></msub> </mrow> </math> the Young subgroup extended to <math> <mrow><msub><mi>B</mi> <mi>n</mi></msub> </mrow> </math> . This paper develops this correspondence and derives formulas for the sizes of double cosets and the number of double cosets in special cases. The size of double cosets gives the induced probability distribution on genomes from uniformly sampling <math> <mrow><msub><mi>B</mi> <mi>n</mi></msub> </mrow> </math> . The representation is utilized to define Markov chains which capture the processes of inversions, transpositions, and translocations.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13407585/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148594285","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}