Journal of Mathematical Biology最新文献

{"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}

{"title":"Taking into account the influence of climatic factors and age in the mathematical modeling and analysis of the dynamic transmission of malaria.","authors":"Séraphin Djaoué, Ezekiel Dangbé, Damakoa Irépran, Antoine Perasso","doi":"10.1007/s00285-026-02442-x","DOIUrl":"10.1007/s00285-026-02442-x","url":null,"abstract":"<p><p>Malaria is the most widespread and deadly parasitic disease in the world. This disease is transmitted from an infected individual to a healthy individual via the female Anopheles mosquito. Children under the age of 5 are most at risk from this infectious disease. Sub-Saharan Africa is most affected by malaria in the world. The geographical distribution and seasonality of the malaria cases observed are closely related to the climatic factors (temperature and precipitation) that influence its transmission dynamics. To control this disease, the use of insecticide treated nets and education of the population for a clean environment without mosquito breeding grounds has been advocated. To perform a mathematical analysis of malaria dynamics, a mathematical model describing malaria transmission must take into account intra-annual climate variation, compliance with measures to reduce contact with mosquitoes, and the age structure of the population. Some mathematical models developed are mainly concerned with the influence of climatic factors on transmission dynamics. Other models are being developed to assess the impact of control factors such as the use of insecticide-treated nets on the behaviour of changes in the number of malaria cases. For a more appropriate analysis, in this paper, we simultaneously assess the impact of climate, the proportion of people who comply with malaria control measures, and the age structure of the population. To take into account the temporal variation of the defined parameters as a function of temperature and precipitation, we describe the dynamics of malaria transmission using a non-autonomous system of ordinary differential equations. The mathematical analysis of the model allowed us to establish the biological properties and asymptotic behavior of the model solutions. From numerical simulations, we assessed the threshold proportion of people who comply with the rules that is necessary to control malaria dynamics, which is 0.5. Using two cities in Cameroon, Maroua and Ngaoundere with different climatic data, we highlighted the influence of climate on the evolution of the number of new malaria cases.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148594410","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 Degenerate Bifurcation Perspective on High Sensitivity in a Modified Leslie-Gower Model with Additive Allee Effect.","authors":"Xiaoling Wang, Kuilin Wu, Lan Zou","doi":"10.1007/s00285-026-02447-6","DOIUrl":"10.1007/s00285-026-02447-6","url":null,"abstract":"<p><p>The population dynamics in a modified Leslie-Gower model with an additive Allee effect are highly sensitive to both parameters and initial population densities, leading to outcomes ranging from coextinction to sustained multistable steady states. This work links this sensitivity to complicated bifurcations. We establish the existence of a codimension 4 nilpotent cusp and a corresponding degenerate Bogdanov-Takens bifurcation with codimension 4, which critically shape the system's response to parameter changes. Moreover, we detected that the number of limit cycles bifurcated from Hopf bifurcation can be as high as five-a phenomenon scarcely documented in previous ecological studies, thereby inducing a pronounced dependence of oscillatory regimes on initial conditions. Numerical simulations confirming heteroclinic loops and multiple limit cycles provide consistent support for the theoretical analysis.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148594315","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":"Elusive chaos: dynamics of a data-based model of flour beetle growth with time delay.","authors":"Samantha J Brozak, Dalia N Cabada Pesantez, Sophia Peralta, John D Nagy, Yang Kuang","doi":"10.1007/s00285-026-02445-8","DOIUrl":"10.1007/s00285-026-02445-8","url":null,"abstract":"<p><p>The LPA model is a discrete-time map that has been well-studied and well-validated with experimental data using Tribolium castaneum. We argue that the long lifespan of adults warrants the use of a continuous-time model, and thus we propose a two-dimensional system of delay differential equations to describe Tribolium dynamics. We show that the time delay allows for the periodic behavior that characterizes flour beetle populations. We illustrate the global stability of the extinction equilibrium for <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></mrow> </math> . Because of nonlinearities in the model, we analyze stability of the positive equilibrium in the special case when there is no adult cannibalism of pupae, exploring the biological parameter space, and finally using a quasi-steady-state argument to reduce the model. We study bifurcations numerically and, unlike previous work, find that larvae development rate and larvae mortality affect the potential for asymptotic cyclic behavior, while other parameters (adult egg production rate per day and adult mortality) influence cycles in the transient phase. This study suggests that model structure and form play an important role in finding chaos.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148594274","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 novel mathematical model of seasonality in Oropouche virus transmission in Amazonas, Brazil.","authors":"Carli Peterson, Darsh Gandhi, Emma Slack, Elizabeth Rubio, Amira Claxton, Christopher M Kribs","doi":"10.1007/s00285-026-02422-1","DOIUrl":"10.1007/s00285-026-02422-1","url":null,"abstract":"<p><p>Oropouche virus (OROV) is a vector-borne arbovirus that has caused more than 500,000 infections across South America, Central America, and the Caribbean. Its primary vector, the midge species Culicoides paraensis, acquires the virus from wild reservoir hosts and transmits it to humans during blood feeding. As outbreaks within the Amazon basin continue to occur and confirmed cases steadily increase, a proper understanding of the interplay between climatic variables, vector behavior, and OROV transmission is needed to develop effective public health interventions. In this paper, we develop a novel mathematical model of Oropouche virus spread in Amazonas, Brazil using ordinary differential equations (ODEs). First, we derive the basic reproductive number at baseline to assess the potential for disease persistence. We then incorporate seasonal forcing and fit the model to weekly incidence data from the 2023-2024 outbreak using least squares optimization. With our model structure, we evaluated multiple candidate seasonality functions and implementations, including precipitation-based forcing functions and others intended to model general seasonality or the right-skewed incidence curve. Among these, quantitative results show that the seasonal variation in OROV transmission is best explained (in the sense of minimum <math><msup><mi>l</mi> <mn>2</mn></msup> </math> error) by an exponentially decaying pulse applied to midge recruitment, which captures the incidence data with a relative <math><msup><mi>l</mi> <mn>2</mn></msup> </math> error of 11.94%. While moderate levels of observational noise can affect the relative ranking of seasonal mechanisms, the exponential pulse remained the best-performing forcing function to describe the observed incidence data.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13395843/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148580865","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 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}