Bulletin of Mathematical Biology最新文献

{"title":"A Filippov Model Describing the Effect of Social Distancing in Controlling Infectious Diseases.","authors":"Aili Wang, Yinjiao Gong, Duo Bai, Weike Zhou, Stacey R Smith","doi":"10.1007/s11538-025-01530-1","DOIUrl":"https://doi.org/10.1007/s11538-025-01530-1","url":null,"abstract":"<p><p>Social distancing is now a familiar strategy for managing disease outbreaks, but it is important to understand the interaction between disease dynamics and social behaviour. We distinguished the fully susceptibles from the social-distancing susceptibles and proposed a Filippov epidemic model to study the effect of social distancing on the spread and control of infectious diseases. The threshold policy is defined as follows: once the number of infected individuals exceeds the threshold value, social-distancing susceptibles take more stringent social-distancing practices, resulting in a decreasing infection rate. The target model exhibits novel dynamics: in addition to the coexistence of two attractors, it also demonstrates the coexistence of three attractors. In particular, bistability of the regular endemic equilibrium and the disease-free equilibrium occurs for the system; multistability of the regular endemic equilibrium, a pseudo-equilibrium and the disease-free equilibrium also occurs for the system. Discontinuity-induced bifurcations, including boundary-node, focus and saddle-node bifurcations, occur for the proposed model, which reveals that a small change in threshold values would significantly affect the outcome. Our findings indicate that for a proper threshold value, the infections can be ruled out or contained at the previously given level if the initial infection is relatively small.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 11","pages":"156"},"PeriodicalIF":2.2,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145249764","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":"Periodic Oscillations and Transient Dynamics Caused by Saturating Density-Dependent Benefits and Costs in Obligate Mutualisms.","authors":"Xue-Meng Song, Feng Zhang, Yan-Ping Liu, Ming-Rui Song, Jia-Xu Han, Rui-Wu Wang","doi":"10.1007/s11538-025-01531-0","DOIUrl":"https://doi.org/10.1007/s11538-025-01531-0","url":null,"abstract":"<p><p>It is generally recognized that oscillatory dynamics of mutualism systems arise from external factors such as environmental fluctuations and additional interspecific interactions. However, we here theoretically demonstrate that the saturating density dependence of mutualistic benefits and costs can lead to the periodic oscillations of obligate mutualism systems. This suggests that the dynamic complexity of mutualisms can also arise intrinsically. Our model differentiates benefits in mutualistic interactions from costs and assumes they respectively influence the reproduction rate and mortality of populations. In the symmetric case, where the model structure and parameters are the same for both species, this model shows multiple equilibria and oscillatory dynamics. The difference between benefit and cost may be the primary determinant of these phenomena. The system exhibits damped or periodic oscillations when this difference is intermediate. The two species can stably coexist when benefits significantly outweigh costs, whereas the system faces extinction when costs become relatively high. Asymmetry in benefit and cost between mutualists dramatically changes the system's dynamical regimes. Essentially, these oscillations of mutualism are caused by the transitions of the system between mutualism and antagonism. In addition, our model reveals the transient dynamics of the mutualism system (a phenomenon of regime shift without parameter change), including saddle crawl-bys (moving slowly by saddles) and ghost attractors (slow change in system state near the attractors). Our findings highlight the crucial role of nonlinear benefits and costs in the dynamical complexity of mutualisms.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 11","pages":"154"},"PeriodicalIF":2.2,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145211782","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, Analysis and Simulation of Cancer Invasion Mediated by Bound and Soluble Enzymes.","authors":"Mariya Ptashnyk, Chandrasekhar Venkataraman","doi":"10.1007/s11538-025-01535-w","DOIUrl":"10.1007/s11538-025-01535-w","url":null,"abstract":"<p><p>We formulate a cell-scale model for the degradation of the extra-cellular matrix by membrane-bound and soluble matrix degrading enzymes produced by cancer cells. Based on the microscopic model and using tools from the theory of homogenisation we propose a macroscopic model for cancer cell invasion into the extra-cellular matrix mediated by bound and soluble matrix degrading enzymes. For suitable and biologically relevant initial data we prove the macroscopic model is well-posed. We propose a finite element method for the numerical approximation of the macroscopic model and report on simulation results illustrating the role of the bound and soluble enzymes in cancer invasion processes.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 11","pages":"155"},"PeriodicalIF":2.2,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12494659/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145225032","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 Dichotomy Law for Certain Classes of Phylogenetic Networks.","authors":"Michael Fuchs, Mike Steel","doi":"10.1007/s11538-025-01536-9","DOIUrl":"10.1007/s11538-025-01536-9","url":null,"abstract":"<p><p>Many classes of phylogenetic networks have been proposed in the literature. A feature of several of these classes is that if one restricts a network in the class to a subset of its leaves, then the resulting network may no longer lie within this class. This has implications for their biological applicability, since some species - which are the leaves of an underlying evolutionary network - may be missing (e.g., they may have become extinct, or there are no data available for them) or we may simply wish to focus attention on a subset of the species. On the other hand, certain classes of networks are 'closed' when we restrict to subsets of leaves, such as (i) the classes of all phylogenetic networks or all phylogenetic trees; (ii) the classes of galled networks, simplicial networks, galled trees; and (iii) the classes of networks that have some parameter that is monotone-under-leaf-subsampling (e.g., the number of reticulations, height, etc.) bounded by some fixed value. It is easily shown that a closed subclass of phylogenetic trees is either all trees or a vanishingly small proportion of them (as the number of leaves grows). In this short paper, we explore whether this dichotomy phenomenon holds for other classes of phylogenetic networks, and their subclasses.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 11","pages":"153"},"PeriodicalIF":2.2,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12484314/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145198385","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":"Lower Bounds on the Sample Complexity of Species Tree Estimation when Substitution Rates Vary Across Loci.","authors":"Max Hill, Sebastien Roch","doi":"10.1007/s11538-025-01533-y","DOIUrl":"10.1007/s11538-025-01533-y","url":null,"abstract":"<p><p>In this paper we analyze the effect of substitution rate heterogeneity on the sample complexity of species tree estimation. We consider a model based on the multi-species coalescent (MSC), with the addition that gene trees exhibit random i.i.d. rates of substitution. Our first result is a lower bound on the number of loci needed to distinguish 2-leaf trees (i.e., pairwise distances) with high probability, when substitution rates satisfy a growth condition. In particular, we show that to distinguish two distances differing by length f with high probability, one requires <math><mrow><mi>Ω</mi> <mo>(</mo> <msup><mi>f</mi> <mrow><mo>-</mo> <mn>2</mn></mrow> </msup> <mo>)</mo></mrow> </math> loci, a significantly higher bound than the constant rate case. The second main result is a lower bound on the amount of data needed to reconstruct a 3-leaf species tree with high probability, when mutation rates are gamma distributed. In this case as well, we show that the number of gene trees must grow as <math><mrow><mi>Ω</mi> <mo>(</mo> <msup><mi>f</mi> <mrow><mo>-</mo> <mn>2</mn></mrow> </msup> <mo>)</mo></mrow> </math> .</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 11","pages":"152"},"PeriodicalIF":2.2,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145181817","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":"On the Improvement of the Sterile Insect Technique by Entomopathogenic Fungi: Impact of Residual Fertility and Re-mating Behaviour.","authors":"Yves Dumont","doi":"10.1007/s11538-025-01529-8","DOIUrl":"10.1007/s11538-025-01529-8","url":null,"abstract":"<p><p>This study investigates the use of the Sterile Insect Technique (SIT) combined with Entomopathogenic Fungi soil treatment (EPFS) to control two major pests: the Mediterranean fruit fly and the Oriental fruit fly. The SIT involves releasing sterile males to mate with wild females, but the challenge lies in female polyandry (re-mating) and residual fertility in sterile males. We develop a continuous release SIT model with single- and double-mated females, but with a novel approach to accounting the residual fertility parameter, <math><mi>ε</mi></math> . We also consider scenarios where the competitiveness of sterile males may decline between the first and the second mating. A key finding is that insect elimination, at least locally, with SIT can only occur when the product of the residual fertility parameter, <math><mi>ε</mi></math> , and the basic reproduction number of sterile mated females, <math><msub><mi>R</mi> <mi>S</mi></msub> </math> , is less than 1. We also prove the existence of a sterile male release threshold, above which global elimination is possible. When <math><mrow><mi>ε</mi> <msub><mi>R</mi> <mi>S</mi></msub> </mrow> </math> is greater than one, elimination is impossible regardless of the size of sterile male releases. We also extend our results to periodic releases. We illustrate our theoretical findings using numerical simulations, with parameters from the Mediterranean fruit fly (medfly), with and without ginger root oil (GRO) treatment, and the oriental fruit fly, with and without Methyl-Eugenol (ME) treatment. Both treatments are known to enhance sterile male competitiveness. We also show that combining SIT with EPFS can greatly improve SIT efficiency, and, in particular, reduce the constraint on residual fertility. We conclude that re-mating and residual fertility can have a significant impact on the effectiveness of SIT. However, this mainly depends on whether SIT is used in combination with EPFS or not, and also on the knowledge of the parameters of sterile-mated females which seem to have been superficially studied in many SIT programs so far.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 10","pages":"151"},"PeriodicalIF":2.2,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12443905/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145074422","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":"Spatiotemporal Dynamics of a Mussel-Algae Model on the Square Domain.","authors":"Daifeng Duan, Zuolin Shen, Yuan Yuan, Quanxing Liu","doi":"10.1007/s11538-025-01526-x","DOIUrl":"10.1007/s11538-025-01526-x","url":null,"abstract":"<p><p>We investigate the spatiotemporal dynamics of a non-local mussel-algae model, defined on a square domain with time delays and Neumann boundary conditions. Initially, we examine the well-posedness of the solutions. By analyzing the multiplicity of eigenvalues, we establish the existence of both Hopf and equivariant Hopf bifurcations. Using tools such as phase space decomposition, center manifold reduction, equivariant Hopf bifurcation theory, and the normal form method, we derive third-order truncated normal forms near the equivariant Hopf bifurcation point. This allows us to classify the system's spatiotemporal patterns into ten distinct types within the parameter plane. Unlike models constructed on one-dimensional domains, the two-dimensional symmetric model demonstrates more complex dynamic behaviors, including standing waves, rotating waves, stripes, and spots. Numerical simulations not only corroborate the theoretical predictions but also align with field observation in ecological systems, shedding light on the mechanisms underlying the formation of regular patterns due to the behavioral aggregation of mussels.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 10","pages":"150"},"PeriodicalIF":2.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145051699","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":"Enhancing Disease Control in Resource-Limited Settings Through Bidirectional Behavioral Responses.","authors":"Sujit Halder, Sudipta Panda, Amit Samadder, Joydev Chattopadhyay","doi":"10.1007/s11538-025-01514-1","DOIUrl":"10.1007/s11538-025-01514-1","url":null,"abstract":"<p><p>Human behavior plays a pivotal role in mitigating the global spread of infectious diseases, rendering it an indispensable characteristic of effective disease control efforts. While prior research has examined behavioral changes in disease control either through the force of infection or prevalence-based recruitment, the combined effects of these approaches remain largely unexplored. To bridge this gap, we develop a mathematical model that integrates behavioral modifications from both perspectives, with a focus on resource-limited settings-a critical factor for managing re-emerging diseases. Our analytical results indicate that disease dynamics are influenced not only by the basic reproduction number ( <math><msub><mi>R</mi> <mn>0</mn></msub> </math> ) but also regulated by a threshold value ( <math><msub><mi>R</mi> <mi>c</mi></msub> </math> ), which can lead to disease persistence through backward bifurcation. The model reveals a complex dynamic view, highlighting the intricate role of behavioral modifications in suppressing multiple waves of infection. To optimize behavioral strategies, we introduce a contour-area optimization method to identify the most effective responses. Using real-world data from the Monkeypox outbreaks in the United States of America. and the Democratic Republic of Congo (spanning January 7 to August 13, 2024), we estimated critical parameters for both regions. The results highlight a significant reduction in <math><msub><mi>R</mi> <mn>0</mn></msub> </math> when behavioral interventions targeted both transmission pathways, compared to focusing solely on one. Furthermore, we provide short- and long-term forecasts of the effects of these interventions, offering actionable insights for resource-constrained countries. This research underscores the importance of behavioral adaptations in strengthening disease control measures and advancing sustainable public health efforts, even in regions with sparse resources.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 10","pages":"149"},"PeriodicalIF":2.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145039186","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":"The implications of host-pathogen co-evolutionary outcomes on macro-epidemics based on a combined-host strategy.","authors":"Qiutong Liu, Yanni Xiao, Stacey R Smith","doi":"10.1007/s11538-025-01517-y","DOIUrl":"10.1007/s11538-025-01517-y","url":null,"abstract":"<p><p>Host defense and pathogen virulence interact and mutually shape each other's evolution. Host-pathogen co-evolutionary outcomes have potentially significant impacts on population dynamics and vice versa. To investigate host-pathogen interactions and explore the impact of micro-level co-evolutionary outcomes on macro-level epidemics, we develop a co-evolutionary model with a combined host-defense strategy. Our results illustrate that host-pathogen co-evolution may induce infection cycling and lead to the vanishing of the disease-induced hydra effect, whereas pathogen mono-evolution strengthens the hydra effect in both range and magnitude. As the recovery rate increases, we find a counter-intuitive effect of increased disease prevalence due to host-pathogen co-evolution: the disease is first highly infectious and lethal, then highly infectious but with low lethality. Such diverse outcomes suggest that this combined co-evolutionary and epidemiological framework holds great promise for a better understanding of infection.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 10","pages":"148"},"PeriodicalIF":2.2,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145028997","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 and Persistence of a Generalized Multi-strain SIS Model.","authors":"Scott Greenhalgh, Tabitha Henriquez, Michael Frutschy, Rebecah Leonard","doi":"10.1007/s11538-025-01516-z","DOIUrl":"10.1007/s11538-025-01516-z","url":null,"abstract":"<p><p>Autonomous differential equation compartmental models hold broad utility in epidemiology and public health. However, these models typically cannot account explicitly for myriad factors that affect the trajectory of infectious diseases, with seasonal variations in host behavior and environmental conditions as noteworthy examples. Fortunately, using non-autonomous differential equation compartmental models can mitigate some of these deficiencies, as the inclusion of time-varying parameters can account for temporally varying factors. The inclusion of these temporally varying factors does come at a cost though, as many analysis techniques, such as the use of Poincaré maps and Floquet theory, on non-autonomous differential equation compartmental models are typically only tractable numerically. Here, we illustrate a rare <math><mi>n</mi></math> -strain generalized Susceptible-Infectious-Susceptible (SIS) compartmental model, with a general time-varying recovery rate, which features Floquet exponents that are algebraic expressions. We completely characterize the persistence and stability properties of our <math><mi>n</mi></math> -strain generalized SIS model for <math><mrow><mi>n</mi> <mo>≥</mo> <mn>1</mn></mrow> </math> . We also derive a closed-form solution in terms of elementary functions for the single-strain SIS model, which is capable of incorporating almost any infectious period distribution. Finally, to demonstrate the applicability of our work, we apply it to recent syphilis incidence data from the United States, utilizing Akaike Information Criteria and Forecast Skill Scores to inform on the model's goodness of fit relative to complexity and the model's capacity to predict future trends.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 10","pages":"147"},"PeriodicalIF":2.2,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12423140/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145028950","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}