Bulletin of Mathematical Biology最新文献

{"title":"Phylogenetic Network Models as Graphical Models.","authors":"Seth Sullivant","doi":"10.1007/s11538-026-01695-3","DOIUrl":"10.1007/s11538-026-01695-3","url":null,"abstract":"<p><p>The displayed tree phylogenetic network model is shown to sit as a natural submodel of the graphical model associated to a directed acyclic graph (DAG). This representation allows us to derive a number of results about the displayed tree model. In particular, the concept of a local modification to a DAG model is developed and applied to the displayed tree model. As an application, some nonidentifiability issues related to the displayed tree models are highlighted as they relate to reticulation edges and stacked reticulations in the networks. We also derive rank conditions on flattenings of probability tensors for the displayed tree model, generalizing classic results for phylogenetic tree models.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13364925/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148429893","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 Analysis of a Mathematical Model for the \"Shock-and-Kill\" Strategy in HIV-1/SIV Brain Infection.","authors":"Yongli Cai, Weiming Wang","doi":"10.1007/s11538-026-01702-7","DOIUrl":"10.1007/s11538-026-01702-7","url":null,"abstract":"<p><p>This paper provides a rigorous mathematical resolution of the open global stability problem for a \"shock-and-kill\" model of HIV-1/SIV infection in brain reservoirs recently formulated by Roda et al. (2021). The model explicitly incorporates the effects of latency-reversing agents and enhanced immune clearance of reactivated cells. We derive an explicit formula for the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> , which serves as the sole threshold parameter governing viral eradication versus persistence and integrates infection pathways from both productive and latent compartments. By combining the next-generation matrix approach with an extended graph-theoretic Lyapunov method for multigraphs with parallel arcs, we rigorously establish that the disease-free equilibrium is globally asymptotically stable when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>≤</mo> <mn>1</mn></mrow> </math> , whereas a unique productive equilibrium exists and is globally asymptotically stable when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> . To resolve the sign-indefinite quadratic perturbations induced by structurally distinct parallel transmission arcs-a fundamental bottleneck of classical graph-theoretic Lyapunov schemes-we develop a refined composite Lyapunov framework equipped with hierarchically calibrated parameters. Systematic asymptotic scaling and multi-parameter tuning eliminate indefinite cyclic quadratic interactions, securing strict negative definiteness of the Lyapunov derivative and overcoming key limitations of conventional graph-based methods. These global stability results provide a definitive mathematical answer to whether therapeutic interventions guarantee viral eradication or lead to persistent brain-reservoir infection. Furthermore, they furnish a rigorous theoretical foundation for the \"shock-and-kill\" strategy and establish mathematically precise conditions to guide the design of safe, effective interventions for eliminating HIV-1/SIV from CNS reservoirs.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148429845","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 Shows that Overall Infection Burden is Reduced More by Vaccines that Decrease Spread or Accelerate Recovery than those that Lower Severe Infections or Death.","authors":"Indunil M Hewage, Sameera Hewage, Elissa J Schwartz","doi":"10.1007/s11538-026-01690-8","DOIUrl":"10.1007/s11538-026-01690-8","url":null,"abstract":"<p><p>Vaccination programs have helped reduce case numbers and the death toll of COVID-19 significantly over the past few years. The spread and control of COVID-19 have been studied by means of ODE-based compartmental models in a number of studies. However, studies on the different benefits of vaccines, other than blocking infections, remain a paucity. In this study, we developed an ODE-based compartmental model with a separate disease progression path for vaccinated individuals. Key parameters were defined to account for the different facets of vaccine effectiveness: (1) blocking infections; (2) decreasing transmission; (3) expediting recovery; (4) reducing severe morbidity; and (5) preventing disease mortality. Sensitivity analyses and numerical simulations on the reproduction number, number of infections, reduction in peak infections, and cumulative disease-induced deaths provided important insights into the impact of different aspects of vaccine effectiveness on disease control. Specifically, vaccine benefits that reduce disease spread or accelerate recovery have a more substantial impact on the overall population (both vaccinated and unvaccinated individuals) than do vaccine benefits that reduce severe infections or death. The latter type of vaccines does not exhibit a considerable impact on the overall epidemic at the population level, but has a major impact only on the vaccinated individuals. In conclusion, infection burden can be reduced drastically with vaccines that have high potential in blocking infections, decreasing infectivity, and expediting recovery.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148387388","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":"Identifiability, Sensitivity, and Genetic Algorithms in Bacterial Biofilm Selection Models.","authors":"Stephen Williams, Daravuth Cheam, Michele K Nishiguchi, Suzanne S Sindi, Shilpa Khatri, Erica M Rutter","doi":"10.1007/s11538-026-01693-5","DOIUrl":"10.1007/s11538-026-01693-5","url":null,"abstract":"<p><p>Bacteria often develop distinct phenotypes to adapt to environmental stress. In particular, they can produce biofilms, dense communities of bacteria that live in a complex extracellular matrix. While previous studies have investigated how bacterial biofilms are regulated under laboratory conditions, they have not considered (1) the data requirements necessary to estimate model parameters and (2) how bacteria respond to recurring stressors in their natural habitats. To address (1), we adapted a mechanistic population model to explore the dynamics of biofilm formation in the presence of predator stress, using synthetic data. We used a Maximum Likelihood Estimation framework to measure crucial parameters underpinning the biofilm formation dynamics. We used genetic algorithms to propose an optimal data collection schedule that minimised parameter identifiability confidence interval widths. Our sensitivity analysis revealed that, within the explored regimes, we could simplify the binding dynamics and eliminate biofilm detachment. To address (2), we proposed a structured version of our model to capture the long-term behaviour and evolutionary selection. In our extended model, the subpopulations feature different maximal rates of biofilm formation. We compared the selection under different predator types and amounts and identified key parameters that affected the speed of selection via sensitivity analysis.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13328132/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148366997","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":"Effects of Seasonal Births and Predation on Disease Spread.","authors":"Allison J Introne, Leah B Shaw","doi":"10.1007/s11538-026-01697-1","DOIUrl":"10.1007/s11538-026-01697-1","url":null,"abstract":"<p><p>For many organisms, births occur in seasonal pulses. When predation on an organism is density-dependent, seasonal population changes also change the per capita predation rate. This in turn can affect disease dynamics in the system. We use a Susceptible-Infected (SI) model to study the effects of seasonal births and nonlinear predation on the spread of infection in a population over time. Motivated by open marine systems, we assume that the total birth or recruitment rate is density-independent and that the predator population is constant. We compare models with constant year-round births and seasonally pulsed births as well as linear and hyperbolic predation functions. We calculate the basic reproductive number and use numerical simulations to examine system behavior when infection is endemic. When predation depends linearly on prey populations, seasonality of births does not affect the average infection level or disease transmissibility. When predation rates saturate, as in systems with hyperbolic predation, higher disease transmissibility and endemic infection levels result. This effect can be exacerbated by seasonality of births, especially at moderate population levels.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13328138/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148366977","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":"Slow Evolution Towards Generalism in a Model of Variable Dietary Range.","authors":"Elliot M Butterworth, Tim Rogers","doi":"10.1007/s11538-026-01674-8","DOIUrl":"10.1007/s11538-026-01674-8","url":null,"abstract":"<p><p>Species sharing a habitat will co-evolve to make use of the available resources, as consumption is modulated by competition and negative feedback loops between consumers and resources. The dietary range of a given species determines the resources it has access to and thus the other species with which it competes. A narrow dietary range avoids competition at the cost of over-reliance on a small selection of resources; conversely a wide dietary range provides more alternatives but also more chance of competition with other species. Here, we investigate the evolution of dietary range within a mathematical model of niche formation. We find highly path dependent co-evolution dynamics characterised by long-lived quasi-stable states. Ultimately, stochastic effects drive the evolution of generalist diets, as we uncover in our analysis and simulations.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13319428/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148350740","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":"CBINN: Cancer Biology-Informed Neural Network for Unknown Parameter Estimation and Missing Physics Identification.","authors":"Bishal Chhetri, B V Rathish Kumar","doi":"10.1007/s11538-026-01698-0","DOIUrl":"10.1007/s11538-026-01698-0","url":null,"abstract":"<p><p>The dynamics of tumor-immune interactions within a complex tumor microenvironment are typically modeled using a system of ordinary differential equations or partial differential equations. These models introduce some unknown parameters that need to be estimated accurately and efficiently from the limited, noisy experimental data. Moreover, due to the intricate biological complexity and limitations in experimental measurements, tumor-immune dynamics are not fully understood, and therefore, only partial knowledge of the underlying physics may be available, resulting in unknown or missing terms within the system of equations. Thus, there are twofold challenges in modeling tumor dynamics: (i) accurate estimation of model parameters and (ii) discovery of the mathematical equations governing the physical and biological systems. These types of problems are referred to as gray-box identification areas, where both experimental data and partial system knowledge are used to recover unknown parameters and missing components. In this study, we develop a cancer biology-informed neural network model (CBINN) to infer the unknown parameters in the system of equations as well as to discover the missing mechanisms from sparse and noisy measurements. We test the performance of the CBINN model on three distinct nonlinear compartmental tumour-immune models and evaluate its robustness across multiple synthetic noise levels. By harnessing these highly nonlinear dynamics, our CBINN framework effectively estimates the unknown model parameters and uncovers the underlying physical laws or mathematical structures that govern these biological systems, from scattered and noisy measurements. The models chosen here represent the dynamic patterns commonly observed in compartmental models of tumor-immune interactions, thereby validating the generalizability and efficacy of our methodology. Structural and practical identifiablility of the model parameters are also discussed using computational and Fisher information matrix based analysis. This work provides valuable guidance for researchers addressing inverse problems and gray-box identification challenges in complex dynamical systems.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148337805","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 Cost-Sensitive Behavioral Modeling Analysis of the Early Identification and Control of Infectious Diseases.","authors":"Mohammad Sharif Ullah, Xiunan Wang, Jin Wang","doi":"10.1007/s11538-026-01696-2","DOIUrl":"10.1007/s11538-026-01696-2","url":null,"abstract":"<p><p>A coupled epidemic-behavior model is proposed to assess how vaccination, testing, and treatment jointly influence early outbreak control, accounting for individual choices based on perceived risk, intervention costs, and policy incentives. In a uniformly mixing population, individuals make strategic decisions regarding vaccination and testing participation based on the trade-offs between personal costs and communal benefits, while the intensity of public health testing adjusts according to infection prevalence; the transmission model includes vaccine efficacy, the probability of false negatives in testing, treatment-related reductions in infectious duration and mortality, as well as nonlinear saturation and awareness feedback mechanisms. Analytical threshold results and simulations (time series and two-dimensional parameter sweeps) indicate that reducing vaccination and testing costs expands the disease-free region, while false negatives consistently diminish the efficacy of increased testing by delaying diagnosis and perpetuating onward transmission; treatment reduces transmission potential but maximizes population benefit when combined with prompt implementation of testing. The approach also delineates parameter regimes in which behavioral feedback provides non-monotonic responses and recurring outbreaks, notwithstanding heightened interventions. The findings suggest that effective epidemic preparedness necessitates synchronized incentives for vaccination and testing, investments to minimize false negatives (such as enhanced test accuracy or repeated testing), and treatment accessibility aligned with rapid case identification to optimize resource distribution and early-response strategies during emerging and re-emerging infectious disease threats.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13309453/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148337871","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 Exact Hypergeometric Posterior Method for Accurate Inference of Population Size from Mark-Recapture Data.","authors":"Danial Mirzaee, Seyed Amir Malekpour, Ata Kalirad","doi":"10.1007/s11538-026-01687-3","DOIUrl":"10.1007/s11538-026-01687-3","url":null,"abstract":"<p><p>Reliable inference of census population size (N) from mark-recapture data is essential in ecology, conservation, and epidemiology, yet standard estimators often rely on asymptotic approximations that can misrepresent uncertainty. We introduce the Exact Hypergeometric Posterior (EHP), obtained by normalizing the hypergeometric likelihood for the classic two-sample design, which yields an exact posterior probability mass function over integer N. Closed-form normalization enables rapid evaluation of posterior summaries and exact highest-posterior-density (HPD) credible intervals. In this study, we show how heavy right tails naturally arise in sparse-recapture regimes and provide a principled truncation using an upper bound K, such as a plausible carrying capacity or sampling-frame limit, to regularize inference when needed. For repeated sampling, independent events can be combined by posterior multiplication and renormalization, yielding substantial gains in precision without large-sample approximations. Additionally, we extend the likelihood to account for loss of marked individuals and differential catchability by introducing an availability (retention) term <math><mrow><mi>ϕ</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo></mrow> </math> and a relative catchability parameter <math><mi>ω</mi></math> via Fisher's noncentral hypergeometric model. Simulations and empirical examples confirm close agreement between analytic posteriors and Monte Carlo reference posteriors using our method. Together, these results provide a transparent, computationally tractable framework for finite-sample population-size inference in closed and partially open systems.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13303620/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148327084","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":"Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics.","authors":"Ari S Freedman, Bjarke F Nielsen, Maximilian M Nguyen, Laurent Hébert-Dufresne, Simon A Levin","doi":"10.1007/s11538-026-01685-5","DOIUrl":"10.1007/s11538-026-01685-5","url":null,"abstract":"<p><p>Infectious disease superspreading caused by heterogeneity in contact behavior has been observed to be an important determinant of epidemic dynamics and size in both empirical and theoretical settings. However, it has also been observed that the importance of this type of superspreading changes throughout an epidemic, generally in a decreasing manner as infections cascade from individuals with many contacts to those with fewer contacts. We provide an exact mathematical formulation of this phenomenon in strongly-immunizing (SIR) epidemics on static contact networks. Building on the edge-based modeling framework, we construct three metrics to track how superspreading changes through the course of an epidemic, respectively measuring infected nodes' contacts, exposures, and transmissions: (1) the mean degree of infected nodes, (2) the mean number of susceptible neighbors of infected nodes, and (3) the mean number of secondary cases that will be caused by newly infected nodes. We prove results about the behaviors of these metrics, highlighting the fact that their peak times all occur at less than half the time it takes for population-level infection prevalence to peak. This suggests that the importance of superspreading will be low when an epidemic is already near its peak, so contact-based control strategies are best employed as early in an outbreak as possible. We discuss implications for accurately measuring epidemiological parameters from incidence, mobility, contact tracing, and transmission data.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13303329/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148327094","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}