Bulletin of Mathematical Biology最新文献

Accuracy Versus Predominance: Reassessing the Validity of the Quasi-Steady-State Approximation. 准确度与优势：准稳态近似的有效性再评估。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-16 DOI: 10.1007/s11538-025-01451-z

Kashvi Srivastava, Justin Eilertsen, Victoria Booth, Santiago Schnell

{"title":"Accuracy Versus Predominance: Reassessing the Validity of the Quasi-Steady-State Approximation.","authors":"Kashvi Srivastava, Justin Eilertsen, Victoria Booth, Santiago Schnell","doi":"10.1007/s11538-025-01451-z","DOIUrl":"https://doi.org/10.1007/s11538-025-01451-z","url":null,"abstract":"The application of the standard quasi-steady-state approximation to the Michaelis-Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific biochemical conditions that dictate the validity of the standard quasi-steady-state approximation remains a challenging endeavor. Emerging research suggests that the accuracy of the standard quasi-steady-state approximation improves as the ratio of the initial enzyme concentration, <math><msub><mi>e</mi> <mn>0</mn></msub> </math> , to the Michaelis constant, <math><msub><mi>K</mi> <mi>M</mi></msub> </math> , decreases. In this work, we examine this ratio and its implications for the accuracy and validity of the standard quasi-steady-state approximation as compared to other quasi-steady-state reductions in its proximity. Using standard tools from the analysis of ordinary differential equations, we show that while <math> <mrow><msub><mi>e</mi> <mn>0</mn></msub> <mo>/</mo> <msub><mi>K</mi> <mi>M</mi></msub> </mrow> </math> provides an indication of the standard quasi-steady-state approximation's asymptotic accuracy, the standard quasi-steady-state approximation's predominance relies on a small ratio of <math><msub><mi>e</mi> <mn>0</mn></msub> </math> to the Van Slyke-Cullen constant, K. Here, we define the predominance of a quasi-steady-state reduction when it offers the highest approximation accuracy among other well-known reductions with overlapping validity conditions. We conclude that the magnitude of <math> <mrow><msub><mi>e</mi> <mn>0</mn></msub> <mo>/</mo> <mi>K</mi></mrow> </math> offers the most accurate measure of the validity of the standard quasi-steady-state approximation.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"73"},"PeriodicalIF":2.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085996","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}

引用次数: 0

Modelling Population-Level Hes1 Dynamics: Insights from a Multi-framework Approach. 人口水平Hes1动力学建模：来自多框架方法的见解。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-16 DOI: 10.1007/s11538-025-01447-9

Gesina Menz, Stefan Engblom

{"title":"Modelling Population-Level Hes1 Dynamics: Insights from a Multi-framework Approach.","authors":"Gesina Menz, Stefan Engblom","doi":"10.1007/s11538-025-01447-9","DOIUrl":"https://doi.org/10.1007/s11538-025-01447-9","url":null,"abstract":"Mathematical models of living cells have been successively refined with advancements in experimental techniques. A main concern is striking a balance between modelling power and the tractability of the associated mathematical analysis. In this work we model the dynamics for the transcription factor Hairy and enhancer of split-1 (Hes1), whose expression oscillates during neural development, and which critically enables stable fate decision in the embryonic brain. We design, parametrise, and analyse a detailed spatial model using ordinary differential equations (ODEs) over a grid capturing both transient oscillatory behaviour and fate decision on a population-level. We also investigate the relationship between this ODE model and a more realistic grid-based model involving intrinsic noise using mostly directly biologically motivated parameters. While we focus specifically on Hes1 in neural development, the approach of linking deterministic and stochastic grid-based models shows promise in modelling various biological processes taking place in a cell population. In this context, our work stresses the importance of the interpretability of complex computational models into a framework which is amenable to mathematical analysis.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"74"},"PeriodicalIF":2.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144086005","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}

引用次数: 0

Mathematical Modeling of Influenza Dynamics: Integrating Seasonality and Gradual Waning Immunity. 流感动力学的数学建模：整合季节性和逐渐减弱的免疫力。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-16 DOI: 10.1007/s11538-025-01454-w

Carlos Andreu-Vilarroig, Gilberto González-Parra, Rafael-Jacinto Villanueva

{"title":"Mathematical Modeling of Influenza Dynamics: Integrating Seasonality and Gradual Waning Immunity.","authors":"Carlos Andreu-Vilarroig, Gilberto González-Parra, Rafael-Jacinto Villanueva","doi":"10.1007/s11538-025-01454-w","DOIUrl":"https://doi.org/10.1007/s11538-025-01454-w","url":null,"abstract":"The dynamics of influenza virus spread is one of the most complex to model due to two crucial factors involved: seasonality and immunity. These factors have been typically addressed separately in mathematical modeling in epidemiology. In this paper, we present a mathematical modeling approach to consider simultaneously both forced-seasonality and gradual waning immunity. A seasonal SIRn model that integrates seasonality and gradual waning immunity is constructed. Seasonality has been modeled classically, by defining the transmission rate as a periodic function, with higher values in winter seasons. The progressive decline of immunity after infection has been introduced into the model structure by considering multiple recovered subpopulations or recovery states with transmission rates attenuated by a susceptibility factor that varies with the age of infection. To show the applicability of the proposed mathematical modeling approach to a real-world scenario, we have carried out a calibration of the model with the data series of influenza infections reported in the 2010-2020 period at the General Hospital of Castellón de la Plana, Spain. The results of the case study show the feasibility of the mathematical approach. We provide a discussion of the main features and insights of the proposed mathematical modeling approach presented in this study.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"75"},"PeriodicalIF":2.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144086000","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}

引用次数: 0

Complex Algal Dynamics and Optimal Control with Algicidal Activity and Reabsorption of Algal Cell Contents. 藻类的复杂动力学与最优控制与杀藻活性和藻类细胞内容物的重吸收。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-15 DOI: 10.1007/s11538-025-01453-x

Wei Wang, Chunxiao She, Hao Wang

{"title":"Complex Algal Dynamics and Optimal Control with Algicidal Activity and Reabsorption of Algal Cell Contents.","authors":"Wei Wang, Chunxiao She, Hao Wang","doi":"10.1007/s11538-025-01453-x","DOIUrl":"https://doi.org/10.1007/s11538-025-01453-x","url":null,"abstract":"Algaecides utilizing bacteriolytic algae are considered as a promising approach for algae control. These bacteria inhibit the continuous reproduction of algae cells in various ways, including lysing the cells, which leads to the release of cellular contents and affects the levels of nitrogen and phosphorus in the environment. In this paper, we establish a novel mathematical model with algicidal activities and the reabsorption of algal cell contents. The model exhibits complex dynamical phenomena: (i) backward and forward bifurcations; (ii) transcritical bifurcation and saddle-node bifurcation discussed via Sotomayor's theorem; (iii) Hopf bifurcation; (iv) the codimension 2 bifurcations, exemplified by the Bogdanov-Takens bifurcation, via the methodologies of normal form theory and the center manifold theorem. We also obtain an explicit formula for the ultimate lower bound of algal bloom. Sensitivity analysis of the basic ecological reproductive indices <math><msub><mi>R</mi> <mn>0</mn></msub> </math> is conducted, and the optimal control problem is formulated by integrating environmental factors and physical algal control methods. The analysis indicates that using algicidal bacteria to lyse algal cells can result in two scenarios: algicidal dominance and nutrient supplementation dominance. The former effectively curbs the sustained reproduction of algal cells and is more effective than physical algal control methods.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"72"},"PeriodicalIF":2.0,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144076130","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}

引用次数: 0

On Discretely Structured Growth Models and Their Moments. 关于离散结构增长模型及其时刻。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-12 DOI: 10.1007/s11538-025-01446-w

Benjamin J Walker, Helen M Byrne

引用次数: 0

Asymptotic Enumeration of Normal and Hybridization Networks via Tree Decoration. 通过树装饰的正态和杂交网络的渐近枚举。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-07 DOI: 10.1007/s11538-025-01444-y

Michael Fuchs, Mike Steel, Qiang Zhang

{"title":"Asymptotic Enumeration of Normal and Hybridization Networks via Tree Decoration.","authors":"Michael Fuchs, Mike Steel, Qiang Zhang","doi":"10.1007/s11538-025-01444-y","DOIUrl":"https://doi.org/10.1007/s11538-025-01444-y","url":null,"abstract":"Phylogenetic networks provide a more general description of evolutionary relationships than rooted phylogenetic trees. One way to produce a phylogenetic network is to randomly place k arcs between the edges of a rooted binary phylogenetic tree with n leaves. The resulting directed graph may fail to be a phylogenetic network, and even when it is it may fail to be a tree-child or normal network. In this paper, we first show that if k is fixed, the proportion of arc placements that result in a normal network tends to 1 as n grows. From this result, the asymptotic enumeration of normal networks becomes straightforward and provides a transparent meaning to the combinatorial terms that arise. Moreover, the approach extends to allow k to grow with n (at the rate <math><mrow><mi>o</mi> <mo>(</mo> <msup><mi>n</mi> <mfrac><mn>1</mn> <mn>3</mn></mfrac> </msup> <mo>)</mo></mrow> </math> ), which was not handled in earlier work. We also investigate a subclass of normal networks of particular relevance in biology (hybridization networks) and establish that the same asymptotic results apply.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"69"},"PeriodicalIF":2.0,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12058904/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143954173","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}

引用次数: 0

Matching Habitat Choice and the Evolution of a Species' Range. 匹配生境选择与物种范围的进化。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-07 DOI: 10.1007/s11538-025-01445-x

Farshad Shirani, Judith R Miller

{"title":"Matching Habitat Choice and the Evolution of a Species' Range.","authors":"Farshad Shirani, Judith R Miller","doi":"10.1007/s11538-025-01445-x","DOIUrl":"https://doi.org/10.1007/s11538-025-01445-x","url":null,"abstract":"Natural selection is not the only mechanism that promotes adaptation of an organism to its environment. Another mechanism is matching habitat choice, in which individuals sense and disperse toward habitat best suited to their phenotype. This can in principle facilitate rapid adaptation, enhance range expansion, and promote genetic differentiation, reproductive isolation, and speciation. However, empirical evidence that confirms the evolution of matching habitat choice in nature is limited. Here we obtain theoretical evidence that phenotype-optimal dispersal, a particular form of matching habitat choice, is likely to evolve only in the presence of a steep environmental gradient. Such a gradient may be steeper than the gradient the majority of species typically experience in nature, adding to the collection of possible explanations for the scarcity of evidence for matching habitat choice. We draw this conclusion from numerical solutions of a system of deterministic partial differential equations for a population's density along with the mean and variance of a fitness-related quantitative phenotypic trait such as body size. In steep gradients, we find that phenotype-optimal dispersal facilitates rapid adaptation on single-generation time scales, reduces within-population trait variation, increases range expansion speed, and enhances the chance of survival in rapidly changing environments. Moreover, it creates a directed gene flow that compensates for the maladaptive core-to-edge effects of random gene flow caused by random movements. These results suggest that adaptive gene flow to range margins, together with substantially reduced trait variation at central populations, may be hallmarks of phenotype-optimal dispersal in natural populations. Further, slowly-growing species under strong natural selection may particularly benefit from evolving phenotype-optimal dispersal.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"70"},"PeriodicalIF":2.0,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12058903/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143976853","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}

引用次数: 0

A Theoretical Framework to Quantify the Tradeoff Between Individual and Population Benefits of Expanded Antibiotic Use. 一个量化扩大抗生素使用的个人和群体利益权衡的理论框架。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-04-30 DOI: 10.1007/s11538-025-01432-2

Cormac R LaPrete, Sharia M Ahmed, Damon J A Toth, Jody R Reimer, Valerie M Vaughn, Frederick R Adler, Lindsay T Keegan

{"title":"A Theoretical Framework to Quantify the Tradeoff Between Individual and Population Benefits of Expanded Antibiotic Use.","authors":"Cormac R LaPrete, Sharia M Ahmed, Damon J A Toth, Jody R Reimer, Valerie M Vaughn, Frederick R Adler, Lindsay T Keegan","doi":"10.1007/s11538-025-01432-2","DOIUrl":"https://doi.org/10.1007/s11538-025-01432-2","url":null,"abstract":"The use of antibiotics during a disease outbreak presents a critical tradeoff between immediate treatment benefits to the individual and the long-term risk to the population. Typically, the extensive use of antibiotics has been thought to increase selective pressures, leading to resistance. This study explores scenarios where expanded antibiotic treatment can be advantageous for both individual and population health. We develop a mathematical framework to assess the impacts on outbreak dynamics of choosing to treat moderate infections not treated under current guidelines, focusing on cholera as a case study. We derive conditions under which treating moderate infections can sufficiently decrease transmission and reduce the total number of antibiotic doses administered. We identify two critical thresholds: the Outbreak Prevention Threshold (OPT), where expanded treatment reduces the reproductive number below 1 and halts transmission, and the Dose Utilization Threshold (DUT), where expanded treatment results in fewer total antibiotic doses used than under current guidelines. For cholera, we find that treating moderate infections can feasibly stop an outbreak when the untreated reproductive number is less than 1.42 and will result in fewer does used compared to current guidelines when the untreated reproductive number is less than 1.53. These findings demonstrate that conditions exist under which expanding treatment to include moderate infections can reduce disease spread and the selective pressure for antibiotic resistance. These findings extend to other pathogens and outbreak scenarios, suggesting potential targets for optimized treatment strategies that balance public health benefits and antibiotic stewardship.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"68"},"PeriodicalIF":2.0,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12043784/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143966187","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}

引用次数: 0

Modeling SARS-CoV-2 Infection Dynamics: Insights into Viral Clearance and Immune Synergy. 模拟SARS-CoV-2感染动力学：对病毒清除和免疫协同作用的见解。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-04-15 DOI: 10.1007/s11538-025-01442-0

Lele Fan, Zhipeng Qiu, Qi Deng, Ting Guo, Libin Rong

{"title":"Modeling SARS-CoV-2 Infection Dynamics: Insights into Viral Clearance and Immune Synergy.","authors":"Lele Fan, Zhipeng Qiu, Qi Deng, Ting Guo, Libin Rong","doi":"10.1007/s11538-025-01442-0","DOIUrl":"https://doi.org/10.1007/s11538-025-01442-0","url":null,"abstract":"Understanding the mechanisms of interaction between SARS-CoV-2 infection and the immune system is crucial for developing effective treatment strategies against COVID-19. In this paper, a mathematical model is formulated to investigate the interactions among SARS-CoV-2 infection, cellular immunity, and humoral immunity. Clinical data from eight asymptomatic or mild COVID-19 patients in Munich are used to fit the model, and the dynamics of natural killer (NK) cells, cytotoxic T lymphocytes (CTLs), B cells, and antibodies are further explored using the average of the best-fitting parameter values. Subsequently, the impact of NK cells, CTLs, B cells, and antibodies on SARS-CoV-2 infection is numerically investigated. The results indicate that (i) the synergy of NK cells, CTLs, and antibodies leads to a rapid decrease in the viral load during SARS-CoV-2 infection; (ii) antibodies play a crucial role compared to other immune mechanisms, and enhancing B cell stimulation may be more effective in clearing the virus from the lungs; (iii) in terms of cytotoxic effects, CTLs are stronger and more sustained than NK cells. Furthermore, the existence and local stability of the model's equilibria are fully classified, and complex dynamics of the model are further investigated using bifurcation theory, revealing multistability phenomena, including multiple attractors and periodic solutions. These findings suggest potential uncertainty and diversity in SARS-CoV-2 infection outcomes.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"67"},"PeriodicalIF":2.0,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143980873","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}

引用次数: 0

A Risk-Structured Model of the Influence of Mental Health on Opioid Addiction. 心理健康对阿片类药物成瘾影响的风险结构模型

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-04-09 DOI: 10.1007/s11538-025-01431-3

Katelyn R Newton, London M Luttrell, Julie C Blackwood, Kathryn J Montovan, Eli E Goldwyn

{"title":"A Risk-Structured Model of the Influence of Mental Health on Opioid Addiction.","authors":"Katelyn R Newton, London M Luttrell, Julie C Blackwood, Kathryn J Montovan, Eli E Goldwyn","doi":"10.1007/s11538-025-01431-3","DOIUrl":"10.1007/s11538-025-01431-3","url":null,"abstract":"In 2021, over 80,000 of the 107,622 overdose deaths in the United States involved opioids, with opioid use disorder (OUD) and fatal overdoses imposing economic costs exceeding $1 trillion in 2017. Mathematical modeling provides an important tool for understanding the dynamics of the opioid epidemic and evaluating the potential benefits of different treatment and prevention strategies. In particular, we extend the Susceptible-Infected-Recovered paradigm for modeling infectious diseases to the opioid crisis. While existing compartmental models of OUD often assume equal risk of addiction across individuals, this assumption overlooks the significant role of risk heterogeneity. Unlike previous models that assume uniform addiction risk, our model incorporates risk stratification to account for the disproportionate burden among individuals with mental health disorders, who represent 20% of the U.S. population but account for over half of opioid prescriptions and misuse. Our compartmental model distinguishes between addiction pathways initiated by prescription opioids and those driven by social influences. Using existing data, we calibrate the model to estimate key parameters and quantify the impact of risk heterogeneity, offering insights to the addiction process.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"66"},"PeriodicalIF":2.0,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143810511","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}

引用次数: 0