Bulletin of Mathematical Biology最新文献

{"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":"https://doi.org/10.1007/s11538-025-01431-3","url":null,"abstract":"<p><p>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.</p>","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}

{"title":"A Network Based Model for Predicting Spatial Progression of Metastasis.","authors":"Khimeer Singh, Byron A Jacobs","doi":"10.1007/s11538-025-01441-1","DOIUrl":"https://doi.org/10.1007/s11538-025-01441-1","url":null,"abstract":"<p><p>Metastatic cancer is reported to have a mortality rate of 90%. Understanding the underlying principles of metastasis and quantifying them through mathematical modelling provides insights into potential treatment regimes. This work presents a partial differential equation based mathematical model embedded on a network, representing the organs and the blood vessels between them, with the aim of predicting likely secondary metastatic sites. Through this framework the relationship between metastasis and blood flow and between metastasis and the diffusive behaviour of cancer is explored. An analysis of the model predictions showed a good correlation with clinical data for some cancer types, particularly for cancers originating in the gut and liver. The model also predicts an inverse relationship between blood velocity and the concentration of cancer cells in secondary organs. Finally, for anisotropic diffusive behaviour, where the cancer experiences greater diffusivity in one direction, metastatic efficiency decreased. This is aligned with the clinical observation that gliomas of the brain, which typically show anisotropic diffusive behaviour, exhibit fewer metastases. The investigation yields some valuable results for clinical practitioners and researchers-as it clarifies some aspects of cancer that have hitherto been difficult to study, such as the impact of differing diffusive behaviours and blood flow rates on the global spread of cancer. The model provides a good framework for studying cancer progression using cancer-specific information when simulating metastasis.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"65"},"PeriodicalIF":2.0,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143810508","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 Impact of Different Degrees of Leadership on Collective Navigation in Follower-Leader Systems.","authors":"Sara Bernardi, Kevin J Painter","doi":"10.1007/s11538-025-01435-z","DOIUrl":"10.1007/s11538-025-01435-z","url":null,"abstract":"<p><p>In both animal and cell populations, the presence of leaders often underlies the success of collective migration processes, which we characterise by a group maintaining a cohesive configuration that consistently moves toward a target. We extend a recent non-local hyperbolic model for follower-leader systems to investigate different degrees of leadership. Specifically, we consider three levels of leadership: indifferent leaders, who do not alter their movement according to followers; observant leaders, who attempt to remain connected with the followers, but do not allow followers to affect their desired alignment; and persuadable leaders, who integrate their attempt to reach some target with the alignment of all neighbours, both followers and leaders. A combination of analysis and numerical simulations is used to investigate under which conditions each degree of leadership allows successful collective movement to a destination. We find that the indifferent leaders' strategy can result in a cohesive and target-directed migration only for short times. Observant and persuadable leaders instead provide robust guidance, showing that the optimal leader behavior depends on the connection between the migrating individuals: if alignment is low, greater follower influence on leaders is beneficial for successful guidance; otherwise, it can be detrimental and may generate various unsuccessful swarming dynamics.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"64"},"PeriodicalIF":2.0,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143794693","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":"Extending Mathematical Frameworks to Investigate Neuronal Dynamics in the Presence of Microglial Ensheathment.","authors":"Nellie Garcia, Silvie Reitz, Gregory Handy","doi":"10.1007/s11538-025-01438-w","DOIUrl":"10.1007/s11538-025-01438-w","url":null,"abstract":"<p><p>Recent experimental evidence has shown that glial cells, including microglia and astrocytes, can ensheathe specific synapses, positioning them to disrupt neurotransmitter flow between pre- and post-synaptic terminals. This study, as part of the special issue \"Problems, Progress and Perspectives in Mathematical and Computational Biology,\" expands micro- and network-scale theoretical frameworks to incorporate these new experimental observations that introduce substantial heterogeneities into the system. Specifically, we aim to explore how varying degrees of synaptic ensheathment affect synaptic communication and network dynamics. Consistent with previous studies, our microscale model shows that ensheathment accelerates synaptic transmission while reducing its strength and reliability, with the potential to effectively switch off synaptic connections. Building on these findings, we integrate an \"effective\" glial cell model into a large-scale neuronal network. Specifically, we analyze a network with highly heterogeneous synaptic strengths and time constants, where glial proximity parametrizes synaptic properties. This parametrization results in a multimodal distribution of synaptic parameters across the network, introducing significantly greater variability compared to previous modeling efforts that assumed a normal distribution. This framework is applied to large networks of exponential integrate-and-fire neurons, extending linear response theory to analyze not only firing rate distributions but also noise correlations across the network. Despite the significant heterogeneity in the system, a mean-field approximation accurately captures network statistics. We demonstrate the utility of our model by reproducing experimental findings, showing that microglial ensheathment leads to post-anesthesia hyperactivity in excitatory neurons of mice. Furthermore, we explore how glial ensheathment may be used in the visual cortex to target specific neuronal subclasses, tuning higher-order network statistics.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"63"},"PeriodicalIF":2.0,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971063/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143779216","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":"Impact of ADE and Dengue Vaccination with Screening on Cost and Disease Burden for Homoserotypic Dengue and Zika.","authors":"Christopher M Kribs, Parker Mays","doi":"10.1007/s11538-025-01440-2","DOIUrl":"https://doi.org/10.1007/s11538-025-01440-2","url":null,"abstract":"<p><p>The tetravalent dengue vaccine Dengvaxia^® may prime dengue-seronegative vaccinees for antibody-dependent enhancement (ADE) of any subsequent dengue (in case of vaccine failure) or Zika infections. Many researchers associate ADE of such cases with more severe outcomes including death. This study uses a mathematical model of transmission dynamics that distinguishes ADE and non-ADE cases for each virus, to identify the potential impact of a dengue screening and vaccination campaign on the economic cost and disease burden of a dual dengue-Zika outbreak, under the hypothesis that severe outcomes are associated with ADE. Results indicate that when all dengue exposure is to a single serotype, in most cases vaccination increases both cost and burden because they are dominated by the high costs associated with complications from ADE Zika cases. However, if per-case ADE Zika costs are lower than estimated (a real possibility given the limited data available), by a factor ranging from 1 to 6 (for cost, except in Vietnam) or 8 (for burden), sufficiently high vaccination coverage can reduce total cost and burden substantially over a year. Analysis also identifies variations across countries, dengue serotypes, and timeframes of evaluation.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"62"},"PeriodicalIF":2.0,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143779217","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 Impact of T-cell Exhaustion Dynamics on Tumour-Immune Interactions and Tumour Growth.","authors":"Nicholas Lai, Alexis Farman, Helen M Byrne","doi":"10.1007/s11538-025-01433-1","DOIUrl":"10.1007/s11538-025-01433-1","url":null,"abstract":"<p><p>Tumours evade immune surveillance through a number of different immunosuppressive mechanisms. One such mechanism causes cytotoxic T-cells, a major driving force of the immune system, to differentiate to a state of 'exhaustion', rendering them less effective at killing tumour cells. We present a structured mathematical model that focuses on T-cell exhaustion and its effect on tumour growth. We compartmentalise cytotoxic T-cells into discrete subgroups based on their exhaustion level, which affects their ability to kill tumour cells. We show that the model reduces to a simpler system of ordinary differential equations (ODEs) that describes the time evolution of the total number of T-cells, their mean exhaustion level and the total number of tumour cells. Numerical simulations of the model equations reveal how the exhaustion distribution of T-cells changes over time and how it influences the tumour's growth dynamics. Complementary bifurcation analysis shows how altering key parameters significantly reduces the tumour burden, highlighting exhaustion as a promising target for immunotherapy. Finally, we derive a continuum approximation of the discrete ODE model, which admits analytical solutions that provide complementary insight into T-cell exhaustion dynamics and their effect on tumour growth.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"61"},"PeriodicalIF":2.0,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11965189/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143762953","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 Framework for Parameter Estimation and Uncertainty Quantification in Systems Biology Using Quantile Regression and Physics-Informed Neural Networks.","authors":"Haoran Hu, Qianru Cheng, Shuli Guo, Huifang Wen, Jing Zhang, Yongqi Song, Kaiqun Wang, Di Huang, Hui Zhang, Chaofeng Zhang, Yanhu Shan","doi":"10.1007/s11538-025-01439-9","DOIUrl":"https://doi.org/10.1007/s11538-025-01439-9","url":null,"abstract":"<p><p>A framework for parameter estimation and uncertainty quantification is crucial for understanding the mechanisms of biological interactions within complex systems and exploring their dynamic behaviors beyond what can be experimentally observed. Despite recent advances, challenges remain in achieving the high accuracy of parameter estimation and uncertainty quantification at moderate computational costs. To tackle these challenges, we developed a novel approach that integrates the quantile method with Physics-Informed Neural Networks (PINNs). This method utilizes a network architecture with multiple parallel outputs, each corresponding to a distinct quantile, facilitating a comprehensive characterization of parameter estimation and its associated uncertainty. The effectiveness of the proposed approach was validated across three study cases, where it was compared to the Monte Carlo dropout (MCD) and the Bayesian methods. Furthermore, a larger-scale model was employed to further demonstrate the excellent performance of the proposed approach. Our approach exhibited significantly superior efficacy in parameter estimation and uncertainty quantification. This highlights its great promise to broaden the scope of applications in system biology modeling.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"60"},"PeriodicalIF":2.0,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143735553","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":"How Missed Doses of Antibiotics Affect Bacteria Growth Dynamics.","authors":"Hwai-Ray Tung, Sean D Lawley","doi":"10.1007/s11538-025-01430-4","DOIUrl":"https://doi.org/10.1007/s11538-025-01430-4","url":null,"abstract":"<p><p>What should you do if you miss a dose of antibiotics? Despite the prevalence of missed antibiotic doses, there is vague or little guidance on what to do when a dose is forgotten. In this paper, we consider the effects of different patient responses after missing a dose using a mathematical model that links antibiotic concentration with bacteria dynamics. We show using simulations that, in some circumstances, (a) missing just a few doses can cause treatment failure, and (b) this failure can be remedied by simply taking a double dose after a missed dose. We then develop an approximate model that is analytically tractable and use it to understand when it might be advisable to take a double dose after a missed dose.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"58"},"PeriodicalIF":2.0,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143735555","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":"Understanding How Chromatin Folding and Enzyme Competition Affect Rugged Epigenetic Landscapes.","authors":"Daria Stepanova, Meritxell Brunet Guasch, Helen M Byrne, Tomás Alarcón","doi":"10.1007/s11538-025-01434-0","DOIUrl":"https://doi.org/10.1007/s11538-025-01434-0","url":null,"abstract":"<p><p>Epigenetics plays a key role in cellular differentiation and maintaining cell identity, enabling cells to regulate their genetic activity without altering the DNA sequence. Epigenetic regulation occurs within the context of hierarchically folded chromatin, yet the interplay between the dynamics of epigenetic modifications and chromatin architecture remains poorly understood. In addition, it remains unclear what mechanisms drive the formation of rugged epigenetic patterns, characterised by alternating genomic regions enriched in activating and repressive marks. In this study, we focus on post-translational modifications of histone H3 tails, particularly H3K27me3, H3K4me3, and H3K27ac. We introduce a mesoscopic stochastic model that incorporates chromatin architecture and competition of histone-modifying enzymes into the dynamics of epigenetic modifications in small genomic loci comprising several nucleosomes. Our approach enables us to investigate the mechanisms by which epigenetic patterns form on larger scales of chromatin organisation, such as loops and domains. Through bifurcation analysis and stochastic simulations, we demonstrate that the model can reproduce uniform chromatin states (open, closed, and bivalent) and generate previously unexplored rugged profiles. Our results suggest that enzyme competition and chromatin conformations with high-frequency interactions between distant genomic loci can drive the emergence of rugged epigenetic landscapes. Additionally, we hypothesise that bivalent chromatin can act as an intermediate state, facilitating transitions between uniform and rugged landscapes. This work offers a powerful mathematical framework for understanding the dynamic interactions between chromatin architecture and epigenetic regulation, providing new insights into the formation of complex epigenetic patterns.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"59"},"PeriodicalIF":2.0,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143735557","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":"Approximate Solutions of a General Stochastic Velocity-Jump Model Subject to Discrete-Time Noisy Observations.","authors":"Arianna Ceccarelli, Alexander P Browning, Ruth E Baker","doi":"10.1007/s11538-025-01437-x","DOIUrl":"10.1007/s11538-025-01437-x","url":null,"abstract":"<p><p>Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion observed. In this paper, we aim to describe the solutions of velocity-jump models for single-agent motion in one spatial dimension, characterised by successive Markovian transitions within a finite network of n states, each with a specified velocity and a fixed rate of switching to every other state. In particular, we focus on obtaining the solutions of the model subject to noisy, discrete-time, observations, with no direct access to the agent state. The lack of direct observation of the hidden state makes the problem of finding the exact distributions generally intractable. Therefore, we derive a series of approximations for the data distributions. We verify the accuracy of these approximations by comparing them to the empirical distributions generated through simulations of four example model structures. These comparisons confirm that the approximations are accurate given sufficiently infrequent state switching relative to the imaging frequency. The approximate distributions computed can be used to obtain fast forwards predictions, to give guidelines on experimental design, and as likelihoods for inference and model selection.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"57"},"PeriodicalIF":2.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11937228/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143708630","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}