Mathematical Biosciences最新文献

{"title":"Modelling the continuum of macrophage phenotypes and their role in inflammation","authors":"Suliman Almansour ,&nbsp;Joanne L. Dunster ,&nbsp;Jonathan J. Crofts ,&nbsp;Martin R. Nelson","doi":"10.1016/j.mbs.2024.109289","DOIUrl":"10.1016/j.mbs.2024.109289","url":null,"abstract":"<div><p>Macrophages are a type of white blood cell that play a significant role in determining the inflammatory response associated with a wide range of medical conditions. They are highly plastic, having the capacity to adopt numerous polarisation states or ‘phenotypes’ with disparate pro- or anti-inflammatory roles. Many previous studies divide macrophages into two categorisations: M1 macrophages are largely pro-inflammatory in nature, while M2 macrophages are largely restorative. However, there is a growing body of evidence that the M1 and M2 classifications represent the extremes of a much broader spectrum of phenotypes, and that intermediate phenotypes can play important roles in the progression or treatment of many medical conditions. In this article, we present a model of macrophage dynamics that includes a continuous description of phenotype, and hence incorporates intermediate phenotype configurations. We describe macrophage phenotype switching via nonlinear convective flux terms that scale with background levels of generic pro- and anti-inflammatory mediators. Through numerical simulation and bifurcation analysis, we unravel the model’s resulting dynamics, paying close attention to the system’s multistability and the extent to which key macrophage–mediator interactions provide bifurcations that act as switches between chronic states and restoration of health. We show that interactions that promote M1-like phenotypes generally result in a greater array of stable chronic states, while interactions that promote M2-like phenotypes can promote restoration of health. Additionally, our model admits oscillatory solutions reminiscent of relapsing–remitting conditions, with macrophages being largely polarised toward anti-inflammatory activity during remission, but with intermediate phenotypes playing a role in inflammatory flare-ups. We conclude by reflecting on our observations in the context of the ongoing pursuance of novel therapeutic interventions.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109289"},"PeriodicalIF":1.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424001494/pdfft?md5=7b3f9fd16861e65bf2cee220684dd62a&pid=1-s2.0-S0025556424001494-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142147233","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":"Predicting the impact of retinal vessel density on retinal vessel and tissue oxygenation using a theoretical model","authors":"Brendan C. Fry ,&nbsp;Croix Gyurek ,&nbsp;Amanda Albright ,&nbsp;George Eckert ,&nbsp;Janet Coleman-Belin ,&nbsp;Alice Verticchio ,&nbsp;Brent Siesky ,&nbsp;Alon Harris ,&nbsp;Julia Arciero","doi":"10.1016/j.mbs.2024.109292","DOIUrl":"10.1016/j.mbs.2024.109292","url":null,"abstract":"<div><div>Vascular impairments, including compromised flow regulation, have been identified as significant contributors to glaucomatous disease. Recent studies have shown glaucoma patients with significantly reduced peripapillary, macular, and optic nerve head vessel densities occurring with early glaucomatous structural changes prior to detectable visual field loss. This study aims to quantify the potential impact of decreased vessel densities on retinal perfusion and oxygen metabolism. In our clinical observations, pre-perimetric glaucoma patients exhibited a 10–13 % reduction in vessel density compared to healthy individuals. Our theoretical model of the retinal vasculature is adapted in this study to assess the potential impact of this reduction in vessel density on retinal oxygenation. The model predicts a 1 % and 38 % decrease in mean oxygen saturation in retinal vessels immediately downstream of the capillaries when vessel density is decreased from its reference value by 10 % and 50 %, respectively. The impact of capillary loss on oxygen extraction fraction and the partial pressure of oxygen in retinal tissue is also predicted. Reductions in vessel density are simulated in combination with impaired flow regulation, and the resulting effects on saturation and flow are predicted. The model results showed a nonlinear relationship between vessel density and downstream saturation, indicating that larger decreases in the density of capillaries have a disproportionate impact on oxygenation. The model further demonstrates that the detrimental effects of minor vessel density reductions are exacerbated when combined with other vascular impairments.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109292"},"PeriodicalIF":1.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142147235","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":"Newton's cradle: Cell cycle regulation by two mutually inhibitory oscillators","authors":"Calin-Mihai Dragoi ,&nbsp;John J. Tyson ,&nbsp;Béla Novák","doi":"10.1016/j.mbs.2024.109291","DOIUrl":"10.1016/j.mbs.2024.109291","url":null,"abstract":"<div><p>The cell division cycle is a fundamental physiological process displaying a great degree of plasticity during the course of multicellular development. This plasticity is evident in the transition from rapid and stringently-timed divisions of the early embryo to subsequent size-controlled mitotic cycles. Later in development, cells may pause and restart proliferation in response to myriads of internal or external signals, or permanently exit the cell cycle following terminal differentiation or senescence. Beyond this, cells can undergo modified cell division variants, such as endoreplication, which increases their ploidy, or meiosis, which reduces their ploidy. This wealth of behaviours has led to numerous conceptual analogies intended as frameworks for understanding the proliferative program. Here, we aim to unify these mechanisms under one dynamical paradigm. To this end, we take a control theoretical approach to frame the cell cycle as a pair of arrestable and mutually-inhibiting, doubly amplified, negative feedback oscillators controlling chromosome replication and segregation events, respectively. Under appropriate conditions, this framework can reproduce fixed-period oscillations, checkpoint arrests of variable duration, and endocycles. Subsequently, we use phase plane and bifurcation analysis to explain the dynamical basis of these properties. Then, using a physiologically realistic, biochemical model, we show that the very same regulatory structure underpins the diverse functions of the cell cycle control network. We conclude that Newton's cradle may be a suitable mechanical analogy of how the cell cycle is regulated.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109291"},"PeriodicalIF":1.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424001512/pdfft?md5=74b24399155a30cd8cb09229d7204800&pid=1-s2.0-S0025556424001512-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142147234","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":"Determinants of successful disease control through voluntary quarantine dynamics on social networks","authors":"Simiao Shi ,&nbsp;Zhiyuan Wang ,&nbsp;Xingru Chen ,&nbsp;Feng Fu","doi":"10.1016/j.mbs.2024.109288","DOIUrl":"10.1016/j.mbs.2024.109288","url":null,"abstract":"<div><p>In the wake of epidemics, quarantine measures are typically recommended by health authorities or governments to help control the spread of the disease. Compared with mandatory quarantine, voluntary quarantine offers individuals the liberty to decide whether to isolate themselves in case of infection exposure, driven by their personal assessment of the trade-off between economic loss and health risks as well as their own sense of social responsibility and concern for public health. To better understand self-motivated health behavior choices under these factors, here we incorporate voluntary quarantine into an endemic disease model – the susceptible–infected–susceptible (SIS) model – and perform comprehensive agent-based simulations to characterize the resulting behavior-disease interactions in structured populations. We quantify the conditions under which voluntary quarantine will be an effective intervention measure to mitigate disease burden. Furthermore, we demonstrate how individual decision-making factors, including the level of temptation to refrain from quarantine and the degree of social compassion, impact compliance levels of voluntary quarantines and the consequent collective disease mitigation efforts. We find that successful disease control requires either a sufficiently low level of temptation or a sufficiently high degree of social compassion, such that even complete containment of the epidemic is attainable. In addition to well-mixed populations, we have also analyzed other more realistic social networks of contacts, including spatial lattices, small-world networks, and real social networks. Our work offers new insights into the fundamental social dilemma aspect of disease control through non-pharmaceutical interventions, such as voluntary quarantine and isolation, where the collective outcome of individual decision-making is crucial.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109288"},"PeriodicalIF":1.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142121452","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":"Predicting resistance and pseudoprogression: are minimalistic immunoediting mathematical models capable of forecasting checkpoint inhibitor treatment outcomes in lung cancer?","authors":"Kevin Robert Scibilia ,&nbsp;Pirmin Schlicke ,&nbsp;Folker Schneller ,&nbsp;Christina Kuttler","doi":"10.1016/j.mbs.2024.109287","DOIUrl":"10.1016/j.mbs.2024.109287","url":null,"abstract":"<div><h3>Background:</h3><p>The increased application of immune checkpoint inhibitors (ICIs) targeting PD-1/PD-L1 in lung cancer treatment generates clinical need to reliably predict individual patients’ treatment outcomes.</p></div><div><h3>Methods:</h3><p>To bridge the prediction gap, we examine four different mathematical models in the form of ordinary differential equations, including a novel delayed response model. We rigorously evaluate their individual and combined predictive capabilities with regard to the patients’ progressive disease (PD) status through equal weighting of model-derived outcome probabilities.</p></div><div><h3>Results:</h3><p>Fitting the complete treatment course, the novel delayed response model (<span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>938</mn></mrow></math></span>) outperformed the simplest model (<span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>865</mn></mrow></math></span>). The model combination was able to reliably predict patient PD outcome with an <strong>overall accuracy of 77%</strong> (sensitivity = 70%, specificity = 81%), solely through calibration with primary tumor longest diameter measurements. It autonomously identified a subset of 51% of patients where predictions with an <strong>overall accuracy of 81%</strong> (sensitivity = 81%, specificity = 81%) can be achieved. All models significantly outperformed a fully data-driven machine learning-based approach.</p></div><div><h3>Implications</h3><p>: These modeling approaches provide a dynamic baseline framework to support clinicians in treatment decisions by identifying different treatment outcome trajectories with already clinically available measurement data.</p></div><div><h3>Limitations and future directions:</h3><p>Conjoint application of the presented approach with other predictive tools and biomarkers, as well as further disease information (e.g. metastatic stage), could further enhance treatment outcome prediction. We believe the simple model formulations allow widespread adoption of the developed models to other cancer types. Similar models can easily be formulated for other treatment modalities.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"376 ","pages":"Article 109287"},"PeriodicalIF":1.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424001470/pdfft?md5=cc3264f4903a5bda0fe2d00c2529cd81&pid=1-s2.0-S0025556424001470-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142116623","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":"Understanding antibody magnitude and durability following vaccination against SARS-CoV-2","authors":"Quiyana M. Murphy ,&nbsp;George K. Lewis ,&nbsp;Mohammad M. Sajadi ,&nbsp;Jonathan E. Forde ,&nbsp;Stanca M. Ciupe","doi":"10.1016/j.mbs.2024.109274","DOIUrl":"10.1016/j.mbs.2024.109274","url":null,"abstract":"<div><p>Vaccination against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in transient antibody response against the spike protein. The individual immune status at the time of vaccination influences the response. Using mathematical models of antibody decay, we determined the dynamics of serum immunoglobulin G (IgG) and serum immunoglobulin A (IgA) over time. Data fitting to longitudinal IgG and IgA titers was used to quantify differences in antibody magnitude and antibody duration among infection-naïve and infection-positive vaccinees. We found that prior infections result in more durable serum IgG and serum IgA responses, with prior symptomatic infections resulting in the most durable serum IgG response and prior asymptomatic infections resulting in the most durable serum IgA response. These findings can guide vaccine boosting schedules.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"376 ","pages":"Article 109274"},"PeriodicalIF":1.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142116624","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":"Competitive networked bi-virus spread: Existence of coexistence equilibria","authors":"Axel Janson ,&nbsp;Sebin Gracy ,&nbsp;Philip E. Paré ,&nbsp;Henrik Sandberg ,&nbsp;Karl Henrik Johansson","doi":"10.1016/j.mbs.2024.109286","DOIUrl":"10.1016/j.mbs.2024.109286","url":null,"abstract":"<div><p>The paper studies multi-competitive continuous-time epidemic processes. We consider the setting where two viruses are simultaneously prevalent, and the spread occurs due to individual-to-individual interaction. In such a setting, an individual is either not affected by any of the viruses, or infected by one and exactly one of the two viruses. One of the equilibrium points is the <em>coexistence equilibrium</em>, i.e., multiple viruses simultaneously infect separate fractions of the population. We provide a sufficient condition for the existence of a coexistence equilibrium. We identify a condition such that for certain pairs of spread matrices either every coexistence equilibrium lies on a line that is locally exponentially attractive, or there is no coexistence equilibrium. We then provide a condition that, for certain pairs of spread matrices, rules out the possibility of the existence of a coexistence equilibrium, and, as a consequence, establishes global asymptotic convergence to the endemic equilibrium of the dominant virus. Finally, we provide a mitigation strategy that employs one virus to ensure that the other virus is eradicated. The theoretical results are illustrated using simulations.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109286"},"PeriodicalIF":1.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142116622","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 birth–death model to understand bacterial antimicrobial heteroresistance from time-kill curves","authors":"Nerea Martínez-López,&nbsp;Carlos Vilas,&nbsp;Míriam R. García","doi":"10.1016/j.mbs.2024.109278","DOIUrl":"10.1016/j.mbs.2024.109278","url":null,"abstract":"<div><p>Antimicrobial heteroresistance refers to the presence of different subpopulations with heterogeneous antimicrobial responses within the same bacterial isolate, so they show reduced susceptibility compared with the main population. Though it is widely accepted that heteroresistance can play a crucial role in the outcome of antimicrobial treatments, predictive Antimicrobial Resistance (AMR) models accounting for bacterial heteroresistance are still scarce and need to be refined as the techniques to measure heteroresistance become standardised and consistent conclusions are drawn from data. In this work, we propose a multivariate Birth-Death (BD) model of bacterial heteroresistance and analyse its properties in detail. Stochasticity in the population dynamics is considered since heteroresistance is often characterised by low initial frequencies of the less susceptible subpopulations, those mediating AMR transmission and potentially leading to treatment failure. We also discuss the utility of the heteroresistance model for practical applications and calibration under realistic conditions, demonstrating that it is possible to infer the model parameters and heteroresistance distribution from time-kill data, i.e., by measuring total cell counts alone and without performing any heteroresistance test.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"376 ","pages":"Article 109278"},"PeriodicalIF":1.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002555642400138X/pdfft?md5=b477bf62a30c550df9d349f4c81d30f9&pid=1-s2.0-S002555642400138X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142057715","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":"In Memory of Edmund John Crampin: Multi-scale and multi-physics phenomena in biology","authors":"Santiago Schnell,&nbsp;Philip K. Maini","doi":"10.1016/j.mbs.2024.109283","DOIUrl":"10.1016/j.mbs.2024.109283","url":null,"abstract":"","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"376 ","pages":"Article 109283"},"PeriodicalIF":1.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142057716","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 mechanistic modeling and estimation framework for environmental pathogen surveillance","authors":"Matthew Wascher ,&nbsp;Colin J. Klaus ,&nbsp;Chance Alvarado ,&nbsp;Jenny Panescu ,&nbsp;Mikkel Quam ,&nbsp;Karen C. Dannemiller ,&nbsp;Joseph H. Tien","doi":"10.1016/j.mbs.2024.109257","DOIUrl":"10.1016/j.mbs.2024.109257","url":null,"abstract":"<div><div>Environmental pathogen surveillance is a promising disease surveillance modality that has been widely adopted for SARS-CoV-2 monitoring. The highly variable nature of environmental pathogen data is a challenge for integrating these data into public health response. One source of this variability is heterogeneous infection both within an individual over the course of infection as well as between individuals in their pathogen shedding over time. We present a mechanistic modeling and estimation framework for connecting environmental pathogen data to the number of infected individuals. Infected individuals are modeled as shedding pathogen into the environment via a Poisson process whose rate parameter <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> varies over the course of their infection. These shedding curves <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> are themselves random, allowing for variation between individuals. We show that this results in a Poisson process for environmental pathogen levels with rate parameter a function of the number of infected individuals, total shedding over the course of infection, and pathogen removal from the environment. Theoretical results include determination of identifiable parameters for the model from environmental pathogen data and simple, explicit formulas for the likelihood for particular choices of individual shedding curves. We give a two step Bayesian inference framework, where the first step corresponds to calibration from data where the number of infected individuals is known, followed by an estimation step from environmental surveillance data when the number of infected individuals is unknown. We apply this modeling and estimation framework to synthetic data, as well as to an empirical case study of SARS-CoV-2 in environmental dust collected from isolation rooms housing university students. Both the synthetic data and empirical case study indicate high inter-individual variation in shedding, leading to wide credible intervals for the number of infected individuals. We examine how uncertainty in estimates of the number of infected individuals from environmental pathogen levels scales with the true number of infected individuals and model misspecification. While credible intervals for the number of infected individuals are wide, our results suggest that distinguishing between no infection and small-to-moderate levels of infection (<span><math><mrow><mo>≈</mo><mn>10</mn></mrow></math></span> infected individuals) may be possible, and that it is broadly possible to differentiate between moderate (<span><math><mrow><mo>≈</mo><mn>40</mn></mrow></math></span>) and high (<span><math><mrow><mo>≈</mo><mn>200</mn></mrow></math></span>) numbers of infected individuals.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109257"},"PeriodicalIF":1.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142038129","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}