Bulletin of Mathematical Biology最新文献

{"title":"Oscillations in a Spatial Oncolytic Virus Model.","authors":"Arwa Abdulla Baabdulla, Thomas Hillen","doi":"10.1007/s11538-024-01322-z","DOIUrl":"10.1007/s11538-024-01322-z","url":null,"abstract":"<p><p>Virotherapy treatment is a new and promising target therapy that selectively attacks cancer cells without harming normal cells. Mathematical models of oncolytic viruses have shown predator-prey like oscillatory patterns as result of an underlying Hopf bifurcation. In a spatial context, these oscillations can lead to different spatio-temporal phenomena such as hollow-ring patterns, target patterns, and dispersed patterns. In this paper we continue the systematic analysis of these spatial oscillations and discuss their relevance in the clinical context. We consider a bifurcation analysis of a spatially explicit reaction-diffusion model to find the above mentioned spatio-temporal virus infection patterns. The desired pattern for tumor eradication is the hollow ring pattern and we find exact conditions for its occurrence. Moreover, we derive the minimal speed of travelling invasion waves for the cancer and for the oncolytic virus. Our numerical simulations in 2-D reveal complex spatial interactions of the virus infection and a new phenomenon of a periodic peak splitting. An effect that we cannot explain with our current methods.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141417862","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":"Optimal Control of Collective Electrotaxis in Epithelial Monolayers.","authors":"Simon F Martina-Perez, Isaac B Breinyn, Daniel J Cohen, Ruth E Baker","doi":"10.1007/s11538-024-01319-8","DOIUrl":"10.1007/s11538-024-01319-8","url":null,"abstract":"<p><p>Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered e.g. using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored. In this work, we construct and calibrate an ordinary differential equation model to predict the average velocity of the centre of mass of a cellular monolayer in response to stimulation with an electric field. We use this model, in conjunction with optimal control theory, to derive physically realistic optimal electric field designs to achieve a variety of aims, including maximising the total distance travelled by the monolayer, maximising the monolayer velocity, and keeping the monolayer velocity constant during stimulation. Together, this work is the first to present a unified framework for optimal control of collective monolayer electrotaxis and provides a blueprint to optimally steer collective migration using other external cues.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11186957/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141417861","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":"0-1 Laws for Pattern Occurrences in Phylogenetic Trees and Networks.","authors":"François Bienvenu, Mike Steel","doi":"10.1007/s11538-024-01316-x","DOIUrl":"10.1007/s11538-024-01316-x","url":null,"abstract":"<p><p>In a recent paper, the question of determining the fraction of binary trees that contain a fixed pattern known as the snowflake was posed. We show that this fraction goes to 1, providing two very different proofs: a purely combinatorial one that is quantitative and specific to this problem; and a proof using branching process techniques that is less explicit, but also much more general, as it applies to any fixed patterns and can be extended to other trees and networks. In particular, it follows immediately from our second proof that the fraction of d-ary trees (resp. level-k networks) that contain a fixed d-ary tree (resp. level-k network) tends to 1 as the number of leaves grows.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141417857","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 Assessment of the Role of Human Behavior Changes on SARS-CoV-2 Transmission Dynamics in the United States.","authors":"Binod Pant, Salman Safdar, Mauricio Santillana, Abba B Gumel","doi":"10.1007/s11538-024-01324-x","DOIUrl":"10.1007/s11538-024-01324-x","url":null,"abstract":"<p><p>The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g., lockdowns) over a long (extended) period of time, (c) social peer-pressure, among others. A novel behavior-epidemiology model, which takes the form of a deterministic system of nonlinear differential equations, is developed and fitted using observed cumulative SARS-CoV-2 mortality data during the first wave in the United States. The model fits the observed data, as well as makes a more accurate prediction of the observed daily SARS-CoV-2 mortality during the first wave (March 2020-June 2020), in comparison to the equivalent model which does not explicitly account for changes in human behavior. This study suggests that, as more newly-infected individuals become asymptomatically-infectious, the overall level of positive behavior change can be expected to significantly decrease (while new cases may rise, particularly if asymptomatic individuals have higher contact rate, in comparison to symptomatic individuals).</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141417859","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 Assessment of the Role of Intervention Programs for Malaria Control.","authors":"Maame Akua Korsah, Stuart T Johnston, Kathryn E Tiedje, Karen P Day, Jennifer A Flegg, Camelia R Walker","doi":"10.1007/s11538-024-01321-0","DOIUrl":"10.1007/s11538-024-01321-0","url":null,"abstract":"<p><p>Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11189351/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141417860","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":"Dimensions of Level-1 Group-Based Phylogenetic Networks.","authors":"Elizabeth Gross, Robert Krone, Samuel Martin","doi":"10.1007/s11538-024-01314-z","DOIUrl":"10.1007/s11538-024-01314-z","url":null,"abstract":"<p><p>Phylogenetic networks represent evolutionary histories of sets of taxa where horizontal evolution or hybridization has occurred. Placing a Markov model of evolution on a phylogenetic network gives a model that is particularly amenable to algebraic study by representing it as an algebraic variety. In this paper, we give a formula for the dimension of the variety corresponding to a triangle-free level-1 phylogenetic network under a group-based evolutionary model. On our way to this, we give a dimension formula for codimension zero toric fiber products. We conclude by illustrating applications to identifiability.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11182832/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141417858","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":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">A Role of Effector CD <ns0:math><ns0:msup><ns0:mn>8</ns0:mn> <ns0:mo>+</ns0:mo></ns0:msup> </ns0:math> T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model.","authors":"Khaphetsi Joseph Mahasa, Rachid Ouifki, Lisette de Pillis, Amina Eladdadi","doi":"10.1007/s11538-024-01323-y","DOIUrl":"10.1007/s11538-024-01323-y","url":null,"abstract":"<p><p>Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD <math><msup><mn>8</mn> <mo>+</mo></msup> </math> T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD <math><msup><mn>8</mn> <mo>+</mo></msup> </math> T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD <math><msup><mn>8</mn> <mo>+</mo></msup> </math> T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD <math><msup><mn>8</mn> <mo>+</mo></msup> </math> T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD <math><msup><mn>8</mn> <mo>+</mo></msup> </math> T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD <math><msup><mn>8</mn> <mo>+</mo></msup> </math> T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD <math><msup><mn>8</mn> <mo>+</mo></msup> </math> T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141330400","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":"Evolutionary Invasion Analysis of Modern Epidemics Highlights the Context-Dependence of Virulence Evolution.","authors":"Sudam Surasinghe, Ketty Kabengele, Paul E Turner, C Brandon Ogbunugafor","doi":"10.1007/s11538-024-01313-0","DOIUrl":"10.1007/s11538-024-01313-0","url":null,"abstract":"<p><p>Models are often employed to integrate knowledge about epidemics across scales and simulate disease dynamics. While these approaches have played a central role in studying the mechanics underlying epidemics, we lack ways to reliably predict how the relationship between virulence (the harm to hosts caused by an infection) and transmission will evolve in certain virus-host contexts. In this study, we invoke evolutionary invasion analysis-a method used to identify the evolution of uninvadable strategies in dynamical systems-to examine how the virulence-transmission dichotomy can evolve in models of virus infections defined by different natural histories. We reveal peculiar patterns of virulence evolution between epidemics with different disease natural histories (SARS-CoV-2 and hepatitis C virus). We discuss the findings with regards to the public health implications of predicting virus evolution, and in broader theoretical canon involving virulence evolution in host-parasite systems.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11178639/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141320629","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":"Dimensional Dependence of Binding Kinetics.","authors":"Megan G Dixon, James P Keener","doi":"10.1007/s11538-024-01311-2","DOIUrl":"10.1007/s11538-024-01311-2","url":null,"abstract":"<p><p>In the context of protein-protein binding, the dissociation constant is used to describe the affinity between two proteins. For protein-protein interactions, most experimentally-measured dissociation constants are measured in solution and reported in units of volume concentration. However, many protein interactions take place on membranes. These interactions have dissociation constants with units of areal concentration, rather than volume concentration. Here, we present a novel, stochastic approach to understanding the dimensional dependence of binding kinetics. Using stochastic exit time calculations, in discrete and continuous space, we derive general reaction rates for protein-protein binding in one, two, and three dimensions and demonstrate that dimensionality greatly affects binding kinetics. Further, we present a formula to transform three-dimensional experimentally-measured dissociation constants to two-dimensional dissociation constants. This conversion can be used to mathematically model binding events that occur on membranes.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141316792","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":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">A Model for the Coexistence of Competing Mechanisms for <ns0:math><ns0:msup><ns0:mtext>Ca</ns0:mtext> <ns0:mrow><ns0:mtext>2</ns0:mtext> <ns0:mo>+</ns0:mo></ns0:mrow> </ns0:msup> </ns0:math> Oscillations in T-lymphocytes.","authors":"Paco Castaneda Ruan, J Cory Benson, Mohamed Trebak, Vivien Kirk, James Sneyd","doi":"10.1007/s11538-024-01317-w","DOIUrl":"10.1007/s11538-024-01317-w","url":null,"abstract":"<p><p><math><msup><mtext>Ca</mtext> <mrow><mtext>2</mtext> <mo>+</mo></mrow> </msup> </math> is a ubiquitous signaling mechanism across different cell types. In T-cells, it is associated with cytokine production and immune function. Benson et al. have shown the coexistence of competing <math><msup><mtext>Ca</mtext> <mrow><mtext>2</mtext> <mo>+</mo></mrow> </msup> </math> oscillations during antigen stimulation of T-cell receptors, depending on the presence of extracellular <math><msup><mtext>Ca</mtext> <mrow><mtext>2</mtext> <mo>+</mo></mrow> </msup> </math> influx through the <math><msup><mtext>Ca</mtext> <mrow><mtext>2</mtext> <mo>+</mo></mrow> </msup> </math> release-activated <math><msup><mtext>Ca</mtext> <mrow><mtext>2</mtext> <mo>+</mo></mrow> </msup> </math> channel (Benson in J Biol Chem 29:105310, 2023). In this paper, we construct a mathematical model consisting of five ordinary differential equations and analyze the relationship between the competing oscillatory mechanisms.. We perform bifurcation analysis on two versions of our model, corresponding to the two oscillatory types, to find the defining characteristics of these two families.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11176111/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141310112","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}