Mathematical Biosciences最新文献

{"title":"An in-silico approach to the dynamics of proliferation potential in stem cells and the study of different therapies in cases of ovarian dysfunction","authors":"A.M. Portillo ,&nbsp;J.A. García-Velasco ,&nbsp;E. Varela","doi":"10.1016/j.mbs.2024.109305","DOIUrl":"10.1016/j.mbs.2024.109305","url":null,"abstract":"<div><div>A discrete mathematical model based on ordinary differential equations and the associated continuous model formed by a partial differential equation, which simulate the generational and temporal evolution of a stem cell population, are proposed. The model parameters are the maximum proliferation potential and the rates of mitosis, death events and telomerase activity. The mean proliferation potential at each point in time is suggested as an indicator of population aging. The model is applied on hematopoietic stem cells (HSCs), with different telomerase activity rates, in a range of variation of maximum proliferation potential in healthy individuals, to study the temporal evolution of aging. HSCs express telomerase, however not at levels that are sufficient for maintaining constant telomere length with aging <span><span>[1]</span></span>, <span><span>[2]</span></span>. Women with primary ovarian insufficiency (POI) are known to have low telomerase activity in granulosa cells and peripheral blood mononuclear cells <span><span>[3]</span></span>. Extrapolating this to hematopoietic stem cells, the mathematical model shows the differences in proliferation potential of the cell populations when telomerase expression is activated using sexual steroids, though the endogenous promoter or with gene therapy using exogenous, stronger promoters within the adeno-associated virus. In the first case, proliferation potential of cells from POI condition increases, but when adeno-associated viruses are used, the proliferation potential reaches the levels of healthy cell populations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142376443","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 joint-threshold Filippov model describing the effect of intermittent androgen-deprivation therapy in controlling prostate cancer","authors":"Aili Wang ,&nbsp;Rong Yan ,&nbsp;Haixia Li ,&nbsp;Xiaodan Sun ,&nbsp;Weike Zhou ,&nbsp;Stacey R. Smith?","doi":"10.1016/j.mbs.2024.109301","DOIUrl":"10.1016/j.mbs.2024.109301","url":null,"abstract":"<div><div>Intermittent androgen-deprivation therapy (IADT) can be beneficial to delay the occurrence of treatment resistance and cancer relapse compared to the standard continuous therapy. To study the effect of IADT in controlling prostate cancer, we developed a Filippov prostate cancer model with a joint threshold function: therapy is implemented once the total population of androgen-dependent cells (AC-Ds) and androgen-independent cells (AC-Is) is greater than the threshold value <span><math><mrow><mi>E</mi><mi>T</mi></mrow></math></span>, and it is suspended once the population is less than <span><math><mrow><mi>E</mi><mi>T</mi></mrow></math></span>. As the parameters vary, our model undergoes a series of sliding bifurcations, including boundary node, focus, saddle, saddle-node and tangency bifurcations. We also obtained the coexistence of one, two or three real equilibria and the bistability of two equilibria. Our results demonstrate that the population of AC-Is can be contained at a predetermined level if the initial population of AC-Is is less than this level, and we choose a suitable threshold value.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142305091","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":"Adolescent vaping behaviours: Exploring the dynamics of a social contagion model","authors":"Sarah I. Machado-Marques,&nbsp;Iain R. Moyles","doi":"10.1016/j.mbs.2024.109303","DOIUrl":"10.1016/j.mbs.2024.109303","url":null,"abstract":"<div><p>Vaping, or the use of electronic cigarettes (e-cigarettes), is an ongoing issue for public health. The rapid increase in e-cigarette usage, particularly among adolescents, has often been referred to as an epidemic. Drawing upon this epidemiological analogy between vaping and infectious diseases as a theoretical framework, we present a deterministic compartmental model of adolescent e-cigarette smoking which accounts for social influences on initiation, relapse, and cessation behaviours. We use results from a sensitivity analysis of the model’s parameters on various response variables to identify key influences on system dynamics and simplify the model into one that can be analysed more thoroughly. We identify a single feasible endemic equilibrium for the proportion of smokers that decreases as social influence on cessation increases. Through steady state and stability analyses, as well as simulations of the model, we conclude that social influences from and on temporary quitters are not important in overall model dynamics, and that social influences from permanent quitters can have a significant impact on long-term system dynamics. In particular, we show that social influence on cessation can induce persistent recurrent smoking outbreaks.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424001639/pdfft?md5=a3403f8b7858cb1615546af170478764&pid=1-s2.0-S0025556424001639-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142270742","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":"Modeling virus-stimulated proliferation of CD4+ T-cell, cell-to-cell transmission and viral loss in HIV infection dynamics","authors":"Jiawei Deng ,&nbsp;Hongying Shu ,&nbsp;Lin Wang ,&nbsp;Xingfu Zou","doi":"10.1016/j.mbs.2024.109302","DOIUrl":"10.1016/j.mbs.2024.109302","url":null,"abstract":"<div><p>Human immunodeficiency virus (HIV) can persist in infected individuals despite prolonged antiretroviral therapy and it may spread through two modes: virus-to-cell and cell-to-cell transmissions. Understanding viral infection dynamics is pivotal for elucidating HIV pathogenesis. In this study, we incorporate the loss term of virions, and both virus-to-cell and cell-to-cell infection modes into a within-host HIV model, which also takes into consideration the proliferation of healthy target cells stimulated by free viruses. By constructing suitable Lyapunov function and applying geometric methods, we establish global stability results of the infection free equilibrium and the infection persistent equilibrium, respectively. Our findings highlight the crucial role of the basic reproduction number in the threshold dynamics. Moreover, we use the loss rate of virions as the bifurcation parameter to investigate stability switches of the positive equilibrium, local Hopf bifurcation, and its global continuation. Numerical simulations validate our theoretical results, revealing rich viral dynamics including backward bifurcation, saddle–node bifurcation, and bistability phenomenon in the sense that the infection free equilibrium and a limit cycle are both locally asymptotically stable. These insights contribute to a deeper understanding of HIV dynamics and inform the development of effective therapeutic strategies.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242387","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":"Efficacy of the Sterile Insect Technique in the presence of inaccessible areas: A study using two-patch models","authors":"P.A. Bliman ,&nbsp;N. Nguyen ,&nbsp;N. Vauchelet","doi":"10.1016/j.mbs.2024.109290","DOIUrl":"10.1016/j.mbs.2024.109290","url":null,"abstract":"<div><p>The Sterile Insect Technique (SIT) is one of the sustainable strategies for the control of disease vectors, which consists of releasing sterilized males that will mate with the wild females, resulting in a reduction and, eventually a local elimination, of the wild population. The implementation of the SIT in the field can become problematic when there are inaccessible areas where the release of sterile insects cannot be carried out directly, and the migration of wild insects from these areas to the treated zone may influence the efficacy of this technique. However, we can also take advantage of the movement of sterile individuals to control the wild population in these unreachable places. In this paper, we derive a two-patch model for <em>Aedes</em> mosquitoes where we consider the discrete diffusion between the treated area and the inaccessible zone. We investigate two different release strategies (constant and impulsive periodic releases), and by using the monotonicity of the model, we show that if the number of released sterile males exceeds some threshold, the technique succeeds in driving the whole population in both areas to extinction. This threshold depends on not only the biological parameters of the population but also the diffusion between the two patches.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424001500/pdfft?md5=041fb684ce157fa53ac9c228a4080586&pid=1-s2.0-S0025556424001500-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142147232","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":"Interplay of virulence factors shapes ecology and treatment outcomes in polymicrobial infections","authors":"C. Herzberg ,&nbsp;E.N. van Meegen ,&nbsp;J.G.C. van Hasselt","doi":"10.1016/j.mbs.2024.109293","DOIUrl":"10.1016/j.mbs.2024.109293","url":null,"abstract":"<div><p>Polymicrobial infections, caused by a community of multiple micro-organisms, are often associated with increased infection severity and poorer patient outcomes. The design of improved antimicrobial treatment strategies for PMIs can be supported by an understanding of their ecological and evolutionary dynamics. Bacterial species present in polymicrobial infections can produce virulence factors to inhibit host immune responses, such as neutrophil recruitment and phagocytosis. The presence of virulence factors can indirectly affect other bacterial species acting as a type of host-mediated interspecies interaction. The aim of this study was to assess how bacterial virulence factors targeting neutrophil function influence ecology and treatment outcomes of PMIs. An agent-based model was constructed which describes a dual-species bacterial population in the presence of neutrophils and a bacteriostatic drug. Our analysis has revealed unforeseen dynamics of the interplay of multiple virulence factors acting as interspecies interaction. We found that the distribution of two phagocytosis-inhibiting virulence factors amongst species can impact whether they have a mutually protective effect for both species. The addition of a virulence factor inhibiting neutrophil recruitment was found to reduce the protective effect of phagocytosis-inhibiting virulence factors. Furthermore we demonstrate the importance of virulence strength of a species relative to other virulent species to determine the fate of a species. We conclude that virulence factors are an important driver of population dynamics in polymicrobial infections, and may be a relevant therapeutic target for treatment of polymicrobial infections.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424001536/pdfft?md5=970ee5fd8e1c951f77badf57edaadad7&pid=1-s2.0-S0025556424001536-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157071","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 mathematical model of melatonin synthesis and interactions with the circadian clock","authors":"Janet Best ,&nbsp;Ruby Kim ,&nbsp;Michael Reed ,&nbsp;H. Frederik Nijhout","doi":"10.1016/j.mbs.2024.109280","DOIUrl":"10.1016/j.mbs.2024.109280","url":null,"abstract":"<div><p>A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregulating two key enzymes in the pineal. The melatonin produced enters the blood and the cerebrospinal fluid and thus the SCN, influencing the circadian clock. We show that the model of melatonin synthesis corresponds well with extant experimental data and responds similarly to clinical experiments on bright light in the middle of the night. Melatonin is widely used to treat jet lag and sleep disorders. We show how the feedback from the pineal to the SCN causes phase resetting of the circadian clock. Melatonin doses early in the evening advance the clock and doses late at night delay the clock with a dead zone in between where the phase of the clock does not change.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142147231","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":"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}