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The influence of a lipid reservoir on the tear film formation. 脂质储层对泪膜形成的影响。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-10 DOI: 10.1093/imammb/dqz018
Kara L Maki, Richard J Braun, Gregory A Barron

We present a mathematical model to study the influence of a lipid reservoir, seen experimentally, at the lid margin on the formation and relaxation of the tear film during a partial blink. Applying the lubrication limit, we derive two coupled non-linear partial differential equations characterizing the evolution of the aqueous tear fluid and the covering insoluble lipid concentration. Departing from prior works, we explore a new set of boundary conditions (BCs) enforcing hypothesized lipid concentration dynamics at the lid margins. Using both numerical and analytical approaches, we find that the lipid-focused BCs strongly impact tear film formation and thinning rates. Specifically, during the upstroke of the eyelid, we find specifying the lipid concentration at the lid margin accelerates thinning. Parameter regimes that cause tear film formation success or failure are identified. More importantly, this work expands our understanding of the consequences of lipid dynamics near the lid margins for tear film formation.

我们提出了一个数学模型来研究实验中看到的眼睑边缘脂质储层对部分眨眼期间泪膜形成和松弛的影响。应用润滑极限,我们推导了两个耦合的非线性偏微分方程,描述了含水泪液和覆盖的不溶性脂质浓度的演变。从先前的工作出发,我们探索了一组新的边界条件(bc),在眼睑边缘强制假设脂质浓度动态。使用数值和分析方法,我们发现脂质聚焦的bc强烈影响泪膜的形成和稀释速率。具体来说,在眼睑上撇期间,我们发现指定眼睑边缘的脂质浓度会加速变薄。确定了导致泪膜形成成功或失败的参数制度。更重要的是,这项工作扩大了我们对眼睑边缘脂质动力学对泪膜形成的影响的理解。
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引用次数: 3
Informed and uninformed empirical therapy policies. 知情和不知情的经验治疗政策。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-10 DOI: 10.1093/imammb/dqz015
Nicolas Houy, Julien Flaig

We argue that a proper distinction must be made between informed and uninformed decision making when setting empirical therapy policies, as this allows one to estimate the value of gathering more information about the pathogens and their transmission and thus to set research priorities. We rely on the stochastic version of a compartmental model to describe the spread of an infecting organism in a health care facility and the emergence and spread of resistance to two drugs. We focus on information and uncertainty regarding the parameters of this model. We consider a family of adaptive empirical therapy policies. In the uninformed setting, the best adaptive policy allowsone to reduce the average cumulative infected patient days over 2 years by 39.3% (95% confidence interval (CI), 30.3-48.1%) compared to the combination therapy. Choosing empirical therapy policies while knowing the exact parameter values allows one to further decrease the cumulative infected patient days by 3.9% (95% CI, 2.1-5.8%) on average. In our setting, the benefit of perfect information might be offset by increased drug consumption.

我们认为,在制定经验治疗政策时,必须对知情和不知情的决策做出适当的区分,因为这允许人们估计收集更多关于病原体及其传播的信息的价值,从而确定研究重点。我们依靠区隔模型的随机版本来描述卫生保健设施中感染生物体的传播以及对两种药物的耐药性的出现和传播。我们关注的是这个模型参数的信息和不确定性。我们考虑一系列适应性经验治疗政策。在不知情的情况下,与联合治疗相比,最佳适应性政策允许将2年内的平均累计感染天数减少39.3%(95%置信区间(CI), 30.3-48.1%)。在知道确切参数值的情况下选择经验性治疗策略,可使累计感染患者天数平均进一步减少3.9% (95% CI, 2.1-5.8%)。在我们的环境中,完美信息的好处可能会被增加的毒品消费所抵消。
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引用次数: 1
Allostery in oligomeric receptor models. 低聚受体模型的变构。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-10 DOI: 10.1093/imammb/dqz016
Gregory Douglas Conradi Smith

We show how equilibrium binding curves of receptor homodimers can be expressed as rational polynomial functions of the equilibrium binding curves of the constituent monomers, without approximation and without assuming independence of receptor monomers. Using a distinguished spanning tree construction for reduced graph powers, the method properly accounts for thermodynamic constraints and allosteric interactions between receptor monomers (i.e. conformational coupling). The method is completely general; it begins with an arbitrary undirected graph representing the topology of a monomer state-transition diagram and ends with an algebraic expression for the equilibrium binding curve of a receptor oligomer composed of two or more identical and indistinguishable monomers. Several specific examples are analysed, including guanine nucleotide-binding protein-coupled receptor dimers and tetramers composed of multiple 'ternary complex' monomers.

我们展示了受体同型二聚体的平衡结合曲线如何可以表示为组成单体的平衡结合曲线的有理多项式函数,而不需要近似和假设受体单体的独立性。该方法使用一种特殊的生成树构造来降低图的幂,适当地考虑了热力学约束和受体单体之间的变构相互作用(即构象耦合)。这种方法是完全通用的;它以表示单体状态转移图拓扑结构的任意无向图开始,并以由两个或多个相同且不可区分的单体组成的受体低聚物的平衡结合曲线的代数表达式结束。分析了几个具体的例子,包括鸟嘌呤核苷酸结合蛋白偶联受体二聚体和由多个“三元配合物”单体组成的四聚体。
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引用次数: 0
Optimal vaccine allocation during the mumps outbreak in two SIR centres. 两个SIR中心流行性腮腺炎暴发期间疫苗的最佳分配。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-10 DOI: 10.1093/imammb/dqz012
Alexey A Chernov, Mark Y Kelbert, Aleksandr A Shemendyuk

The aim of this work is to investigate the optimal vaccine sharing between two susceptible, infected, removed (SIR) centres in the presence of migration fluxes of susceptibles and infected individuals during the mumps outbreak. Optimality of the vaccine allocation means the minimization of the total number of lost working days during the whole period of epidemic outbreak $[0,t_f]$, which can be described by the functional $Q=int _0^{t_f}I(t),{textrm{d}}t$, where $I(t)$ stands for the number of infectives at time $t$. We explain the behaviour of the optimal allocation, which depends on the model parameters and the amount of vaccine available $V$.

这项工作的目的是调查在腮腺炎暴发期间存在易感者和感染者迁移通量的两个易感、感染、移除(SIR)中心之间的最佳疫苗共享。疫苗分配的最优性是指在整个疫情爆发期间损失的工作日总数$[0,t_f]$最小,可以用函数$Q=int _0^{t_f}I(t),{textrm{d}}t$来描述,其中$I(t)$表示时刻$t$的感染人数。我们解释了最优分配的行为,这取决于模型参数和可用疫苗的数量。
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引用次数: 7
Analytic solutions for calcium ion fertilisation waves on the surface of eggs - erratum. 卵表面钙离子受精波的解析解-勘误。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-10 DOI: 10.1093/imammb/dqaa002
Bronwyn H Bradshaw-Hajek, Philip Broadbridge

The paper, "Analytic solutions for calcium ion fertilisation waves on the surface of eggs" by the current authors (this journal 2019), adopted an incorrect solution to Legendre's equation that had been tabulated in a well known compendium of solutions of differential equations. The solution to the linear equation and the consequent solution of the considered nonlinear problem, are corrected here. The solution maintains the same character and the conclusions are the same. Numerical evaluations and graphic outputs have been modified.

现任作者的论文《卵子表面钙离子受精波的解析解》(2019年本刊)采用了列在著名微分方程解纲要中的勒让德方程的错误解。这里对线性方程的解和所考虑的非线性问题的后续解进行了修正。解的性质不变,结论不变。对数值评价和图形输出进行了修改。
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引用次数: 0
Modelling the inclusion of swelling pressure in a tissue level poroviscoelastic model of cartilage deformation. 软骨变形的组织水平孔粘弹性模型中溶胀压力的模拟。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-10 DOI: 10.1093/imammb/dqaa001
Jonathan P Whiteley, Eamonn A Gaffney

Swelling pressure in the interstitial fluid within the pores of cartilage tissue is known to have a significant effect on the rheology of cartilage tissue. The swelling pressure varies rapidly within thin regions inside pores known as Debye layers, caused by the presence of fixed charge, as observed in cartilage. Tissue level calculation of cartilage deformation therefore requires resolution of three distinct spatial scales: the Debye lengthscale within individual pores; the lengthscale of an individual pore; and the tissue lengthscale. We use asymptotics to construct a leading order approximation to the swelling pressure within pores, allowing the swelling pressure to be systematically included within a fluid-solid interaction model at the level of pores in cartilage. We then use homogenization to derive tissue level equations for cartilage deformation that are very similar to those governing the finite deformation of a poroviscoelastic body. The equations derived permit the spatial variations in porosity and electric charge that occur in cartilage tissue. Example solutions are then used to confirm the plausibility of the model derived and to consider the impact of fixed charge heterogeneity, illustrating that local fixed charge loss is predicted to increase deformation gradients under confined compression away from, rather than at, the site of loss.

软骨组织孔隙间质液中的肿胀压力对软骨组织的流变学有重要影响。膨胀压力在被称为德拜层的孔隙内的薄区域内迅速变化,这是由固定电荷的存在引起的,正如在软骨中观察到的那样。因此,软骨变形的组织水平计算需要三个不同的空间尺度的分辨率:单个毛孔内的德拜长度尺度;单个孔的长度;还有组织的长度。我们使用渐近性来构建孔隙内膨胀压力的阶近似,允许膨胀压力系统地包含在软骨孔隙水平的流固相互作用模型中。然后,我们使用均匀化来推导软骨变形的组织水平方程,这些方程非常类似于那些控制孔隙粘弹性体的有限变形的方程。推导出的方程允许软骨组织中孔隙度和电荷的空间变化。然后使用示例解来证实所推导模型的合理性,并考虑固定电荷非均质性的影响,说明局部固定电荷损失预计会在远离而不是在损失位置的受限压缩下增加变形梯度。
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引用次数: 2
Stochastic optimal control of pre-exposure prophylaxis for HIV infection. HIV感染暴露前预防的随机最优控制。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-08 DOI: 10.1093/imammb/dqac003
Jasmina Ðorđević, Kristina Rognlien Dahl
The aim of the paper is to apply the stochastic optimal control problem in order to optimize the number of individual which will have the pre-exposure prophylaxis (PReP) treatment in the stochastic model for HIV/AIDS with PReP. By using the stochastic maximum principle, we derive the stochastic optimal control of PReP for the unconstrained control problem. Furthermore, by combining the stochastic maximum principle with a version of the Lagrange multiplier method, we solve the PReP problem for two different types of budget constrains with a given constrain for the costs (possible of different kind, transportation, price of the treatment, etc.). Obtained results for the different percentage of the individuals who got the vaccine, as well as results for unconstrained and constrained problems, are illustrated by a numerical example.
针对HIV/AIDS暴露前预防(PReP)随机模型,应用随机最优控制问题来优化接受暴露前预防(PReP)治疗的个体数量。利用随机极大值原理,导出了无约束控制问题的暴露前预防随机最优控制。进一步,将随机极大值原理与拉格朗日乘数法相结合,在给定成本约束(不同种类的可能性、运输、治疗价格等)的情况下,求解了两种不同类型预算约束的PReP问题。通过一个数值例子说明了接种疫苗的不同个体百分比的结果,以及无约束和有约束问题的结果。
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引用次数: 0
Potential reduction in transmission of COVID-19 by digital contact tracing systems 通过数字接触者追踪系统可能减少COVID-19的传播
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-09-01 DOI: 10.1101/2020.08.27.20068346
M. Plank, A. James, Audrey Lustig, N. Steyn, Rachelle N. Binny, S. Hendy
Digital tools are being developed to support contact tracing as part of the global effort to control the spread of COVID-19. These include smartphone apps, Bluetooth-based proximity detection, location tracking, and automatic exposure notification features. Evidence on the effectiveness of alternative approaches to digital contact tracing is so far limited. We use an age-structured branching process model of the transmission of COVID-19 in different settings to estimate the potential of manual contact tracing and digital tracing systems to help control the epidemic. We investigate the effect of the uptake rate and proportion of contacts recorded by the digital system on key model outputs: the effective reproduction number, the mean outbreak size after 30 days, and the probability of elimination. We show that effective manual contact tracing can reduce the effective reproduction number from 2.4 to around 1.5. The addition of a digital tracing system with a high uptake rate over 75% could further reduce the effective reproduction number to around 1.1. Fully automated digital tracing without manual contact tracing is predicted to be much less effective. We conclude that, for digital tracing systems to make a significant contribution to the control of COVID-19, they need be designed in close conjunction with public health agencies to support and complement manual contact tracing by trained professionals.
作为控制COVID-19传播的全球努力的一部分,正在开发数字工具以支持接触者追踪。其中包括智能手机应用程序、基于蓝牙的接近检测、位置跟踪和自动曝光通知功能。迄今为止,关于数字接触者追踪替代方法有效性的证据有限。我们使用不同环境下COVID-19传播的年龄结构分支过程模型来估计人工接触者追踪和数字追踪系统帮助控制疫情的潜力。我们研究了数字系统记录的接触率和比例对关键模型输出的影响:有效繁殖数、30天后的平均爆发规模和消除概率。我们发现,有效的人工接触追踪可以将有效复制数从2.4减少到1.5左右。增加一个吸收率超过75%的数字跟踪系统可以进一步将有效繁殖数降低到1.1左右。没有人工接触跟踪的全自动数字跟踪预计效率会低得多。我们的结论是,要使数字追踪系统为控制COVID-19做出重大贡献,就需要与公共卫生机构密切合作设计这些系统,以支持和补充训练有素的专业人员进行的人工接触者追踪。
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引用次数: 9
A stochastic model for cancer metastasis: branching stochastic process with settlement. 肿瘤转移的随机模型:带有沉降的分支随机过程。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-05-29 DOI: 10.1093/imammb/dqz009
Christoph Frei, Thomas Hillen, Adam Rhodes

We introduce a new stochastic model for metastatic growth, which takes the form of a branching stochastic process with settlement. The moving particles are interpreted as clusters of cancer cells, while stationary particles correspond to micro-tumours and metastases. The analysis of expected particle location, their locational variance, the furthest particle distribution and the extinction probability leads to a common type of differential equation, namely, a non-local integro-differential equation with distributed delay. We prove global existence and uniqueness results for this type of equation. The solutions' asymptotic behaviour for long time is characterized by an explicit index, a metastatic reproduction number $R_0$: metastases spread for $R_{0}>1$ and become extinct for $R_{0}<1$. Using metastatic data from mouse experiments, we show the suitability of our framework to model metastatic cancer.

我们引入了一个新的转移生长随机模型,该模型采用带有沉降的分支随机过程的形式。移动的粒子被解释为癌细胞簇,而静止的粒子对应于微肿瘤和转移。通过对期望粒子位置、它们的位置方差、最远粒子分布和消光概率的分析,得到一类常见的微分方程,即具有分布延迟的非局部积分微分方程。证明了这类方程的整体存在唯一性结果。解的长期渐近性表现为一个明确的指数,即转移繁殖数$R_0$:当$R_{0}>1$时,转移扩散,而当$R_{0}时,转移消失。
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引用次数: 5
Identifying the number of unreported cases in SIR epidemic models. 确定SIR流行病模型中未报告病例的数量。
IF 1.1 4区 数学 Q4 BIOLOGY Pub Date : 2020-05-29 DOI: 10.1093/imammb/dqz013
A Ducrot, P Magal, T Nguyen, G F Webb

An SIR epidemic model is analysed with respect to the identification of its parameters and initial values, based upon reported case data from public health sources. The objective of the analysis is to understand the relationship of unreported cases to reported cases. In many epidemic diseases the reported cases are a small fraction of the unreported cases. This fraction can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to the Hong Kong seasonal influenza epidemic in New York City in 1968-1969.

根据公共卫生来源报告的病例数据,对SIR流行病模型的参数和初始值的确定进行了分析。分析的目的是了解未报告病例与报告病例之间的关系。在许多流行病中,报告的病例只占未报告病例的一小部分。这个比例可以通过从报告的病例数据中识别模型的参数来估计。该分析应用于1968-1969年香港季节性流感在纽约市的流行。
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引用次数: 23
期刊
Mathematical Medicine and Biology-A Journal of the Ima
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