Alfio Quarteroni
In this paper we will address the problem of developing mathematical models for the numerical simulation of the human circulatory system. In particular, we will focus our attention on the problem of haemodynamics in large human arteries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
This contribution aims to shed light on mathematical epidemic dynamics modelling from the viewpoint of analytical mechanics. To set the stage, it recasts the basic SIR model of mathematical epidemic dynamics in an analytical mechanics setting. Thereby, it considers two possible re-parameterizations of the basic SIR model. On the one hand, it is proposed to re-scale time, while on the other hand, to transform the coordinates, i.e.\ the independent variables. In both cases, Hamilton's equations in terms of a suited Hamiltonian as well as Hamilton's principle in terms of a suited Lagrangian are c…
Mathematical modelling of decision cycles in a competitive environment with neutral parties
本文通过将生态启发的种群模型与Kuramoto方程耦合建模决策的行动-感知周期，扩展了对抗性种群的指挥与控制模型，以明确捕捉竞争，并强调了竞争敏捷性与决策过程对种群成功的重要性。
The Impact of Temperature and Isolation on COVID-19 in India: A Mathematical Modelling approach
本研究通过延迟微分方程模型，分析温度与隔离延迟对印度COVID-19传播的影响，发现温度降低和隔离延迟增加均会提高平均感染人数，预测冬季感染上升。
Stochastic Mathematical Modelling Study for Understanding the Extinction, Persistence and Control of SARS-CoV-2 Virus at the Within-host Level
本文通过随机微分方程建立SARS-CoV-2宿主体内仓室模型，分析解的存在性、有界性、持续性及无感染平衡态的指数稳定性，并利用随机最优控制研究抗病毒药物和免疫调节剂的有效性，揭示环境噪声可导致疾病灭绝。
We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by philosophy, especially by Gilbert Simondon's philosophy of individuation, Alfred North Whitehead's philosophy of organism, and concepts from cybernetics. Here, a mathematical formalism is presented to better describe and define the system metamodel of the allagmatic method, thereby further generalising it and extending its reach to a more formal treatment and allowing…
These are lecture notes for five sessions in the AMSI Winter School on 'Computational Modelling of Heterogeneous Media' held at QUT in July 2019 [https://ws.amsi.org.au/]. Aim: Discuss a mix of new mathematical approaches for multiscale modelling, heterogeneous material in particular, along with corresponding novel computational techniques and issues. I include discussion of a developing toolbox that empowers you to implement effective multiscale `equation-free' computation [https://github.com/uoa1184615/EquationFreeGit.git].
Brain-related experiments are limited by nature, and so biological insights are often restricted or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new biological hypotheses, researchers started using mathematical models that can simulate tumour evolution. However, most of these models focus on single-scale 2D cell dynamics, and cannot capture the complex multi-scale tumour invasion patterns in 3D brains. A particular role in these invasion patterns is likely played by the distribution of micro-fibres. To inves…
The virus SARS-COV-2 caused disease COVID-19 has been declared a pandemic by WHO. Currently, over 210 countries and territories have been affected. Careful, well-designed drugs and vaccine for the total elimination of this virus seem to be the need of the hour. In this context, the invivo mathematical modelling studies can be extremely helpful in understanding the efficacy of the drug interventions. These studies can also help understand the role of the crucial inflammatory mediators and the behaviour of immune response towards this novel coronavirus. Motivated by these facts, in this paper, w…
"Mayer waves" are long-period (6 to 12 seconds) oscillations in arterial blood pressure, which have been observed and studied for more than 100 years in the cardiovascular system of humans and other mammals. A mathematical model of the human cardiovascular system is presented, incorporating parameters relevantto the onset of Mayer waves. The model is analyzed using methods of Lyapunov stability and Hopf bifurcation theory. The analysis shows that increase in the gain of the baroreflex feedback loop controlling venous volume may lead to the onset of oscillations, while changes in the other para…
The introduction of Wolbachia-carrying mosquitoes into the population has recently been proposed as an alternative strategy against dengue. Although laboratory experiments have shown that the Wolbachia bacterium can reduce the levels of dengue virus in mosquitoes, it is also important to assess the performance of Wolbachia in reducing the incidence of dengue in human populations.In this thesis, deterministic mathematical models of human and mosquito populations in which either one or two dengue serotypes circulate are developed. We adapt these models to enable the investigation of dengue disea…
Chemical clock reactions are characterised by a relatively long induction period followed by a rapid `switchover' during which the concentration of a \emph{clock chemical} rises rapidly. In addition to their interest in chemistry education, these reactions are relevant to industrial and biochemical applications. A substrate-depletive, non-autocatalytic clock reaction involving household chemicals (vitamin C, iodine, hydrogen peroxide and starch) is modelled mathematically via a system of nonlinear ordinary differential equations. Following dimensional analysis the model is analysed in the phas…
Local drug delivery has received much recognition in recent years, yet it is still unpredictable how drug efficacy depends on physicochemical properties and delivery kinetics. The purpose of the current study is to provide a useful mathematical model for drug release from a drug delivery device and consecutive drug transport in biological tissue, thereby aiding the development of new therapeutic drug by a systemic approach. In order to study the complete process, a two-layer spatio-temporal model depicting drug transport between the coupled media is presented. Drug release is described by cons…
Leukaemia accounts for around 3% of all cancer types diagnosed in adults, and is the most common type of cancer in children of paediatric age. There is increasing interest in the use of mathematical models in oncology to draw inferences and make predictions, providing a complementary picture to experimental biomedical models. In this paper we recapitulate the state of the art of mathematical modelling of leukaemia growth dynamics, in time and response to treatment. We intend to describe the mathematical methodologies, the biological aspects taken into account in the modelling, and the conclusi…
Following the ideas of L.N.Gumilev, we introduce the mathematical model of ethnogenesis which describes the dynamics of subgroups in the developing polity in terms of ordinary differential equations. The bust dynamics associated with the rise and fall of civilisations is modelled as an excitation process, which is the non-linear phenomenon, well known in mathematical biology. We consider deterministic as well as the stochastic version of the model. We also expand the model to study the interaction between two polities undergoing ethnogenesis. Investigation is performed using analytical methods…
Respiratory syncytial virus (RSV) is a leading cause of acute lower respiratory tract infection worldwide, resulting in approximately sixty thousand annual hospitalizations of <5-year-olds in the United States alone and three million annual hospitalizations globally. The development of over 40 vaccines and immunoprophylactic interventions targeting RSV has the potential to significantly reduce the disease burden from RSV infection in the near future. In the context of RSV, a highly contagious pathogen, dynamic transmission models (DTMs) are valuable tools in the evaluation and comparison of th…
Recent experimental evidence suggests that acute myeloid leukemias may originate from multiple clones of malignant cells. Nevertheless it is not known how the observed clones may differ with respect to cell properties such as proliferation and self-renewal. There are scarcely any data on how these cell properties change due to chemotherapy and relapse. We propose a new mathematical model to investigate the impact of cell properties on multi-clonal composition of leukemias. Model results imply that enhanced self-renewal may be a key mechanism in the clonal selection process. Simulations suggest…
The retina is the entrance of the visual system. Although based on common biophysical principles the dynamics of retinal neurons is quite different from their cortical counterparts, raising interesting problems for modellers. In this paper I address some mathematically stated questions in this spirit, discussing, in particular: (1) How could lateral amacrine cell connectivity shape the spatio-temporal spike response of retinal ganglion cells ? (2) How could spatio-temporal stimuli correlations and retinal network dynamics shape the spike train correlations at the output of the retina ? These q…
Mathematical Modelling of Oscillatory Dynamics in Circular Traffic Systems
本文通过耦合延迟微分方程和符号系统，解析建模环形交通中的驻波振荡，揭示稳定性阈值与滞后，为自动驾驶控制提供抑制策略。
The plant hormones brassinosteroid (BR) and gibberellin (GA) have important roles in a wide range of processes involved in plant growth and development. In this paper we derive and analyse new mathematical models for the BR signalling pathway and for the crosstalk between the BR and GA signalling pathways. To analyse the effects of spatial heterogeneity of the signalling processes, along with spatially-homogeneous ODE models we derive coupled PDE-ODE systems modelling the temporal and spatial dynamics of molecules involved in the signalling pathways. The values of the parameters in the model f…
The outcomes of warfare have rarely only been characterised by the quantity and quality of individual combatant force elements. The ability to manoeuvre and adapt across force elements through effective Command and Control (C2) can allow smaller or weaker forces to overcome an adversary with greater resource and fire-power. In this paper, we combine the classic Lanchester combat model with the Kuramoto-Sakaguchi model for phase oscillators on a network to create a flexible Networked-Lanchester-C2 representation of force-on-force military engagement. The mathematical model thus unifies three of…
The Mathematical Theory of Behavioural Swarms: Towards Modelling the Collective Dynamics of Living Systems
针对经典群体模型难以捕捉生命系统适应性异质行为的局限，提出含动态内部活性变量的行为群体数学理论，通过微分系统整合自适应决策，经多领域应用验证其预测宏观涌现模式的能力，在个体驱动集体的系统建模中具独特优势。
Towards a mathematical framework for modelling cell fate dynamics
本文指出传统基于Waddington景观等方法建模细胞命运存在过度简化问题，提出将随机动力系统作为一种灵活且无多余假设的数学框架来描述细胞命运动力学。
Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. While PEG modification appeared to improve plasma retention and initial infectivity it also increased the virus particle arrival time. We derive a mathematical mode…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。