Results 221 to 230 of about 227,477 (267)

Modelling with Differential Equations

1996
In most of the examples of Chapter 8 we were given or assumed that our variable was modelled by a particular function of time, y = f(t), and then we found the rate of change, y′ = f′(t). Very often our modelling assumptions are expressed in terms of rates of change.
Dilwyn Edwards, Michael Hamson
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Climate models with delay differential equations

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017
A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be
Andrew, Keane, Bernd, Krauskopf, Claire M, Postlethwaite   +2 more
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Modelling with Differential Equations

2016
Apparently the word model does not raise much confidence among general public or journalists. The terms “model” and “modelling” are in fact relatively new, therefore it is perhaps not surprising that their meaning is not very well understood. Of course, scientists have always made models also in the modern sense of the word, but maybe they used some ...
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Differential Equations Models

1993
A natural way to begin the treatment of models of vertical transmission is to extend the classical epidemic models as contained, for example, in the book of Bailey [1975]. In order to provide a baseline for understanding the effects of vertical transmission and to introduce some of the standard terminology we briefly describe the classical Kermack ...
Stavros Busenberg, Kenneth Cooke
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Ordinary Differential Equation Models for Adoptive Immunotherapy

Bulletin of Mathematical Biology, 2017
Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their ...
Talkington, Anne, Dantoin, Claudia, Durrett, Rick   +2 more
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A Bifurcation Analysis of a Differential Equations Model for Mutualism

Bulletin of Mathematical Biology, 2006
We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions. The model is similar in spirit to a commonly cited model [Dean, A.M., Am. Nat. 121(3), 409-417 (1983)], but corrects problems due to singularities in that model.
Graves, Wendy Gruner, Peckham, Bruce, Pastor, John   +2 more
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Robust Estimation for Ordinary Differential Equation Models

Biometrics, 2011
Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers.
Cao, Jiguo, Wang, L., Xu, Jia
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Differential Equations and Models

2010
In science, engineering, economics, and in most areas having a quantitative component, we are interested in describing how systems evolve in time, that is, in describing a system’s dynamics. In the simplest one-dimensional case the state of a system at any time t is denoted by a function, which we generically write as u = u(t).
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Modeling uncertainty with Measure Differential Equations

2019 American Control Conference (ACC), 2019
Recently, a new type of evolution equations for measures, called Measure Differential Equations (briefly MDE), was introduced, based on the concept of Probability Vector Field. The latter is a map associating to a probability measure on a manifold a probability measure on the tangent bundle, whose projection on the base is the original measure.
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Differential Equation Models

1983
The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems.
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