25
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Applications of mathematics in clinical setting
Machine learning is on its way to provide the type of personalized health care referred to by the OP. In June of this year the FDA (US Food and Drug Administration) has proposed a regulatory framework ...
21
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Unconventional examples of mathematical modelling
Economics offers many examples of simple models for various systems not based on physical principles. One nice example is Hotelling's line model, which gives rise to Hotelling's "law". It considers ...
18
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Unconventional examples of mathematical modelling
The book
Enns, Richard H., It’s a nonlinear world., Springer Undergraduate Texts in Mathematics and Technology. New York, NY: Springer (ISBN 978-0-387-75338-6/hbk; 978-0-387-75340-9/ebook). xii, 383&...
17
votes
Accepted
Applications of mathematics in clinical setting
An example of a simple mathematical/evolutionary game theory model used to determine treatment scheduling in clinical treatment of metastic and castrate resistant prostate cancer can be found at https:...
14
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Applications of mathematics in clinical setting
I'm going to conflate mathematics with statistics as Carlo Beenakker did. Then the earliest application that I know of is that Decision Trees were invented by Breiman et al. to analyze the issue of- ...
13
votes
Accepted
Graphs resembling the math genealogy graph must have concentration in a small number of families?
Precisely this question was the starting point of the Galton - Watson theory of branching processes. To quote the opening paragraph of their 1875 paper On the Probability of the Extinction of Families:...
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11
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Virus community spread mathematical modeling
One of basic model is SIR model which has a good potential for describing epidemics. In this model $S$ denotes susceptible people, which are people that can be infected. The variable $I$ denotes the ...
10
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Applications of mathematics in clinical setting
I know of one mathematical system that was used before the widespread use of CT scans of brain in diagnosing stroke type. That of Scoring methods, which gave at those days a clinical decision that is ...
10
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Accepted
Searching for an early, highly theoretical, even philosophical, math paper on models or small-world networks
Stanley Milgram, The Small World Problem, Psychology Today 2, 60 (1967)
seems to fit the bill: +50 years old, "kind of philosophical", and yes, iconic -- cited more than 9,000 times. There ...
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9
votes
Unconventional examples of mathematical modelling
My favorite example is the use of hidden Markov models to analyze defensive strategies in basketball, as explained in Characterizing the spatial structure of defensive skill in professional basketball,...
9
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Unconventional examples of mathematical modelling
It appears that there are applications of dynamical systems to music. See, e.g., Rick Bidlack, Music from chaos: nonlinear dynamical systems as generators of musical materials or Boon and Decroly, ...
8
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Application for Differential Equation of higher order
The stationary / travelling wave / soliton regime of the KdV equation and its cousins give a lot of examples. For the original KdV, under the travelling wave ansatz we have the third order equation
$$ ...
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8
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Generalized linear models: What's the benefit of the underlying theory?
What are the benefits of a unified framework? You are right that we are rapidly going into some much used special cases line logistic regression or Poisson regression, but there is still benefit in ...
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7
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Unconventional examples of mathematical modelling
Although it's presented as a game, the fox-and-duck problem may be cast as a control problem from the perspective of the fox. The aim of the fox is to catch the duck, while the duck conversely tries ...
7
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Unconventional examples of mathematical modelling
There are a lot of applications of ideas in dynamical systems to social media for things like event detection and forecasting. Some of the literature has to be taken with a grain of salt because of ...
7
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Accepted
How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?
• Concerning the first of the two questions in the title, "How many persons pass your 1.5 meter neighbourhood during 1 week?"
Here is a graph from Mixing patterns between age groups in social networks,...
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7
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Examples of ODEs with complex constant coefficients and applications to physics?
A standard/classic example is a model for tippe top inversion. This model is a linear ODE with constant complex coefficients: $$
\ddot{z} + i \alpha \dot{z} + \beta \dot{z} + i \gamma z + \delta z = ...
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6
votes
Accepted
Virus community spread mathematical modeling
this wikipedia article Mathematical modelling of infectious disease may be a good starting point; epidemiology mathematical models is a combination of terms that does the magic with e.g. google.
...
6
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Suggestions for reducing the transmission rate?
This is just a slight expansion of my comment.
When the environment changes, behavioral parameters (that is, parameters like $M$ that describe people's behavior --- in this case the behavior of ...
6
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Accepted
Current status on Richardson's model (growth model)
Minor remark: I have always known this model as the Eden model, it seems that most probabilists currently refer to it as such.
To answer your question, yes there are many interesting open questions, ...
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5
votes
Unconventional examples of mathematical modelling
There are papers studying a zombie outbreak using infectious disease modelling (an SIR continuous-time Markov model): see e.g.
P. Munz et al, When zombies attack!: Mathematical modelling
of an ...
5
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Unconventional examples of mathematical modelling
You mention the motion of a pendulum as conventional. Perhaps extending to
a chaotic double pendulum would serve as a useful contrast:
...
5
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How to study the global stability for this 3D system?
This is more a long comment than an answer, but I know that a similar problem, also originated from (macromolecular) biology, was studied and solved by Gaetano Fichera, Maria Adelaide Sneider and ...
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5
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Virus community spread mathematical modeling
There is actually a very simple model that works reasonably well over time periods with little change. No model can work across all time periods because various communities (or cities) change their ...
5
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Accepted
Time of peak of an SIR epidemic
Seems like you fell in love with those equations and, especially, with the $I$ component of them:-). So let me try to show you how you can derive as many approximations as you want yourself, test them ...
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5
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When is one dynamical system an approximation of another?
The concepts defined in 1. and 2. are well-known and called just "conjugacy" and "semiconjugacy". But more relevant, if you have a topology, is the standard concept of "...
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4
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Math behind climate modeling.
Your question is a bit naive imho. There is not ONE big equation used to predict climate evolution and there is definitely no exact mathematical description of climate.
There are numerous models ...
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4
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Need help with a model, Whatsapp data analysis
I think you'll want some further assumptions like $\lambda_j>\lambda$ (inter-conversation pauses are longer than intra-conversation pauses).
Also, it should simplify the model to let $\lambda_j=\...
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4
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Unconventional examples of mathematical modelling
Martin Gardner's Lady in the lake problem should serve as an illustrative example of a differential game of evasion.
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