# Questions tagged [mathematical-modeling]

This tag is used to refer to mathematical/probabilistic/statistical modeling questions, usually this tag is used to ask about questions that are related with the mathematical formalism of the model instead of the correctness of a specific model in practice.

113 questions
Filter by
Sorted by
Tagged with
195 views

• 71
185 views

### Poisson Process x SIR model [closed]

Consider the simplest SIR model: $$S'=-a SI$$ $$I'=a SI - b I$$ $$R'=b I$$ It is known that the waiting time of an infeccious person in the compartment $I$ follows an exponential behavior with rate $b$...
• 123
1 vote
82 views

### How to smoothly interpolate gravitational field between trajectories in high dimension?

I'm looking for the adequate numerical interpolation technique to solve the following problem. This is probably trivial for physicists who study gravitational fields, but I didn't find clear answers ...
• 19
185 views

### Equation in epidemic SIR model with the influence of vaccinations

I am currently preparing a presentation on different modifications of the SIR model. In my sources about the use of vaccines, I came across the following model for a specific rate at which the ...
• 41
1 vote
80 views

### Advice on constructing a Non-structural Flood Mitigation Model [closed]

I am not sure if this is the right site to post this. But I seek some valuable suggestions, and I believe I can get them here. At present, I am in the final semester of my BSMS Mathematics course. I ...
89 views

### Mathematical formulation of beam: get stress/strain from forces and momentum

I'm working with static beams with Euler–Bernoulli model which ODE is $$\dfrac{d^2}{dx^2} \left(EI \cdot \dfrac{d^2w}{dx^2}\right) = q(x).$$ With a beam along the $x$ axis, the solution consists of ...
• 253
1 vote
453 views

### Why should the logarithmic series distribution model the number of "Items" bought?

Suppose you're a shopkeeper in the business of selling Items. An "Item" is a thing whose only property is that the quantity that can be bought by a purchaser must be a positive integer; all ...
• 11.4k
1 vote
69 views

• 253
131 views

### How to mix Lagrange mechanics + KKT conditions?

Question: How can I mix the concepts of Lagrange Mechanics and KKT conditions? I've learned that Lagrange Mechanics derivation comes from variational calculus, and in some formulations, we can add ...
• 253
327 views

### Examples of ODEs with complex constant coefficients and applications to physics?

This question is asked on stackexchange: Are there examples for ODEs with complex coefficients with applications in physics? but received no answers. I am reposting it here on the hope that it catches ...
• 646
34 views

### What is the meaning of column integrated fluxes?

I am solving an equation where one term $\bar{P}$ is given and is called the integrated column flux. In the equation, the term $P$ is the precipitation. I am doing this on the discrete domain. Anyone ...
• 101
27 views

### How to define Mock Hadley Cell in mathematical modeling?

I am computing a force term in which one component is $F_{ext}$. To define this, the following content given in the paper. To capture the possible large-scale effects on precipitation clusters, we ...
• 101
495 views

### Integer linear constraint(s) for y= x1 XOR x2 [closed]

Is there any way to convert $y=x_1~ \text{XOR} ~x_2$ to linear constraints? It means we write some linear relations with: if $x_1=x_2 =0$ or $x_1=x_2=1$ $\to$ $y=0$, else, $y=1$?
• 25
1 vote
81 views

### Resources/Reading Materials on PASA (optimal control theory)

I am currently working on my undergraduate thesis, and my adviser suggested that I look into a Polyhedral Active Set Algorithm (PASA) for my paper. I have been trying to find resources/materials on it ...
• 151
198 views

### Literature on reaction diffusion equations

My research area is age structure modelling, basically when applied to reaction diffusion equations. We mainly discuss the existence of travelling wave solutions; I want to work on the stability of ...
101 views

### How to quantify the non-commutativity of human body motion? [closed]

Some years ago, there was that question on this forum:"How to quantify noncommutativity?". I am asking that question in a context, human movement, which implies kinematic chains (like in ...
1 vote
73 views

### Real life applications of distributions through models or simulations [closed]

What are the areas we can apply distributions in classical harmonic analysis? I don't mean probability distributions but distributions that are continuous linear functionals on the space of test ...
• 91
264 views

### Current status on Richardson's model (growth model)

A very simple stochastic growth model on a lattice is the Richardson's model (Actually originally defined by Murray Eden in the 60s). Each point of the lattice can be either occupied or vacant, once ...
• 179
98 views

### Epidemics: distribution of interarrival times

In models of disease transmission, after an individual is getting infected, he can generate a number of secondary infections. The number of secondary infections depends on the infectiousness of the ...
• 179
131 views

### Reference request: probabilistic models on climate (change)

I am looking for probabilistic models to address climate change. Are they known in the existing literature? I have found the post Math behind climate modeling. concerning PDE models. Many thanks for ...
1 vote
70 views

6k views

### Applications of mathematics in clinical setting

What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level? To clarify, by patient-disease-drug level, I mean the mathematical work ...
4k views

### Unconventional examples of mathematical modelling

I'll soon be teaching a (basic) course on mathematical control theory. The first part of the course will focus on mathematical modelling of dynamical systems. More precisely, I will present examples ...
1 vote
69 views

### A mathematical area capable of describing nonstationary game-like problem [closed]

Here is my definition of the problem that I am trying to model: Let's have two agents and an environment. Each agent can do two types of actions. They are either supporting the environment or don't. ...
• 111
100 views

### Global stability question for system with a unique locally-asymptotically-stable steady state

I have an ordinary differential system of dimension 3 that contains a locally-asymptotically-stable unique fixed point. Additionally, the system is strictly-positively invariant and bounded. Now, ...
• 513
412 views

### How to study the global stability for this 3D system?

I am studying a biological system (HIV) and arrived at this simplified dynamical system: \begin{align} x_1' &= a_1 + a_2x_2 - a_1x_2 - a_4x_1 - a_5\frac{1+a_6x_3}{1+a_7x_3}x_1\\ x_2' &= a_5\...
• 513
1 vote
40 views

### Mathematical modeling of multi-site reaction-diffusion

(I asked a similar question on Mathematics SE, but based on the Help section it might be better suited for this site, as it is focused on research-level mathematical modeling.) I am wondering if ...
• 111