Questions tagged [mathematical-modeling]

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

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Modeling scoring functions

I'm looking for general direction on topics to explore for this problem. I think I'm not searching for the right statistical concepts and therefore coming up empty handed. Also, I'm a computer ...
2k views

How to determine number of turns needed to fill spool with known length of wire?

I've been scratching my head on this problem for a while, even bounced it off of some friends who are way better at math than myself with no luck, so I'm hoping someone here can help. I'm trying to ...
1 vote
864 views

Proof for positivity of solutions of an ODE system

I have an ODE system that takes a mathematical model describing the dynamics between HCV and the immune system. My question is about the proof that the solution of the ODE system is positive if the ...
20 views

What does it mean to use mathematical models to understand qualitative vs quantitative behavior? [closed]

I have been running into this recently, and I want to confirm I have the right idea. For example, Neff et al. (2023) state, "Although we study a mathematically very simple box model in order to ...
14 views

prove existence, uniqueness and non-negativity of the system of ODE

I have an epidemic model with 9 compartments, where all epidemic parameters are non-negative. \label{model} \begin{split} &\frac{dS}{dt} = \beta N -\delta S-\phi \frac {SI}{...
1 vote
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Exploring Markov Models for Determining Car Insurance Costs

Question: I'm currently delving into the realm of Markov models to understand how they can be applied to determine the cost of car insurance. Thus far, I've come across the bonus-malus system and ...
14 views

General state space form for ARIMA(p,d,q)(P,D,Q)

I cannot for the life of me find a resource which gives the general state space form for an ARIMA(p,d,q)(P,D,Q) model. I am reading Time Series Analysis by State Space Methods, by Durbin & Koopman,...
1k views

Mathematical model building with dependent and independent variables

I have been working with data and building models on data. I have developed models in regression using cubic and power series. It works fine for variables with one dependent and one independent ...
79 views

3d fractal helix modeling

I'm trying to build a 3d visual to illustrate a concept. Imagine a circular helix. We could define a cylinder that contains that helix. But now imagine this cylinder takes the helicoïd shape too ! We ...
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Conversion of Abstract Units to Time in Polynomial Modeling of Snowboarder's Motion

I am currently working on a project where I model the motion of a snowboarder using a 4th-degree polynomial. The polynomial is currently defined in abstract units along the x-axis and y-axis. I have ...
26 views

Why does $I + S \xrightarrow{\lambda} 2S$ correspond to $\frac{di}{dt} = -\lambda \langle k \rangle i(t) s(t)$ in this model?

Chapter 10 of Dynamical Processes on Complex Networks contains a model of information spreading. This model is strongly based on a SIR model of epidemics. In this model, there were three kinds of ...
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How to solve a 2D ODE system of the form $\frac{\text{d}\vec{x}}{\text{d}t}=(M-\Delta e^{-\lambda t})\vec{x}+\vec{x}_0$

Let $x=x(t)$ and $y=y(t)$ for $t>0$, with $x(0)=y(0)=1$. \begin{align} \frac{\text{d}x}{\text{d}t} %%% &= %%% -\left( A + \alpha e^{-\lambda t}\right)x + By + x_0\\ %%% \frac{\text{d}y}{\text{d}...
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Problem in performing sensitivity analysis in prey-predator model

I tried to create a general prey predator model to simulate sensitivity analysis using PRCC and Latin hypercube sampling. But I can a bar plots which are empty. What is wrong in my approach? The code: ...
1k views

Statistics on three variables/factors

I have what is probably a simple problem. I'm trying to say something about sells of candy bars. I got data of sells for a population of children. There are three parameters (factors) to this data: ...
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How to use Euler-Lagrange equation to model a linear particle?

Suppose I have a particle with mass $m$ situated on a frictionless line which we can model using $\mathbb{R}$. Suppose that we supply/push the particle $m$ with a force $f(t)$. Let the position of ...
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How can I get the inverse of the transfer function $\Phi$? a question from Page 56 of Lemma 4.5 in the book "ESSENTIALS OF ROBUST CONTROL" [closed]

Let $\Phi(s) = = \gamma^2 I + B^*\left( (sI-A)(C^*C)^{-1}(sI+A^*) \right)^{-1}B + B^*(sI+A^*)^{-1}C^*D - D^*C(sI-A)^{-1}B - D^*D.$ How to compute the inverse of $\Phi$, in Page 56 of Zhou's book "...
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