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.

learn more… | top users | synonyms

0
votes
1answer
35 views

I'm having trouble finding the right direction to take in this HIV modeling exercise

Cells that are susceptible to HIV infection are called T (target) cells. Let $T(t)$ be the population of uninfected T-cells, $T*(t)$ that of the infected T-cells, and $V(t)$ the population of the HIV ...
2
votes
1answer
40 views

Notions of consistency / heterogeneity in sets of vector values

The problem Let us consider a row vector u of size $n\in\mathbb{N}$, containing only binary values (0,1): $$u=(u_1,...,u_n), n\in\mathbb{N}$$ $$\forall i \in \{1...n\}, u_i \in\{0,1\}$$ I would like ...
0
votes
1answer
25 views

Modelling a continious-time queue which behaves differently when there are more or less people being served.

For my research I am trying to model a continuous-time queue which behaves differently when there are more or less people being served. The arrival rate in the queue is constant, however the departure ...
0
votes
1answer
47 views

After how many bounces is the ball subsequently always less than 5cm from the ground?

a). A ball is thrown vertically upwards with a speed of 20 metres per second from a point 3 metres above the ground. Find the speed with which it hits the ground. b). If the ball rebounds with a ...
-5
votes
0answers
43 views

Determine Stability of nonlinear ODE in Biological Mathematics

Please help me find the stability of the critical points given in problem 3 below. I was able to determine using matlab, but he is telling me to use partial derivatives to do this. Do I need to make a ...
0
votes
1answer
21 views

Stability of a function with logaritms

I am trying to proof that the following equation is stable if $|1-ln(\alpha)|<1$; $$f(x)=\alpha x e^{- \beta x}$$ So the equilibrity points would be $x=0$ and $x=\frac{ln\alpha}{\beta}$, the ...
1
vote
0answers
23 views

Learning to Apply Mathematical Concepts ( i.e. function modelling, etc.)

Firsty, I want to state my situation clearly. I am one of those students who are incredibly good at absorbing mathematical concepts but without knowing how to apply them. I get A's but it is growing ...
0
votes
0answers
43 views

How to model these following rules of physics mathematically? [closed]

I want to simulate these particles based upon the properties provided. For example I want to put 10 As and 10 Bs and want to see how it behaves through simulation. We have two kinds of particles: A ...
3
votes
0answers
38 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
0
votes
1answer
21 views

Best method for assessing repeatability between year 1 and year 2

I have a data set of values for a particular measured metric for employees for the year 2013, and a set of values for the same measured metric for the year 2014. I am looking to assess the ...
-1
votes
0answers
22 views

Dynamical System mathematical modeling question [closed]

An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity ...
0
votes
0answers
23 views

Competition Model - System of differential equations

Two plants are feeding off the same substrate, whose weight at time t is S(t). One of the plants began to feed off the substrate 20 days earlier than the other. Devise a system of differential ...
0
votes
0answers
22 views

Differential Equation of a Probability Density Function

I have a deterministic rule of my variable (ODE model), $\frac{dY}{dt} = at$, in which $a$ is a parameter in my deterministic model (let's say growth rate) and $t$ is the time. I know that on every ...
0
votes
1answer
15 views

How does one solve ODE with some domain constraints?

So far I have no clue, how to go about this .. in school we did not go over constraint based ODES. So let's say we have $\ x'' = -ax' $ $\ y'' = -ay' - b $ Note: a,b are constant and x(t), y(t). ...
0
votes
0answers
35 views

Question about noise term in SDEs

Do any properties/assumptions of SDEs prevent the noise term from being extremely large? Using a simple population growth model as an example, $\frac{dNt}{dt} = (r_{t} + W_{t})Nt , N0$ given, ...
0
votes
0answers
20 views

Finding the correction factor of a model

If I have a model, and data against that model. The model says that it should be linear, and the data begins linear and drops away from the line as x decreases. Is there some function I can multiply ...
0
votes
1answer
28 views

How to make a cobweb diagram

I am struggling making a cobweb diagram for the function $$x_{t+1}=8x_t/{1+2x_t}$$ So I understand when making the cobweb diagram, that I have to draw the line $y=x$ But where I have trouble ...
0
votes
1answer
16 views

Discrete Population Model Crashing

Consider the discrete population model $$U_{t+1} = au_t^2/(b^2+u_t^2)$$ Where $a >0$ If $a^2 > 4b^2$ show that the population may be driven to extinction if it becomes less than a critical ...
1
vote
1answer
37 views

Finding eigenvalues to classify the steady state of a system

I have this system of differential equations which model chemical concentrations in a certain reactions: $$\dot{x}=a-x-\frac{2xy}{1+x^2}\qquad \dot{y}=bx\left(1-\frac{y}{1+x^2}\right)$$ for $a,b ...
0
votes
0answers
17 views

Graph analysis and phenomenon modeled by the curve $S(t)= 1/(1+e^{-t})$

So the question is: The graph looks like: So where I stand with this question is that I am struggling to find something that it models. Once I find some phenomenon that it looks similar to, I ...
0
votes
0answers
27 views

Interpreting phase-plane portraits

I have found the phase plane for a "predator-prey model" system of differential equations: $$\dot{x}=x^2-x^3-xy \qquad \dot{y}=yx-ya$$ where $x$ represents the population of prey and $y$ represents ...
0
votes
0answers
48 views

What probability analysis did the allies use during WWII after they cracked the Enigma, or how can this probability be quantified?

In the recent film, The Imitation Game, after cracking the Enigma they mentioned that the allies didn't simply use every cracked message but instead analysed the probability the Germans would find out ...
0
votes
0answers
12 views

How define a disturbance figure as input?

I have a 2 dimension figure of disturbance.I have to consider this as input of model predictive control. How can i do this.How can i have a model for this disturbance?
1
vote
1answer
28 views

Interpreting differential equation models

Consider the model $$\dot{x}=x[x(1-x)-y], \qquad \dot{y}=y(x-a)$$ where $x \geq0$ represents the population of prey and $y\geq0$ represents the population of a predator, with $a\geq0$ as a control ...
1
vote
1answer
36 views

intuition for mixing problems with ODEs

assume we have a mixing problem with a salt solution coming into a water tank. the flow rate in and flow out rate are equal (5 L/hour), the concentration of salt flowing in is 1 g/L and the tank ...
3
votes
3answers
182 views

Books about mathematical biology [closed]

What good books can be recommended on the subject of mathematical biology? I don't know anything about this subject. But now I am interested in this subject. Because I want to do research in this ...
0
votes
2answers
182 views

Four Color Theorems: Graphs vs. Maps [closed]

This question has changed dramatically from its original form. Please See the improved question. ORIGINAL QUESTION: There are two variants of the four color theorem that are commonly cited: (4CTG): ...
0
votes
2answers
33 views

solving linear ODEs for mixing problems with function notation

consider this mixing problem for differential equations: a tank holds 100 L of water that initially has no sugar in it. Sugar water with 5 grams / L of sugar enters at rate of 2 L per minute. Water is ...
0
votes
0answers
20 views

Modelling: Use Newton's law to write down an equation for the position $x$ of the mass.

Here is the background for the question: Consider a one-dimensional frictionless spring-mass system, where the forces acting on the mass $m$ at position $x$ are the forces of gravity $F_g =-mg$ with ...
1
vote
0answers
28 views

Is Principal Component Analysis applicable to this type of situation?

I'm trying to model the response of ant populations to pheromones in this way: The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
0
votes
1answer
55 views

SEIR model need help solving first order linear ODE

I've recently been working on simulating an SEIR (susceptible, exposed, infected, recovered) project for an endemic disease using matlab solving via Euler's method. I have taken a picture of the ...
2
votes
1answer
25 views

Parabola properties assumptions

I am trying to model projectile trajectory but I'm having some trouble. I didn't realise parabolas are this complicated... I have some assumptions that I would like to be clarified. If I specify a ...
0
votes
2answers
42 views

Parabola describing projectile motion.

I am trying to create a function that will generate a parabola that describes projectile motion. Here are my inputs: The starting x-y coordinate of the throw The initial x-y velocity vector. I ...
1
vote
1answer
27 views

Questions about Disease Model

A non-fatal infectious disease divides a population into two groups: normal or ill. Assume that the average number of contacts that each ill individual has with normal individuals is $a$ multiply the ...
0
votes
1answer
31 views

Discrete Dynamical Systems & Credit Card Debt: How to solve for payment

I have the following problem, taken out of Giordano, Fox, and Horton's A First Course in Mathematical Modeling: Your current credit card balance is $\$12,000$ with a current rate of $19.9\%$ per ...
0
votes
1answer
43 views

Lotka-Volterra equations modified

Okay, so I'm just learning about the Lotka-Volterra and the question I have regards the following model: $dx/dt = x(1-y/2)$ $dy/dt = -y(1 - (x/0.8) + (x^2)/4)$ I need to state what term has been ...
3
votes
1answer
38 views

Interpretation of a model

$$ \frac{dx}{dt}=ax(x-b)(1-x)-\frac{xy}{1+cx}$$ $$\frac{dy}{dt}=-ey+\frac{xy}{1+cx}$$ Make a apropriate interpretation of this model. What I thought are: $\frac{dx}{dt}\ \& \ \frac{dy}{dt}$ are ...
0
votes
0answers
10 views

Indicate whether each of the following equations is linear or nonlinear.

Indicate whether each of the following equations is linear or nonlinear. If linear, determine the solution; if nonlinear, find any steady states of the equation. $x_n=(1-\alpha )x_{n-1}+\beta x_n$ ...
3
votes
0answers
81 views

A mathematical abstraction of colours?

Does any formal system exist built upon the mechanics of Additive Colour Theory? Additive Colour Theory is the description of the behaviour of the visible spectrum of light as it combines-the ...
0
votes
1answer
27 views

Critical points of quadratic forms

Let $A$ be an $n\times n$ symmetric matrix, let $b$ be an $n$-vector, let $c \in \mathbb{R}$ and set $Q(x) = 1/2 x^T Ax-x^T b+c$. Prove that $x_0$, defined as a solution to $Ax_0=b$ is a critical ...
0
votes
1answer
25 views

find the maximum

I'm stuck in this problem (Instructions and my work is showed on the picture below) I just don't know what to do right after find the values of D, to prove that the maximum of F(D) is attained at the ...
0
votes
0answers
25 views

Modeling Question: Finding a Fit for the form W=kl(g^2)

I have a modeling question on my assignment that I am unsure about. I am given a set of points $W, l,$ and $g$. I have to find some $k$ for the data to optimally fit $W=klg^2$. At first, I tried ...
0
votes
1answer
25 views

Lotka-Volterra coordinates transformation

I would like to ask the following: Given a Lotka-Volterra predator-prey system, \begin{align} & \frac{dx}{dt}={\alpha}x-{\beta}xy \\ & \frac{dy}{dt}=-{\gamma}y+{\delta}xy \end{align} , with ...
1
vote
2answers
61 views

Lotka-Volterra First Integral and Fixed Point

I have the following problem that I am dealing with, quite a long time, I must say. Let us assume that we have a predator-prey, Lotka-Volterra system given to us by: \begin{align} & ...
1
vote
1answer
55 views

Differential Equation - Blood Alcohol

Let C(t) be the concentration of alcohol in a person's bloodstream. We propose a mathematical model which states that, once a person stops drinking alcohol, C decreases at a rate that is proportional ...
1
vote
1answer
30 views

Determining probabilities Markov Chain

If I have a Markov Chain $X_0, X_1, X_2 \dots$ that has a transition probability matrix $ \textbf{P} = \matrix{~ & 0 & 1 & 2 \cr 0 & 0.3 & 0.2 & 0.5 \cr ...
2
votes
1answer
102 views

Modelling Concentration

I'm currently doing a research project that involves modelling E. Coli growth in a wetland. The data I've been given is the E. Coli mass concentration ($mgC/L$) at various times throughout the two ...
-1
votes
1answer
14 views

For the three measurements b=0, 3, 12 at times t=0, 1, 2 find the best parabola y=C+Dt+E$t^2$

So I know how to do least squares regression using matrices to solve for Ax=b. I simply do $A^TAx=A^Tb$. However I don't really know how to account for the second power in a typical parabola ...
0
votes
1answer
24 views

What is the least squares solution given a line passes through original and following points?

So I am looking for the line y=Dt through the origin that fits the data y=4 at t=1, y=5 at t=2 and y=8 at t=3. This is what I have done so far. I know the three equations that are supposed to be ...
0
votes
1answer
27 views

Write the system of equations describing the populations in this system…

In a closed ecosystem, we have that Frogs,represented by $F(t)$, eat fleas, represented by $f(t)$, and the fleas eat fungus, represented by $g(t)$. Assuming that fungus grows at rate A, fleas eat the ...