1
vote
0answers
23 views

I need to model a population where every component have a fixed life span.

I have a certain population, which growth is function of a certain factor. I have already modeled the growth. Now I need to impose that every individual in the population have a fixed life length. Can ...
2
votes
2answers
20 views

How to determine new dimensionless variables when non-dimensionsionalizing a system of ODEs?

I am following this a research paper called "Evolution of Within-Host Antibiotic Resistance in Gonorrhea", which can be found here. I have one question regarding the method of non-dimensionalization. ...
0
votes
1answer
26 views

Definition of “epidemic” when using SIR models

I haven't studied differential equations for a long time, but I have just started looking at material on the SIR model of epidemics. My problem is that the resources that I've looked at haven't given ...
0
votes
0answers
33 views

Finding the largest eigenvalue of a sparse matrix

I would like to find the largest eigenvalue of a sparse matrix by hand- this is part of analyzing a mathematical model for infectious diseases. The nonzero entries are very complicated - hence Maple ...
1
vote
2answers
65 views

Units of time in simple differential equation

Very simple question: There is a well-known model in epidemiology called SIR model. It describes the changes in the number of susceptible, infectious and recovered individuals in a population. It is ...
1
vote
0answers
20 views

Simple differential equation modelling question.

The question is: A chemical dissolves in water at a rate equal to 10% of the amount of undissolved chemical per hour. At time $t$ hours the amount of undissolved chemicalis $x$ grams. Initially the ...
0
votes
0answers
30 views

System of $2$ nonlinear DEs

Please tell me if I'm on the right track for solving the following system: $$\frac{d{U}}{dt}=a - b U -\frac{\beta U V}{U+V} \\ \frac{d{V}}{dt}=\frac{\beta U V}{U+V}-(b+c+d)V $$ Steps: $1.$ I added ...
2
votes
1answer
43 views

How did they find this equilibrium condition?

I'm studying from a book titled "Mathematical Models in Population Biology and Epidemiology" and we're dealing with SIS models. In a chapter called "Infective Periods of Fixed Length", we get to this ...
1
vote
1answer
59 views

Analyzing the stability of equilibria

There's a model with a condition $r>\mu$: $$\begin{align} S'&=r(S+I)-\beta SI-\mu S \\ I'&=\beta SI-(\mu +\alpha)I \end{align}$$ I can easily see that the equilibria of the second ...
0
votes
1answer
52 views

Express the new parameters in terms of the old parameters (SIQR model for mathematical epidemiology)

In the model considered here the population is divided into susceptibles (S), infectives (I), isolated or quarantined individuals (Q), and recovered individuals (R), for whom permanent immunity is ...
0
votes
1answer
30 views

Finding the basic reproduction number of a particular model

I have been reading a paper about a host-parasites models and for the model: $$\begin{array}{rll} \displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\ ...
4
votes
0answers
97 views

What differential equation might model this almost-harmonic oscillator?

I need to precisely control the motion of a damped, driven (nearly) harmonic oscillator: $$ \ddot x(t) + \alpha\dot x(t) + \omega_0^2 x(t) \approx V(t) $$ I use the $\approx$ symbol because this is ...
2
votes
0answers
71 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
0
votes
1answer
105 views

Gompertz growth model problem

The growth of tumor cells is characterized with Gompertz model. $N'=-aNln(bN),$ where N(t) is proportional to the number of cells in the tumor, while a and b denote positive parameters. ...
0
votes
1answer
52 views

Modeling with Differential Equations - Help?!?!

So here's the problem that I'm working on at the moment: Tank 1 initially contains 50 gals of water with 10 oz of salt in it, while Tank 2 initially contains 20 gals of water with 15 oz of salt in ...
1
vote
0answers
30 views

Matlab functions of variables

So I am writing a function to compute the following equations for an SIR model: So here's my code: ...
2
votes
1answer
61 views

ODE water drop modeling question

I have been working on a ODE homework which involves modeling the velocity of a drop of water falling from the sky. The ODE that models its velocity is given by: $$ mv'=kv^2-mg, \qquad ...
1
vote
0answers
22 views

How do impulsive differential equations work? Can you provide an example?

I have heard of impulsive differential equations being used in some epidemiological models of infectious disease. I haven't heard of them before in my math education, and I was wondering how they ...
0
votes
1answer
39 views

How can I solve an ODE when $F(x_0)=F'(x_0)=0$ is given at an unknown point $x=x_0$ using bvp5c?

I'm attempting to solve the following ODE using MATLAB bvp5c. I've used bvp5c for other typical multipoint boundary value problems but I have no idea how to deal with ODEs with conditions given at an ...
1
vote
0answers
48 views

Predictor-Corrector for Adams-Moulton

What is the order of the corrector of Adams-Moulton type required in order to apply Milne's method for estimating the error in PECE mode? Find the coefficient of the leading term in the truncation ...
0
votes
1answer
31 views

Conceptual Car Density

This is more a conceptual question that requires a physical answer rather than a mathematical one. The question is Explain why a density wave moves forward for light traffic. Consider both cases in ...
1
vote
1answer
30 views

Finding maximum displacement from a BVP

I have solved the following BVP (Border Value Problem): $$y'''' = -P, y(0) = y(L) = 0, y'(0) = y'(L) = 0$$ Where $L=4 , P=24$ The DE describing it is: $y(x) = -x^2(x-4)^2$ This apparently is ...
1
vote
0answers
40 views

Sensitivity of coefficients in ODE

I am trying to formulate a mathematical model as part of an op-research problem, and I'm running into a roadblock concerning differential equations of a certain kind; I was hoping to understand if ...
-2
votes
2answers
74 views

mathematical biology (steady-states)

non-dimensionalisation equation: \begin{equation} \frac {du}{d\tau}=\frac{\overline{\lambda}_{1} u}{u+1} -\overline{r}_{ab}uv -\overline{d}u \end{equation} where $\overline{\lambda}_{1}= \frac ...
0
votes
0answers
41 views

Eloquent method to analyse a four dimensional system ODEs qualitatively

Given a nonlinear four dimensional system of ODEs, I have found the fixed point and linearized to acquire the Jacobian. I am beginning to calculate the eigenvalues of the Jacobian from the quartic ...
0
votes
1answer
90 views

Mathematical Biology and modelling

Consider the two species competition model given by $$ \frac{da}{dt }= \frac {λ_1 a} {a+K_1} - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= λ_2 b (1-\frac{b}{K_2}) - ...
0
votes
1answer
107 views

Mathematicals biology

Consider the two species competition model given by $$ \frac{da}{dt }= [λ_1 a /(a+K1)] - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= [λ_2 b *(1-b/K2)] - r_{ba}\cdot ab , \ ...
1
vote
1answer
115 views

mathematical biology

Consider the single species population model defined by $$\frac{dR}{dt} = \frac{gR}{R+R_m} - dR,$$ for $t > 0$, where $g,R_m$, and $d$ are all positive parameters and $R(0) =R_0$. (a) Describe ...
0
votes
1answer
28 views

How to show the monotonicity of exponential growth?

I have a basic exponential growth model given by $N'(t)=N(t)\times r$ where $N(t)$ is the current population and $r>0$. My problem is to show if the initial population $N(0)=N_0>0$, then the ...
4
votes
0answers
233 views

Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
0
votes
0answers
68 views

Solving a weird Diff equation…

Good day people I am modelling a water bottle rocket. Using the conservation of mass : $$-{\rho}vA + \frac{d}{dt}∫dM = 0 \tag{1}$$ Since the mass, O2 pressure, O2 volume and velocity change over ...
-1
votes
2answers
55 views

Modeling with First Order Equations [closed]

A ball with mass 015kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is air resistance of magnitude v^2/1325 directed opposite to the velocity , where the ...
0
votes
1answer
58 views

The mean infective period in a SIR Model

I'm going to quote the relevant passage in the textbook and then ask my question. The assumption that the infectives leave the infective class at rate $\alpha I$ per unit time requires a ...
2
votes
1answer
99 views

Solving $f'''+\frac{n+1}{2}ff''-nf'^2+n=0$ with $n=e^\pi$

How do I solve $$f'''+\frac{n+1}{2}ff''-nf'^2+n=0$$ with $n=e^\pi$ or arbitrary $n$? This equation occurs in my model for the time evolution of the value of Bitcoin.
0
votes
1answer
77 views

SIR Models - interpretation (epidemiology) - help!

I am doing a project on modelling the spread of diseases and am using a SIR (susceptible, infected and recovered) model to do so. I need help interpreting this plot: What does this plot say about ...
2
votes
2answers
123 views

Ideas about an Ordinary Differential Equations research work (University level)

Good afternoon to everyone, I need some ideas about a Ordinary Differential Equations research work. It is for the ODE subject that I am doing at my Mathematics degree in my University. They asked me ...
1
vote
1answer
2k views

Mathematical model of Quadcopter?

I want to know how to make the mathematical model of Quadcopter? Is there any differential equation for quadcopter? I want to simulate quadcopter as a mathematical model so I want to know how can I ...
0
votes
0answers
135 views

Market uptake and market share modelling

I have been trying to figure out how to model the market uptake and share. I have a model for single product launch into a market and want to make the model able to reflect competition among two or ...
1
vote
1answer
225 views

Simple Non-Linear ODE - would like to find solution

In the modeling of the oscillation of a meniscus in a straw, the following non-linear ODE was derived. $$y'' = 1/y - 1$$ $y$ is a dimensionless displacement that is solely a function of time. The ...
2
votes
1answer
167 views

Interpretation of Phase Portrait

I have the following system $x'=f(X)$ of ODES: \begin{align} x_1'=& -4x_1^3(x_2-2)^2 \\ x_2'=& 2x_1^4(2-x_2) \end{align} Solving for equilibria: I got $1$ at $(0, 2)$. I plotted this and I am ...
4
votes
1answer
174 views

Finding the jacobian of a differential system with a piecewise function

My system: $$\frac{\mathrm{dx} }{\mathrm{d} t}=-ax^2+y^2-\gamma z$$ $$\frac{\mathrm{dy} }{\mathrm{d} t}=- h(y)-\beta y $$ $$\frac{\mathrm{dz} }{\mathrm{d} t}=x+h(y)-\beta z $$ where $h$ is the ...
1
vote
1answer
174 views

Euler angle in ellipsoid rotation

I am modeling an ellipsoid tumbling in a flow field. I have derived an expression for the Euler angle $\phi(t)$ of the rotation in the $x$-$y$ plane as a function of time, but its range is only $\pi$, ...
1
vote
0answers
94 views

Math model - constrain GDP given different growth rates of industries

ideas needed to model national GDP given different sector growth rates subject to some contraints Given: GDP equations for $n$ industries depend on growth rates and time i.e. $g(r_1,t), g(r_2, t), ...
4
votes
1answer
141 views

Water Systems: When can I use buckets of water to simulate an ODE.

It is quite common to use physical systems to perform calculations (see here and here). This is for a number of reasons: sometimes the physical system is efficient, sometimes it helps us understand ...
0
votes
1answer
301 views

Relationship between Turing bifurcation, saddle-node bifurcation, and Hopf bifurcation?

Quoting from http://jxshix.people.wm.edu/2009-harbin-course/mississippi-bifurcation-2.pdf a Turing bifurcation occurs when for an ODE and related PDE $u' = f(u,v), v' = g(u,v)$ $u_t = d_1 \nabla ...
2
votes
1answer
74 views

How do you set up a system of ODE's for this problem?

The problem is as follows: Black and White balls are being created inside an arbitrary volume at rates of $Q_{B}$ and $Q_{W}$. They also disappear from the volume at rates $\lambda_{B}$ and ...
0
votes
1answer
58 views

How can I model a rotating system which does not have constant acceleration?

I've sampled a rotating system to come up with a list of positions and velocities at certain times. I want to be able to predict how long it will take to reach a certain speed and how far it will have ...
1
vote
1answer
183 views

Pursuit curves and arc length question

I am studying pursuit curves where a fast pirate ship which pursues a heavily laden treasure ship which tracks along a straight line. The ratio of the speeds of the ships is r > 1 (which is fixed) and ...
0
votes
1answer
45 views

Solving a form of the logistic equation to arrive a given solution

I am writing my bachelor thesis on modelling of city growth and using the book Cities and Complexity by Michael Batty. On page 394, while modelling the growth as spatial epidemic, he writes: ...
2
votes
1answer
628 views

Python numerical solution for a nonlinear second order ODE with two boundary conditions

I want to solve numerical the next equation, in Python $$u''(x) = \left( a - \Big(b\big(u(x)^{2}\big)\Big) \right) \big(u'(x)\big)^{3}$$ it is a nonlinear second order $ODE$ with two $B.C$. ...