# 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 to do an ODE work (of about 15 pages) and I have to search an specific theme for it

In addition, my work should be able to have a numerical application. My first thought was the Lotka-Volterra equations about dynamics of biological systems of predator-prey, but I cannot use it since other people did it last year.

Do you know something similar to the Lotka-Volterra equations that can be interesting to work on it? I mean, some equations with practical applications in an specific field, it is possible to Economy but I don't care if it has applications to other fields like Biology, etc.

Greetings :D

## 2 Answers

There is a number of growth models in economics (well, some of them are actually related to each other), the dynamics of which are described by ODE's. You may check the Solow-Swan model or Ramsey-Cass-Koopmans model (these are the ones that I know of). If you're new to this area, I would start with the basic Solow model to get the intuition on how it works.

You can look at epidemic models. Roughly they describe the process of an epidemic in large populations. Also you can do numerical applications about them. For example one of them is SIR model which is given by the following system of differential equations $$\frac{dS}{dt} = - \beta S I\\\frac{dI}{dt} = \beta S I - \gamma I\\\frac{dR}{dt} = \gamma I$$ where $\beta$, $\gamma$ are parameters and

S(t) is used to represent susceptibles to the disease.
I(t) denotes the number of individuals who have been infected with the disease.
R(t) is the compartment used for those individuals who have been infected and then removed from the disease.


For a quick reference look at wiki