Tag Archives: Differential Equations

Kenny and Epidemic Models

My name is Kenny. I’m an Applied Mathematics student at Boise State University, with other interests in Computer Science and programming.

An area of math that I’m interested in is differential equations and modeling. Using differential equations we can model a number of natural phenomenons. Namely, predator-prey, competing predator-predator, mass on ┬áspring, and epidemic models. The last one may be modeled, simply, by the system of differential equations:

\begin{align*}
\frac{dS}{dt} &= -\beta{}SI \\
\frac{dI}{dt} &= \beta{}SI-\gamma{}I \\
\frac{dR}{dt} &= \gamma{}I
\end{align*}
Where $S(t)$ is a function of individuals not yet infected, $I(t)$ a function of infected individuals, $R(t)$ a function of recovered individuals and $\beta{}$ and $\gamma{}$ are constants of infection and recovery, respectively.

You can read more about Differential Equations on the Wikipedia page. You can also find more information about epidemic models.