Population dynamics

This model describes the population dynamics of an E. coli / C. glutamicum co-culture as a two-species competition with Monod-type growth. Each species grows according to its substrate affinity and maximum growth rate, and C. glutamicum additionally carries a density-dependent death term.

It is a simpler precursor to the dynamic enterobactin model, with no shared siderophore variable, and illustrates the baseline competition dynamics of the two organisms.

\begin{align*}
  \frac{d E.\ coli}{dt} &= E.\ coli \cdot a_e \cdot \mu_e \\ 
  \frac{d C.\ gluta}{dt} &= C.\ gluta \cdot a_c \cdot \mu_c - \theta \cdot C.\ gluta \cdot C.\ gluta
\end{align*}