Just to show simple this can get and not put you off so early, here's a few more simplifications. What if we're only concerned with very short-term dynamics (e.g. seasonal)? Then we can dispense with burial and arguably mixing which may occur on longer time scales. Then we get simply,

\begin{align} \frac {\partial C}{\partial t} = aR - \lambda C \\ \end{align}

Maybe we've even got good reason to discard one of the two terms on the right-hand side of that equation (test production and taphonomic loss), in which case it gets even simpler.

\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}