Past exam of the mathematics and the environment and mathematical physiology course of the University of Oxford / 2008 / B / 5 / ii / Solution

Mass action givesThus $E+C=E_0$ and $S+C+P=S_0$ are conserved. Eliminating free enzyme yields the stated two-equation system.

With $s=S/S_0$, $c=C/E_0$ and $\tau =t/T$, substitution givesThe dimensionless initial data are $\boxed{s(0)=1,c(0)=0}$. The parameter named $\delta$ here is an enzyme kinetic coefficient and is unrelated to the loss parameter used in the later blood-cell question.