Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 1 / 6C / c / Solution

The deterministic equation has solution $n(t)=n(0)e^{(B-D)t}$ and is identical in form to the equation for the stochastic expected value. It therefore identifies only the net rateThe variance equation also contains the total event rate $s=B+D$. Once $r$ and $s$ are inferred,The deterministic trajectory cannot distinguish frequent births and deaths that nearly cancel from infrequent events with the same net growth, whereas fluctuations can.