¹The number of people who will die during the ﬁrst period in the continuous-time model is measured by the diﬀerence between an initial population of size 1 and the size of the population remaining alive after one period, $1 − ℵ1 = 1− e−d$ . $[ExpEps]$ in MathFacts implies that $e−d ≈ 1− d$ ; therefore the proportion who have died will be approximately $1− (1− d) = d$ . Hence for small death rates, in order for the same population to survive for one period in a continuous-time model with death rate $d$ and the discrete-time model with death rate $D$ , one would need $d ≈ D$ .