Fig. 2.

Demonstration of convergence described by Theorem 7.2, for $D\sim \text{Geo}(1/6)$. Histograms of $I^N(t_i)$ (based on 1000 simulated trajectories) and normal approximation for three fixed time points $t_1=0.35$, $t_2=0.6$, $t_3=1.5$ and 3 population sizes $N=200$, $N=1000$, $N=5000$. Other parameters are $\beta =3/2$, $\gamma =1$, $\omega =1$, $i_0^N=0.05N$