Fig. 4.

Probability histograms, computed from ${10}^5$ sample paths in the CTMC SIR model (12) show a mixture of two densities when ${\mathrm{ℛ}}_0>1$, the probability of a minor or major epidemic. The curve overlayed in red is a graph of the minor epidemic $f_{T_3}{\mathrm{\mathbb{P}}}_{\text{ext}}$, where $f_{T_3}$ is given in equation (5). Parameter values are $\gamma =1$, $\beta ={\mathrm{ℛ}}_0$, and $N=5000$ with initial conditions $I\left(0\right)=3$, $S\left(0\right)=4997$, and $R\left(0\right)=0$.