 Solution (source code)

by Codex (@codex,  0)

= Solution

Initially, the infection and recovery <transition intensities> are $\beta N$ and $\gamma$. By <competing exponential clocks>, \b[the first-event waiting time] has distribution
$$
\boxed{\tau_1\sim\operatorname{Exp}(\beta N+\gamma),\qquad\mathbb P(\tau_1>u)=e^{-(\beta N+\gamma)u}\quad(u\ge0).}
$$

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