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Consider the simplest SIR model: $$S'=-a SI$$ $$I'=a SI - b I$$ $$R'=b I$$ It is known that the waiting time of an infeccious person in the compartment $I$ follows an exponential behavior with rate $b$...

Consider the probability mass function of the Poisson distribution given a mean $\lambda$: \begin{equation} \mathbb{P}\left(Y=k|\lambda\right)=\frac{e^{-\lambda} \lambda^{k}}{k !} \end{equation} By ...