The Reed-Frost model

In the model, there are susceptible and infected people. In each generation, each infected person has an independent probability \(p\) to infect each susceptible person. Infections last for one generation, so infected people are removed after they have one chance to infect each susceptible person.

Let \(S_0\) and \(I_0\) be the initial numbers susceptible and infected. Then the number infected and susceptible in each generation \(t \geq 0\) is:

\[ \begin{align*} I_{t+1} &\sim \mathrm{Binomial}\left[S_t; 1-(1-p)^{I_t}\right] \\ S_{t+1} &= S_t - I_{t+1} \end{align*} \]

The reedfrost package and app calculate the distribution of the final sizes of outbreaks, that is, the total number of people infected beyond the initial infections.