Establish the following identity:
$$\mathbf { E } \left[ \Delta \tilde { R } _ { n } \right] = \rho \mathbf { E } \left[ \tilde { I } _ { n } \right]$$
where each infected person recovers at the end of the day with probability $\rho \in ]0,1[$, independently of others, and $\Delta \tilde{R}_n = \tilde{R}_{n+1} - \tilde{R}_n$.