Let $( s , i , r ) \in E$ where $E = \{ ( s , i , r ) \in \mathbf{N}^3,\, s + i + r = M \}$. Conditional on the event $\left( \left( \tilde { S } _ { n } , \tilde { I } _ { n } , \tilde { R } _ { n } \right) = ( s , i , r ) \right)$, what is the probability, denoted $p ( i )$, for a susceptible person to be infected during this day? Each of the $s$ healthy persons meets, independently of the others, $K$ persons chosen at random from the $M$ persons in the total population. As soon as at least one of the meetings is with an infected person, the healthy person becomes infected the next morning.
Let $( s , i , r ) \in E$ where $E = \{ ( s , i , r ) \in \mathbf{N}^3,\, s + i + r = M \}$. Conditional on the event $\left( \left( \tilde { S } _ { n } , \tilde { I } _ { n } , \tilde { R } _ { n } \right) = ( s , i , r ) \right)$, what is the probability, denoted $p ( i )$, for a susceptible person to be infected during this day?
Each of the $s$ healthy persons meets, independently of the others, $K$ persons chosen at random from the $M$ persons in the total population. As soon as at least one of the meetings is with an infected person, the healthy person becomes infected the next morning.