In a family of three people (two children and their father), the father returns from work with a cold. Thereafter, the spread of the cold through the family may be modeled as a stochastic general epidemic. The infections contact rate between members of the family is = 0.5 per day and any person who catches the cold remains infections for a time which is exponentially distributed with mean 4 days.

In fact, the whole family of three ends up catching the cold. The two children return to school while still infectious. There are 29 other children in their class, all of whom are susceptible to the cold. In this environment, the infectious contact rate is = 0.75 per day.

(iii) Using a deterministic model:

(a) Find the number of children who have the cold when the epidemic is at its height. (Correct to two decimal places).