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Posted on 2016-10-11 18:56:00 in Math by TEDDY

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 β = 0.5 per day and any person who catches the cold remains infections for a time which is exponentially distributed with mean 4 days. 

(i) Find the probability distribution of the number of members of the family who never catch the cold. Hence write down the probability that the whole family caught the cold (correct to one decimal places). 

(ii) Determine the epidemic parameter. 

(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). 
(b) How many children in the class escape without catching the cold? (Correct to three decimal places).

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