A chain binomial Model is considered by assuming that, in a household of size N, the probability of Pat being infected by contact with a given infective is {1- exp (-λt)}, where t is the infectious duration period, λ is the infection rate of that infective. The aim of the present work is to find the infectious duration time distribution, the mean and the coefficient of variation of each generation and every possible chain in the model under consideration. It is also found that the infectious duration time, coefficient of variation decreases as N and the number of infectives increases. Finally an application to infectious hepatitis household data is introduced.