The dimension of Reed-Frost epidemic models with randomized susceptibility levels

A generalized Reed-Frost epidemic process is discussed in which variability among susceptible individuals is incorporated by randomizing the levels of resistance of the individuals to the infection. Our purpose is to derive the exact distribution of the ultimate number of susceptibles surviving the disease. This is achieved by a simple conditional argument and by using a particular family of polynomials defined recursively. The results can be viewed as a continuation of those obtained by the authors for the alternative situation with randomized infectivity levels.