Additionally, fixed probabilities p C and p H , corresponding to a susceptible individual escaping community-acquired infection during the epidemic and escaping infection when exposed to a single infected household member, respectively, were initially assumed [160] . Two important, realistic extensions to this framework are to incorporate different levels of risk factors for individuals [161] and to introduce dependence of p H on an infectious period [162] . The latter inclusion was enabled by appealing to results of Ball et al. [163] . These types of methods are largely based upon the ability to generate closed form formulae for the final size distribution of the models.