In other words, in this model of an emerging infectious disease epidemic with heterogeneities in susceptibility and infectiousness, the dynamics of mean total incidence of infection is exactly equivalent to the basic model where the infectiousness is appropriately averaged using equation (20) . Once an expression is derived for the average infectiousness b (t, t), the results such as equations (9) or (12) can be used without further consideration of the heterogeneities in infectiousness or susceptibility.