A note on the moments of the final size of the general epidemic model

Abstract

In the general epidemic model we study the first two moments of the final size. Beginning with the backwards equation, algebraic methods are used to find their asymptotic series expansions as the population size increases.

A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models

“…Total size revisited. Dunstan (1980) gives recursive expressions for the first and second moments of the total size of the general stochastic epidemic, which are very similar in form to that given, for the moment generating function of the area under the trajectory of infectives, in Theorem 2.5. In this section we give a similar recursive expression for the probability generating function of the total size distribution, within our more general framework.…”

“…The above-mentioned results of Dunstan (1980), see also Abakuks (1973), are easily obtained upon twice differentiating Theorem 2.5 and setting…”

“…The asymptotic results derived by Dunstan (1980), concerning the mean and variance of the total size of the general stochastic epidemic as N~00, are now easily generalized to epidemics with non-exponential infectious periods. Returning to Theorem 2.6, we note that ll'k(S) is a polynomial of degree k in s. Thus we may express ll'k(S) as…”