Table 1.

Table of notation

Notation	Definition
$\beta$	Transmission rate
$\gamma$	Rate of recovery (days${}^{-1}$)
$e_{\mathit{ij}}$	Percentage effectiveness against infection of i doses of vaccine j
$V_{\mathit{ij}}$	Daily number of individuals who have received dose i of vaccine j
N	Number of individuals in the population
${\mu }_i$	Factor reducing infectiveness due to i doses