Key epidemiological parameters, such as the basic reproduction number R_0
and the critical vaccination coverage v_c, of new emerging infectious
diseases are often estimated from the initial exponential phase of an
outbreak. Besides the observed incidence of new cases, such estimation
relies on information about the community structure in which the disease
spreads and the infectivity profile of infected individuals. In this report
we show analytically that the community structure only plays a minor role
for the estimates. In fact, for nearly all heterogeneous community
structures considered we show that neglecting this structure increases the
estimates for R_0 and v_c slightly. As a consequence, by ignoring the often
unknown community structures and assuming the simpler scenario of
homogeneous mixing, we obtain slightly conservative estimates for these
quantities. Joint work with Frank Ball, Jean-Stéphane Dhersin, Viet Chi
Tran, Pieter Trapman and Jacco Wallinga.