  We perform an analytical sensitivity analysis for a model of a
continuous-time branching process evolving on a fixed network. This allows us
to determine the relative importance of the model parameters to the growth of
the population on the network. We then apply our results to the early stages of
an influenza-like epidemic spreading among a set of cities connected by air
routes in the United States. We also consider vaccination and analyze the
sensitivity of the total size of the epidemic with respect to the fraction of
vaccinated people. Our analysis shows that the epidemic growth is more
sensitive with respect to transmission rates within cities than travel rates
between cities. More generally, we highlight the fact that branching processes
offer a powerful stochastic modeling tool with analytical formulas for
sensitivity which are easy to use in practice.
