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We study epidemic arrival times in meta-population disease models through thelens of front propagation into unstable states. We demonstrate that severalfeatures of invasion fronts in the PDE context are also relevant to the networkcase. We show that the susceptible-infected-recovered model on a network islinearly determined in the sense that the arrival times in the nonlinear systemare approximated by the arrival times of the instability in the systemlinearized near the disease free state. Arrival time predictions are extendedto an susceptible-exposed-infected-recovered model. We then study a recentmodel of social epidemics where high order interactions of individuals lead tofaster invasion speeds. For these pushed fronts we compute corrections to theestimated arrival time in this case. Finally, we show how inhomogeneities inlocal infection rates lead to faster average arrival times.

Epidemic spreading on complex networks as front propagation into an unstable state