  Reachability and other path-based measures on temporal graphs can be used to
understand spread of infection, information, and people in modelled systems.
Due to delays and errors in reporting, temporal graphs derived from data are
unlikely to perfectly reflect reality, especially with respect to the precise
times at which edges appear. To reflect this uncertainty, we consider a model
in which some number $\zeta$ of edge appearances may have their timestamps
perturbed by $\pm\delta$ for some $\delta$. Within this model, we investigate
temporal reachability and consider the problem of determining the maximum
number of vertices any vertex can reach under these perturbations. We show that
this problem is intractable in general but is efficiently solvable when $\zeta$
is sufficiently large. We also give algorithms which solve this problem in
several restricted settings. We complement this with some contrasting results
concerning the complexity of related temporal eccentricity problems under
perturbation.
