  Herein we provide a closed form perturbative solution to a general $M$-node
network SIS model using the transport rates between nodes as a perturbation
parameter. We separate the dynamics into a short-time regime and a
medium/long-time regime. We solve the short-time dynamics of the system and
provide a limit before which our explicit, analytical result of the first-order
perturbation for the medium/long-time regime is to be employed. These stitched
calculations provide an approximation to the full temporal dynamics for rather
general initial conditions.
  To further corroborate our results, we solve the mean-field equations
numerically for an infectious SIS outbreak in New Zealand (NZ, \emph{Aotearoa})
recomposed into 23 subpopulations where the virus is spread to different
subpopulations via (documented) air traffic data, and the country is
internationally quarantined. We demonstrate that our analytical predictions
compare well to the numerical solution.
