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Herein we provide a closed form perturbative solution to a general $M$-nodenetwork SIS model using the transport rates between nodes as a perturbationparameter. We separate the dynamics into a short-time regime and amedium/long-time regime. We solve the short-time dynamics of the system andprovide a limit before which our explicit, analytical result of the first-orderperturbation for the medium/long-time regime is to be employed. These stitchedcalculations provide an approximation to the full temporal dynamics for rathergeneral initial conditions.  To further corroborate our results, we solve the mean-field equationsnumerically for an infectious SIS outbreak in New Zealand (NZ, \emph{Aotearoa})recomposed into 23 subpopulations where the virus is spread to differentsubpopulations via (documented) air traffic data, and the country isinternationally quarantined. We demonstrate that our analytical predictionscompare well to the numerical solution.

Perturbative solution to the SIS epidemic on networks