Perturbative solution to the SIS epidemic on networks

TL;DR

This paper presents a perturbative analytical solution for the SIS epidemic model on networks, providing insights into short- and long-term dynamics and validated with real-world data from New Zealand.

Contribution

It introduces a novel perturbative approach to solve the network SIS model analytically, bridging short- and long-term epidemic dynamics.

Findings

Analytical solutions closely match numerical simulations.

Effective modeling of epidemic spread in subpopulations.

Perturbative method applicable to general initial conditions.

Abstract

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.