Perturbative solution to susceptible-infected-susceptible epidemics on networks

Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Sep;88(3):032713. doi: 10.1103/PhysRevE.88.032713. Epub 2013 Sep 23.


Herein we provide a closed form perturbative solution to a general M-node network susceptible-infected-susceptible (SIS) model using the transport rates between nodes as a perturbation parameter. We separate the dynamics into a short-time regime and a medium-to-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-to-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, 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.

MeSH terms

  • Communicable Diseases / epidemiology*
  • Communicable Diseases / transmission*
  • Disease Susceptibility*
  • Epidemics*
  • Models, Theoretical*
  • Time Factors