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Finding the best network structure for disease spread is complex. This study reveals unique optimal network structures for low/high infection rates and surprising results for intermediate rates.

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Area of Science:

  • Network science
  • Mathematical modeling
  • Epidemiology

Background:

  • Determining optimal network structures for dynamical processes is a significant challenge.
  • Susceptible-infected-susceptible (SIS) dynamics on annealed networks are influenced by degree distribution.

Purpose of the Study:

  • To develop an analytic framework for solving the inverse problem of identifying optimal network structures for SIS dynamics.
  • To investigate the relationship between infection rates and optimal network degree distributions.

Main Methods:

  • Developed an analytic framework to solve the inverse problem for SIS dynamics on annealed networks.
  • Characterized network structures using degree distributions.

Main Results:

  • Unique optimal degree distributions (≤2 nodal degrees) exist for low/high infection rates.
  • Multitudinous optimal degree distributions with broader support emerge at intermediate infection rates.
  • Network heterogeneity generally decreases as infection rate increases.

Conclusions:

  • The study provides a framework for understanding how network structure impacts disease spread.
  • Identified a specific infection rate where all degree distributions yield maximum spread.
  • Findings offer insights into network-dynamical process interplay with practical applications.