  In this brief, we study epidemic spreading dynamics taking place in complex
networks. We specifically investigate the effect of synergy, where multiple
interactions between nodes result in a combined effect larger than the simple
sum of their separate effects. Although synergistic effects play key roles in
various biological and social phenomena, their analyses have been often
performed by means of approximation techniques and for limited types of
networks. In order to address this limitation, this paper proposes a rigorous
approach to quantitatively understand the effect of synergy in the
Susceptible-Infected-Susceptible model taking place in an arbitrary complex
network. We derive an upper bound on the growth rate of the synergistic
Susceptible-Infected-Susceptible model in terms of the eigenvalues of a matrix
whose size grows quadratically with the number of the nodes in the network. We
confirm the effectiveness of our result by numerical simulations on empirically
observed human and animal social networks.
