Before revision:  In this context, 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.
After revision:  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.