  The effects of local and global connectivity on the spread of synergistic
susceptible-infected-removed epidemics were studied in lattice models with
infinite- and finite-range rewiring (small-world and small-world-like models).
Several effects were found numerically and supported analytically within a
simple model: (i) rewiring enhanced resilience to epidemics with strong
constructive synergy on networks with high local connectivity; (ii) rewiring
enhanced spread of epidemics with destructive or weak constructive synergy on
networks with arbitrary local connectivity; (iii) rewiring enhanced spread of
epidemics, independent of synergy, in networks with low local connectivity.
