We show how one can trace in a systematic way the coarse-grained solutions of
individual-based stochastic epidemic models evolving on heterogeneous complex
networks with respect to their topological characteristics. In particular, we
have developed algorithms that allow the tuning of the transitivity (clustering
coefficient) and the average mean-path length allowing the investigation of the
"pure" impacts of the two characteristics on the emergent behavior of detailed
epidemic models. The framework could be used to shed more light into the
influence of weak and strong social ties on epidemic spread within small-world
network structures, and ultimately to provide novel systematic computational
modeling and exploration of better contagion control strategies