"The spread of infectious diseases is significantly influenced by the underlying structure of social and contact networks. Epidemic models often use moment systems to describe the evolution of the expected average prevalence of infections. Employing moment closures, which commonly involve network structure, simplifies the moment system by reducing the number of coupled ODEs. The clustering of nodes accelerates disease spread through dense local connections, suggesting the use of closures that account for this phenomenon. Closures for networks with highly heterogeneous degree distributions, such as the Super Compact Pairwise (SCP) closure, may more accurately predict the spread of diseases on real-world complex networks.

We explore the dynamics of Susceptible-Infected-Susceptible (SIS) epidemics on small-world networks, characterized by high clustering and low average path length. Using the Watts–Strogatz model, we investigate how topological features of networks, such as clustering and degree distribution, impact epidemic spread, thresholds, and endemic prevalence. We provide an overview of various closures and compare their effectiveness in modelling disease dynamics. Results indicate that the closure involving clustering shows better agreement with stochastic simulations, particularly near critical epidemic thresholds."