Modelling the spread of diseases in clustered networks

It is now well appreciated that population structure can have a major impact on disease dynamics, outbreak sizes and epidemic thresholds. Indeed, on some networks, epidemics occur only for sufficiently high transmissibility, whereas in others (e.g. scale-free networks), no such threshold effect exists. While the effects of variability in connectivity are relatively well known, the effects of clustering in the population on disease dynamics are still debated. We develop a simple and intuitive model for calculating the reproductive number R0 on clustered networks with arbitrary degree distribution. The model clearly shows that in general, clustering impedes epidemic spread; however, its effects are usually small and/or coupled with other topological properties of the network. The model is generalized to take into account degree-dependent transmissibility (e.g., relevant for disease vectors). The model is also used to easily rederive a known result concerning the formation of the giant component.

► We study epidemics spreading through clustered population networks.
► The reproductive number R0 of epidemics is formulated on clustered networks.
► The formulation holds for networks of arbitrary degree distribution.
► The effects of clustering are often small and coupled with other network properties.
► The formulation can also take into account degree-dependent transmissibility.