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Description

I will discuss a class of random spatial networks and show that they have small world-like properties, but the level of clustering is tunable and we can make it arbitrarily small. In some limits we are able to derive a system of integro-differential equations which allows us to accurately predict both the temporal and spatial dynamics of SIR disease. We can use these equations to determine when the network behaves like a small world network with significant long-range transmissions and when the dynamics are dominated by the short-range transmission. Interestingly, we show that the "small-world" properties of disease spread can exist even in the limit of no clustering, and thus the concept of a small-world network is determined more by whether the network has a combination of short-range and long-range connections than whether the network has many clustered connections.