The impact of network structure on epidemic dynamics

Calculation of R0 is more involved in the network setting and typically requires simplifying assumptions to be made. As an example, the presence of loops in the network is usually ignored. This enables analysis to be undertaken, albeit at the cost of neglecting some aspects of network structure—such as cliques— that may impact upon the spread of infection.

For a static network, each individual has a fixed set of contacts and so an important quantity36'37 is the probability of transmission from an infective node to a susceptible node along a given edge over the entire duration of their infection. Newman calls this the "transmissibility" of infection23 and represents its value by T. In the infection setting described earlier, in which infection is transmitted at rate 3 along a given edge and the duration of infectiousness is exponentially distributed with mean 1/y, it is easy to show that T = 3/(3 + y).

For a homogeneous network, in which every individual has k neighbors, the basic reproductive number equals

Notice that the average number of secondary infections is proportional to the average number of neighbors minus one.36 The minus one accounts for the fact that every infectious individual, except for the initial infective, must have acquired infection from one of their neighbors.

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