Abstract
In networks, nodes may preferentially contact other nodes with similar (assortatively mixed) or dissimilar (disassortatively mixed) numbers of contacts. Different patterns of contact support different epidemic dynamics, potentially affecting the efficacy of control measures such as contact tracing, which aims to identify and isolate nodes with infectious contacts. We used stochastic simulations to investigate the effects of mixing patterns on epidemic dynamics and contact-tracing efficacy. For uncontrolled epidemics, outbreaks occur at lower infection rates for more assortatively mixed networks, with faster initial epidemic growth rate and shorter epidemic duration than for disassortatively mixed networks. Contact tracing performs better for assortative mixing where epidemic size is large and tracing rate low, but it performs better for disassortative mixing at higher contact rates. For assortatively mixed networks, disease spreads first to highly connected nodes, but this is balanced by contact tracing quickly identifying these same nodes. The converse is true for disassortative mixing, where both disease and tracing are less likely to target highly connected nodes. For small epidemics, contact tracing is more effective on disassortative networks due to the greater resilience of assortative networks to link removal. Multi-step contact tracing is more effective than single-step tracing for assortative mixing, but this effect is smaller for disassortatively mixed networks.
Highlights
For a wide range of epidemic and epizootic diseases, individuals can be usefully modelled as nodes in a network, where the network links represent potentially infectious contacts between individuals
For networks that are poorly characterized, the efficacy of contact tracing is difficult to determine without exact knowledge of the underlying contact network, i.e. who is connected to whom? By analysing disease transmission on theoretical networks with different mixing patterns, we aim to identify the implications of non-random mixing for epidemic dynamics and control strategies
The structural differences of preferentially mixed networks are demonstrated by the size of the giant component (GC) as a function of the cut-off parameter K for three different values of the assortativity coefficient r
Summary
For a wide range of epidemic and epizootic diseases, individuals can be usefully modelled as nodes in a network, where the network links represent potentially infectious contacts between individuals. This network representation applies to many complex systems such as the Internet, the World Wide Web (Albert & Barabasi 2002), social and transportation networks (Liljeros et al 2001; Jones & Handcock 2003; Hufnagel et al 2004) and livestock movement networks (Kiss et al 2006b; Robinson et al 2007). Contact tracing is more effective on clustered networks than on random networks (Eames & Keeling 2003; Kiss et al 2005), and on scale-free networks a higher tracing effort is needed to control an epidemic than on random Poisson networks (Kiss et al 2006b)
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