Abstract
The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists.
Highlights
The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree
Later we present a detailed analysis of the epidemic threshold
In this case the model is identical to the Barabási-Albert model of network growth[56], which is known to lead to scale-free topologies, where the degree distribution follows a power law pk ∝k−γ with exponent γ = 3 and the degree variance σ2 diverges in the disease-free state
Summary
The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Around 655000 people died of malaria in 20102 and more than 100000 confirmed cases of Zika infection have occurred in the Americas in the past year[3] Combating such epidemic diseases efficiently in the mega-cities of the future is likely to require a heightened understanding of the dynamics of the diseases and the social networks on which they spread. In the past two decades, epidemic spreading has been extensively studied on different complex networks to understand the influence of the social contact network structure on the disease prevalence[4,5,6,7]. If the variance of the degree distribution is infinite, such as in certain scale-free networks, the epidemic threshold vanishes and the SIR disease percolates on the network for all non-zero infectiousness levels via hierarchical spreading from hub nodes to lower degree nodes[12]. Scale-free networks allow unlikely diseases with low infectiousness to spread and become endemic
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