Modeling the Spread of Vector-Borne Diseases on Bipartite Networks

Background: Vector-borne diseases for which transmission occurs exclusively between vectors and hosts can be modeled as spreading on a bipartite network. Methodology/Principal Findings: In such models the spreading of the disease strongly depends on the degree distributions of the two classes of nodes. It is sufficient for one of the classes to have a scale-free degree distribution with a slow enough decay for the network to have asymptotically vanishing epidemic threshold. Data on the distribution of {\it Ixodes ricinus} ticks on mice and lizards from two independent studies are well described by a scale-free distribution compatible with an asymptotically vanishing epidemic threshold. The commonly used negative binomial, instead, cannot describe the right tail of the empirical distribution. Conclusions/Significance: The extreme aggregation of vectors on hosts, described by the power-law decay of the degree distribution, makes the epidemic threshold decrease with the size of the network and vanish asymptotically.