Modeling the spread of vector-borne diseases on bipartite networks

Vector-borne diseases for which transmission occurs exclusively between vectors and hosts can be modeled as spreading on a bipartite network. In such models the spreading of the disease strongly depends on the degree distribution 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 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. 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.