Incorporating tick feeding behaviour into R0 for tick-borne pathogens

Tick-borne pathogens pose a considerable disease burden in Europe and North America, where increasing numbers of human cases and the emergence of new tickborne pathogens has renewed interest in resolving the mechanisms underpinning their geographical distribution and abundance. For Borrelia burgdorferi and tick-borne encephalitis (TBE) virus, transmission of infection from one generation of ticks to another occurs when older nymphal ticks infect younger larval ticks feeding on the same host, either indirectly via systemic infection of the vertebrate host or directly when feeding in close proximity. Here, expressions for the basic reproduction number, R0, and the related tick type-reproduction number, T, are derived that account for the observation that larval and nymphal ticks tend to aggregate on the same minority of hosts, a tick feeding behaviour known as co-aggregation. The pattern of tick blood meals is represented as a directed, acyclic, bipartite contact network, with individual vertebrate hosts having in-degree, k_in, and out-degree, k_out, that respectively represent cumulative counts of nymphal and larval ticks fed over the lifetime of the host. The in- and out-degree are not independent when co-aggregation occurs such that T α < k_in*k_out >/< k_in >, where <.> indicates expected value. When systemic infection in the vertebrate host is the dominant transmission route R0^2 = T, whereas when direct transmission between ticks co-feeding on the same host is dominant then R0 = T and the effect of co-aggregation on R0 is more pronounced. Simulations of B. burgdorferi and TBE virus transmission on theoretical tick-mouse contact networks revealed that aggregation and co-aggregation have a synergistic effect on R0 and T, that co-aggregation always increases R0 and T, and that aggregation only increases R0 and T when larvae and nymphs also co-aggregate. Co-aggregation has the greatest absolute effect on R0 and T when the mean larval burden of hosts is high, and the largest relative effect on R0 for pathogens sustained by co-feeding transmission, e.g. TBE virus in Europe, compared with those predominantly spread by systemic infection, e.g. B. burgdorferi. For both pathogens, though, co-aggregation increases the mean number of ticks infected per infectious tick, T, and so too the likelihood of pathogen persistence.