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Incorporating tick feeding behaviour into \(R_0\) for tick-borne pathogens. (English) Zbl 1516.92108

Summary: Tick-borne pathogens pose a considerable disease burden in Europe and North America, where increasing numbers of human cases and the emergence of new tick-borne 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, \( R_0\), 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, \( k_{\operatorname{in}} \), and out-degree, \( k_{\operatorname{out}} \), 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 \[T \propto \frac{ \langle k_{\operatorname{in}} k_{\operatorname{out}} \rangle}{ \langle k_{\operatorname{in}} \rangle} ,\] where \(\langle \cdot \rangle\) indicates expected value. When systemic infection in the vertebrate host is the dominant transmission route \(R_0^2 = T\), whereas when direct transmission between ticks co-feeding on the same host is dominant then \(R_0 = T\) and the effect of co-aggregation on \(R_0\) 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 \(R_0\) and \(T\), that co-aggregation always increases \(R_0\) and \(T\), and that aggregation only increases \(R_0\) and \(T\) when larvae and nymphs also co-aggregate. Co-aggregation has the greatest absolute effect on \(R_0\) and \(T\) when the mean larval burden of hosts is high, and the largest relative effect on \(R_0\) 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.

MSC:

92D30 Epidemiology
47A75 Eigenvalue problems for linear operators
92C42 Systems biology, networks
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