Tick seeking assumptions and their implications for Lyme disease predictions

In vector-borne disease modeling, a key assumption is the host-vector interaction pattern encapsulated in the host seeking rate. Here, a model for Lyme disease dynamics with different host seeking rates is used to investigate how different patterns of tick-host interaction affect the model predictions in the context of tick-borne disease control. Three different host seeking behaviors (the frequency-dependent rate, the density-dependent rate and the Holling type 2 rate) are compared. The comparison of results illustrates not only variable relationships between rodents and tick abundance but also different implications for disease control: (i) for the model with the frequency-dependent rate, reducing rodents is always bad for containing the disease; (ii) for density-dependent or the Holling type 2 rate, reducing or increasing rodent population should be carefully considered, since large host population may facilitate the development of immature ticks, resulting in the immature tick population level so low to sustain the transmission cycle. Furthermore, we distinguish different mechanisms of dilution effects (pathogen reduction with the increasing of the host biodiversity) from different tick-host interaction patterns.