A simple model for the establishment of tick-borne pathogens of Ixodes scapularis: A global sensitivity analysis of R0

The basic reproduction number of a pathogen, R0, determines whether a pathogen will spread (R0 > 1), when introduced into a fully susceptible population or fade out (R0 < 1), because infected hosts do not, on average, replace themselves. In this paper we develop a simple mechanistic model for the basic reproduction number for a group of tick-borne pathogens that wholly, or almost wholly, depend on horizontal transmission to and from vertebrate hosts. This group includes the causative agent of Lyme disease, Borrelia burgdorferi, and the causative agent of human babesiosis, Babesia microti, for which transmission between co-feeding ticks and vertical transmission from adult female ticks are both negligible. The model has only 19 parameters, all of which have a clear biological interpretation and can be estimated from laboratory or field data. The model takes into account the transmission efficiency from the vertebrate host as a function of the days since infection, in part because of the potential for this dynamic to interact with tick phenology, which is also included in the model. This sets the model apart from previous, similar models for R0 for tick-borne pathogens.