Dynamics of two pathogens in a single tick population.

A mathematical model for a two-pathogen, one-tick, one-host system is presented and explored. The model system is based on the dynamics of Amblyomma americanum, Rickettsia parkeri, and Rickettsia amblyommatis. The goal of this model is to determine how long an invading pathogen, R. parkeri, persists within a tick population, A. americanum, in which a resident pathogen, R. amblyommatis, is already established. The numerical simulations of the model demonstrate the parameter ranges that allow for coexistence of the two pathogens. Sensitivity analysis highlights the importance of vector-borne, tick-to-host, transmission rates on the invasion reproductive number and persistence of the pathogens over time. The model is then applied to a case study based on a reclaimed swampland field site in south-eastern Virginia using field and laboratory data. The results pinpoint the thresholds required for persistence of both pathogens in the local tick population. However, R. parkeri, is not predicted to persist beyond 3 years. Understanding the persistence and coexistence of tick-borne pathogens will allow public health officials increased insight into tick-borne disease dynamics.