Implications of vector attachment and host grooming behaviour for vector population dynamics and distribution of vectors on their hosts

Towards gaining a mechanistic understanding of the co-feeding transmission dynamics of tick-borne diseases, we develop a delay differential equation model for vector-host population dynamics. In addition to the intrinsic demographic dynamics of both vector and host populations, the model has the distribution dynamics of vector individuals on hosts governed by vector attachment and host grooming behaviour. We introduce the concept of basic infestation number, derive analytic formulae for calculating it and use these formulae to characterize the distribution patterns. We also show how some of these patterns naturally lead to bi-stability and nonlinear oscillations in the vector and host populations.