Synchronized Tick Population Oscillations Driven by Host Mobility and Spatially Heterogeneous Developmental Delays Combined

Abstract

We consider a coupled system of delay differential equations for a single-species tick population dynamics, assuming feeding adult ticks are distributed by their hosts in a spatially heterogeneous environment consisting of two patches where egg ticks produced will complete their life cycles with different, normal and diapause, developmental delays. We show that the mobility of adult tick host and the diapause developmental delay combined drive a synchronized oscillation in the total tick populations around a uniquely defined positive equilibrium, and this synchronization makes the oscillatory patterns much simpler in comparison with multi-peak oscillations exhibited in the absence of host mobility.

Tick paralysis induced by Ixodes gibbosus: enigmatic cases in domestic mammals from Cyprus

“…One possible explanation is that the phenomenon results from the matching culmination of various factors having different cycle lengths ( 22 ). For instance, there may be factors that synchronize tick population oscillations, linked to temperature, humidity, microhabitat, and different developmental stages of ticks and life cycle duration, which can be between 2 to 6 years ( 24 , 25 ). Data on beech tree seed production (masting) from the literature indicate that the abundance of I. ricinus nymphs can increase dramatically 2 years after a masting event ( 26 ).…”