The influence of seasonality and diapausing stages in patchy models for tick populations: a global attraction analysis

Abstract Lyme borreliosis, tick-borne encephalitis, and human granulocytic anaplasmosis are remarkable examples of tick-borne diseases. Motivated by their notable epidemiological role, this paper explores the interplay among seasonality, diapause, and diffusion on the population dynamics of ticks. To reach this goal, we analyze a metapopulation model in a fragmented ecosystem of m -patches, with ticks as a motivating example. Specifically, we offer a new methodology to derive criteria of global attraction in nonautonomous metapopulation models with delay (without assuming monotonicity requirements). A strength of our approach is that the results apply to metapopulations with any number of patches and topology. From a practical point of view, our theoretical analysis allows us to corroborate some previous experimental work. Another important conclusion of this paper is that the presence of sinks can benefit the tick population, simplifying the dynamical behavior of the whole metapopulation and increasing the total population size. To assess the real repercussions of the results, we analyze our model with parameters derived from real observations.