Global attractivity of tick population dynamics model with patch structure and multiple time-varying delays

The impact of multiple time delays and the variation of populations between patches make population dynamics research more realistic and challenging. The main goal of this work is to study the effect of delay on the asymptotic behavior of tick population dynamics model with patch structure and multiple time-varying delays. We make use of the fluctuation lemma and inequality techniques to tackle the positivity, persistence and the global attractivity of the considered high-dimensional system. Finally, we give an example with three numerical simulations to verify that our theoretical results are completely new and complement some earlier existing ones. Our work is conducive to further understanding the more complex laws of tick population dynamics.