Global attractivity in tick population models incorporating seasonality and diapausing stages

Abstract

The goal of this paper is to understand the interplay between seasonality and diapause on the population dynamics of ticks. To analyse this challenge, we study a mathematical model in which the population is divided into two groups: individuals with regular development and individuals undergoing diapause. A key ingredient in the model is that the common birth and death rates depend on time in order to describe the seasonal fluctuations of the environment. From a mathematical point of view, this paper offers a novel methodology to derive criteria of global attraction. In some classical models, we give delay-dependent conditions that cover the best delay-independent criteria of global attraction. We discuss how our approach improves existing results in relevant literature. Moreover, our results are simple and versatile enough to match experimental observations. To illustrate this potential, we analyse our model with parameters coming from real observations. A message of this paper is that seasonality plays a critical role in the population dynamics of ticks.