The impact of dispersal and allee effects on tick invasion: a spatially-explicit discrete-time modelling approach

Abstract

We develop a spatially-explicit discrete-time model that describes tick population dynamics and incorporates the developmental stages for an individual tick. The model allows for two types of movements across patches: (1) active tick movement and (2) movement of ticks through a host. We analyse the dynamics of the model under a nonlinear fecundity term that exhibits an Allee effect. We show that the system has bounded solutions and, under certain conditions on the parameters, is monotone. Using the next generation matrix approach, we define the net reproductive number of the multi-patch model, , and establish conditions under which determines the local and global asymptotic stability of the extinction equilibrium. We then show that the model exhibits rich dynamics including a monostable equilibrium, multi-stable equilibria, and cycles. Finally, we perform some numerical studies to further examine how dispersal and Allee effects impact tick survival and system stability.