A spatially-explicit stochastic model for the Gulf Coast Tick

Tick ecology is complicated and has many potentially negative effects including disease transmission, host population declines, altered dynamics, and cascading interactions that disrupt entire ecological systems. Such negative effects could be mitigated through a careful analysis and understanding of how ticks disperse over a landscape. In this paper we develop a stage-structured spatially-explicit stochastic model for the Gulf Coast Tick (GCT), Amblyomma maculatum. In this model, each tick individual belongs to one of four developmental stages: egg, larvae, nymph, or adult. We divide a 2-dimensional landscape into discrete spatial patches and model two types of tick movement across these patches: (1) active where ticks use their own energy to move about or (2) passive where ticks move about through host movement. Using a two-dimensional grid landscape and incorporating demographic stochasticity, we investigate tick invasion across the landscape, including invasion speed, the significance of environmental variability, and the effect of heterogeneous habitats on invasion. We also highlight the significant impact that adult ticks have on invasion and suggest control mechanisms to alleviate the negative impacts of the tick invasion. This model can be adapted to apply to various tick species to study geographic range expansion scenarios.