Modeling the Influence of Questing Behavior and Host Accessibility on Tick Population Dynamics

Ixodes scapularis, the blacklegged tick, vectors several human pathogens, making an understanding of its population dynamics essential to assessing and predicting disease risk. Tick demography depends on a sequence of biological events, including reproduction, off-host survival, and successful host attachment for blood feeding, each of which is influenced by host community and questing behavior. In this paper, we develop a stage-structured nonlinear system of difference equations that incorporates this sequence of events through history- and ratio-dependent host-attachment, allowing the model to retain biological detail while remaining assessable by classical discrete-time analysis techniques. The model is parameterized to represent general northeastern and southeastern ecosystems in the United States, where host community composition and questing behavior differ. Analytical and numerical bifurcation analysis show that the system can converge to a positive fixed point, oscillate in a 2-cycle, or exhibit bistability between these attractors, with long-term outcomes depending on initial conditions. The 2-cycle arises through a +1/-1 bifurcation as the demographic reproductive number increases, reflecting a mismatch between cohort progression and host accessibility. Southern host communities expand the parameter region supporting stable fixed points, while high survival and abundant adult hosts can destabilize populations in both regions. These results demonstrate that long-term tick population outcomes are governed by the interactions between demographic processes, host community structure, and environmental conditions.