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

Ixodes scapularis, the blacklegged tick, vectors several human pathogens, making understanding 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 developed a stage-structured nonlinear system of difference equations that incorporates this sequence of events through ratio-dependent host-attachment, allowing the model to retain biological detail while remaining assessable by classical discrete-time analysis techniques.

The model was 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 shows that the system exhibits a $+1$/$-1$ bifurcation pair as the demographic reproductive number increases, which gives rise to a stable positive existence fixed point and an unstable 2-cycle.

Ratio-dependent feeding success limits population sizes by restricting successful feeding.

Questing behavior determines both the frequency and composition of host encounters, further influencing successful feeding.

These results demonstrate that long-term tick population outcomes are governed by the balance between cohort advancement and host-attachment opportunities.