A Model of Annual Tick Population Density in the Eastern United States as a Function of Questing Behavior and Host Availability

[2607.13280] A Model of Annual Tick Population Density in the Eastern United States as a Function of Questing Behavior and Host Availability Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Dynamical Systems arXiv:2607.13280 (math) [Submitted on 14 Jul 2026 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: A Model of Annual Tick Population Density in the Eastern United States as a Function of Questing Behavior and Host Availability Authors: Carli Peterson , Erika Gallo , Christopher Kribs View a PDF of the paper titled A Model of Annual Tick Population Density in the Eastern United States as a Function of Questing Behavior and Host Availability, by Carli Peterson and 1 other authors View PDF HTML (experimental) Abstract: Understanding the ecological processes that regulate populations of the blacklegged tick, Ixodes scapularis, is essential for explaining regional differences in tick abundance and the risk of tick-borne diseases. In this study, we develop a stage-structured nonlinear system of difference equations by ordering and composing the seasonal biological events that govern tick and host life cycles. The model incorporates ratio-dependent host-attachment, allowing host-finding success to depend jointly on host availability and tick abundance. Parameter estimates from both northeastern and southeastern ecosystems in the United States are used to examine how regional differences in host community composition and questing behavior influence tick population dynamics. Analysis shows that a $+1$/$-1$ bifurcation pair occurs at the demographic persistence threshold, producing an exchange of stability between the extinction and positive fixed points together with the emergence of an unstable cohort-based 2-cycle. Quantitative results show that ratio-dependent host-finding success limits population growth by restricting successful feeding, while questing behavior alters both the frequency and composition of host encounters. Together, these mechanisms regulate tick persistence and long-term abundance, providing a demographic foundation for understanding variation in tick abundance and Lyme disease risk. Comments: 33 pages, 4 figures Subjects: Dynamical Systems (math.DS) Cite as: arXiv:2607.13280 [math.DS] (or arXiv:2607.13280v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2607.13280 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Carli Peterson [ view email ] [v1] Tue, 14 Jul 2026 21:31:14 UTC (304 KB) [v2] Fri, 14 Aug 2026 23:11:03 UTC (304 KB) Full-text links: Access Paper: View a PDF of the paper titled A Model of Annual Tick Population Density in the Eastern United States as a Function of Questing Behavior and Host Availability, by Carli Peterson and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2026-07 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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