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Related Experiment Video

Updated: Apr 21, 2026

A Capsule-Based Model for Immature Hard Tick Stages Infestation on Laboratory Mice

A Capsule-Based Model for Immature Hard Tick Stages Infestation on Laboratory Mice

Published on: July 9, 2020

Delay differential systems for tick population dynamics.

Guihong Fan¹, Horst R Thieme², Huaiping Zhu³

¹Department of Mathematics and Philosophy, Columbus State University, Columbus, GA, 31907, USA. fan_guihong@columbusstate.edu.

Journal of Mathematical Biology

|October 29, 2014

Summary

This study models tick population dynamics using delay differential equations to understand Lyme disease spread. Mathematical analysis determines tick population persistence based on the basic reproduction number, crucial for disease vector control.

Keywords:

Basic reproduction number Delay differential systems Global stability Integral equations Local stability Persistence Stage structure Tick populations

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Last Updated: Apr 21, 2026

A Capsule-Based Model for Immature Hard Tick Stages Infestation on Laboratory Mice

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Published on: July 9, 2020

Tick Microbiome Characterization by Next-Generation 16S rRNA Amplicon Sequencing

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Published on: August 25, 2018

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Area of Science:

Mathematical Biology
Epidemiology
Ecology

Background:

Ticks are critical vectors for Lyme disease transmission.
Understanding tick population dynamics is essential for managing tick-borne diseases.

Purpose of the Study:

To model the stage structure of tick populations using delay differential equations.
To define and analyze the basic reproduction number (R0) for stage-structured tick populations.
To investigate conditions for tick population persistence and stability.

Main Methods:

Formulation of a system of delay differential equations for tick population dynamics.
Definition of the basic reproduction number (R0) for stage-structured populations.
Analysis of equilibrium points and conditions for global asymptotic stability.

Main Results:

Tick populations are uniformly persistent if R0 > 1 and die out if R0 < 1.
Sufficient conditions for the global asymptotic stability of the unique positive equilibrium were identified.
The system can exhibit oscillatory behavior due to negative feedback and time delays.

Conclusions:

The basic reproduction number (R0) is a key determinant of tick population persistence.
Time delays in developmental stages can influence population stability and lead to oscillations.
This modeling approach provides insights into tick population dynamics relevant to disease control.