A patchy model for tick population dynamics with patch-specific developmental delays

Area of Science:

• Ecology
• Mathematical Biology
• Epidemiology

Background:

• Tick-borne disease (TBD) spread is influenced by host movement and environmental conditions affecting tick populations.
• Adjacent regions with varying environmental suitability impact tick development and disease transmission dynamics.

Purpose of the Study:

• To develop and analyze a mathematical model simulating tick populations in two distinct environmental patches.
• To investigate the influence of host mobility and patch-specific tick suitability on TBD spread.

Main Methods:

• A two-patch mathematical model using coupled delay differential equations was formulated.
• Singular perturbation analyses and monotone dynamical systems theory were employed.
• Numerical simulations were conducted to explore model behavior.

Main Results:

• The model demonstrates how differing environmental conditions and host movement affect tick population dynamics.
• Patch-specific basic reproduction numbers and host mobility are key determinants of disease spread patterns.
• Theoretical analysis and simulations provide insights into tick population dynamics.

Conclusions:

• Host mobility and environmental patch characteristics are critical factors in tick-borne disease transmission.
• The model offers a framework for understanding and predicting TBD spread in heterogeneous landscapes.
• Findings can inform targeted tick population control strategies.