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

Marco Tosato; Xue Zhang; Jianhong Wu; Marco Tosato; Xue Zhang; Jianhong Wu

doi:10.3934/mbe.2022250

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 5: 5329-5360. doi: 10.3934/mbe.2022250

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

1.
Laboratory for Industrial and Applied Mathematics, York University, Toronto M2J4A6, Canada
2.
Department of Mathematics, Northeastern University, Shenyang 110057, China

Academic Editor: Feng-Bin Wang

Received: 22 December 2021 Revised: 25 February 2022 Accepted: 10 March 2022 Published: 24 March 2022

Tick infestation and tick-borne disease spread in a region of multiple adjacent patches with different environmental conditions depend heavily on the host mobility and patch-specific suitability for tick growth. Here we introduce a two-patch model where environmental conditions differ in patches and yield different tick developmental delays, and where feeding adult ticks can be dispersed by the movement of larger mammal hosts. We obtain a coupled system of four delay differential equations with two delays, and we examine how the dynamical behaviours depend on patch-specific basic reproduction numbers and host mobility by using singular perturbation analyses and monotone dynamical systems theory. Our theoretical results and numerical simulations provide useful insights for tick population control strategies.
- ticks,
- diapause,
- delay differential equations,
- spatial model,
- Hopf bifurcations
Citation: Marco Tosato, Xue Zhang, Jianhong Wu. A patchy model for tick population dynamics with patch-specific developmental delays[J]. Mathematical Biosciences and Engineering, 2022, 19(5): 5329-5360. doi: 10.3934/mbe.2022250

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Abstract

Tick infestation and tick-borne disease spread in a region of multiple adjacent patches with different environmental conditions depend heavily on the host mobility and patch-specific suitability for tick growth. Here we introduce a two-patch model where environmental conditions differ in patches and yield different tick developmental delays, and where feeding adult ticks can be dispersed by the movement of larger mammal hosts. We obtain a coupled system of four delay differential equations with two delays, and we examine how the dynamical behaviours depend on patch-specific basic reproduction numbers and host mobility by using singular perturbation analyses and monotone dynamical systems theory. Our theoretical results and numerical simulations provide useful insights for tick population control strategies.

References

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