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Discrete stage-structured tick population dynamical system with diapause and control.

Ning Yu1, Xue Zhang1

  • 1Department of Mathematics, Northeastern University, Shenyang 110819, China.

Mathematical Biosciences and Engineering : MBE
|January 19, 2023
PubMed
Summary

This study models tick populations, including diapause, and evaluates acaricide spraying for control. Mathematical analysis shows that acaricide effectiveness depends on the net reproduction number ($R_0$) and spraying strategy.

Keywords:
acaricide sprayingdiapausediscrete non-monotonic systemtick population dynamicstranscritical bifurcationuniform persistence

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Area of Science:

  • Mathematical Ecology
  • Vector-Borne Disease Control
  • Population Dynamics

Background:

  • Tick populations pose significant threats as vectors for various diseases.
  • Understanding tick population dynamics is crucial for effective control strategies.
  • Diapause, a state of suspended development, complicates tick population modeling.

Purpose of the Study:

  • To develop and analyze a discrete, stage-structured tick population model incorporating diapause.
  • To evaluate the efficacy of acaricide spraying as a tick control method.
  • To compare the impact of constant versus periodic acaricide application on tick populations.

Main Methods:

  • A discrete, stage-structured dynamical system was formulated, stratifying ticks into immature (normal and diapause) and mature subgroups.
  • Qualitative analysis was performed, including computation of the net reproduction number ($R_0$).
  • The model was analyzed under constant and periodic acaricide spraying scenarios.

Main Results:

  • The tick-free fixed point is globally asymptotically stable when $R_0 < 1$.
  • A unique coexistence fixed point exists and is asymptotically stable if and only if $R_0 > 1$.
  • Transcritical bifurcation occurs at $R_0 = 1$, and comparative analysis of spraying strategies was conducted.

Conclusions:

  • The net reproduction number ($R_0$) is a critical parameter determining tick population stability.
  • Acaricide spraying can effectively control tick populations, with efficacy influenced by the spraying schedule.
  • Mathematical modeling provides valuable insights for optimizing tick control strategies.