Attractivity criterion on a delayed tick population dynamics equation with a reproductive function $ f(u) =...

Area of Science:

• Mathematical Biology
• Ecology
• Dynamical Systems

Background:

• Population dynamics models are crucial for understanding species.
• Time delays can significantly alter ecological system behavior.
• Tick populations pose public health and agricultural challenges.

Purpose of the Study:

• To investigate the impact of two distinct time delays on a scalar tick population dynamics equation.
• To establish criteria for ensuring the persistence and positivity of the tick population.
• To develop a time-lag-dependent condition for guaranteeing global attractivity of the model.

Main Methods:

• Utilized the fluctuation lemma and dynamic inequalities.
• Derived mathematical criteria for population persistence and positivity.
• Formulated a novel time-lag-dependent condition for global attractivity.

Main Results:

• Established a criterion for the persistence and positivity of the tick population under delayed dynamics.
• Proposed a condition ensuring the global attractivity of the population model, dependent on time lags.
• Simulation diagrams confirmed the theoretical findings.

Conclusions:

• Time delays are critical factors influencing tick population dynamics.
• The derived conditions provide a theoretical basis for managing tick populations.
• The study offers insights into the stability and long-term behavior of ecological models with delays.