Impulsive releases of sterile mosquitoes and interactive dynamics with time delay

Jia Li1, Shangbing Ai1

  • 1Department of Mathematical Sciences, The University of Alabama, Huntsville, AL, USA.

Insights

This study models sterile mosquito releases, focusing on sexually active ones, to understand population dynamics. Different release strategies impact wild mosquito populations, with findings supporting complex interactions and periodic solutions.

Area of Science:

  • Mathematical Biology
  • Ecology
  • Population Dynamics

Background:

  • Sterile insect technique (SIT) is a key pest control strategy.
  • Understanding the dynamics of sterile and wild mosquito populations is crucial for effective SIT implementation.
  • Previous models often overlook the specific behavior of sexually active sterile mosquitoes.

Purpose of the Study:

  • To investigate the impact of periodic and impulsive release strategies of sterile mosquitoes on population dynamics.
  • To develop novel mathematical models incorporating time delays and focusing on sexually active sterile mosquitoes.
  • To analyze and compare the dynamics arising from different release strategies.

Main Methods:

  • Formulation of new mathematical models with time delays, considering only sexually active sterile mosquitoes.
  • Analysis of model dynamics under various release strategies (periodic and impulsive).
  • Derivation of model formulations and proof of the existence of periodic solutions under specific conditions.

Main Results:

  • Demonstration of complex dynamical behaviors in the sterile insect population models.
  • Identification of conditions under which periodic solutions exist, indicating stable population cycles.
  • Numerical examples illustrating the intricate interactions between wild and sterile mosquito populations.

Conclusions:

  • The inclusion of sexually active sterile mosquitoes and time delays significantly influences population dynamics.
  • Different release strategies yield distinct model dynamics, highlighting the importance of strategic planning in SIT.
  • Further research is warranted to explore the full implications of these complex dynamics for pest control.