Sustained oscillatory mosquito population suppression analysis based on a hybrid switching dynamical system model

Area of Science:

• Mathematical Biology
• Dynamical Systems Theory
• Vector Control

Background:

• Mosquito population suppression is crucial for disease control.
• Existing models often simplify the complexities of sterile insect release strategies.
• The interplay between sampling periods and sterile mosquito lifespan impacts suppression dynamics.

Purpose of the Study:

• To develop a hybrid dynamical system for modeling mosquito population suppression.
• To analyze the long-term dynamics considering time- and state-dependent switching.
• To provide insights for optimizing sterile mosquito release strategies.

Main Methods:

• Development of a hybrid dynamical system incorporating time- and state-dependent switching.
• Analysis of long-term dynamics, including convergence to pseudo-equilibrium.
• Application of Poincaré mapping to analyze harmonic and subharmonic solutions.

Main Results:

• The wild mosquito population converges to a pseudo-equilibrium under specific conditions.
• Sufficient conditions for the existence and stability of unique (pseudo)-harmonic solutions were established.
• Explicit criteria for globally asymptotically stable subharmonic solutions were derived.

Conclusions:

• The hybrid dynamical system effectively models mosquito population suppression.
• Theoretical findings offer practical insights for developing effective sterile mosquito release strategies.
• The study contributes to understanding the mathematical dynamics of vector control interventions.