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Oscillation threshold for a mosquito population suppression model with time delay.

Yuan Xian Hui^1,2, Geng Hong Lin¹, Qi Wen Sun¹

¹Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, PRC.

Mathematical Biosciences and Engineering : MBE

|November 9, 2019

Summary

Introducing sterile mosquitoes can control mosquito populations. This study reveals an oscillation threshold for sterile mosquito release rates, determining if populations stabilize or continue to fluctuate, confirmed by simulations.

Keywords:

mosquito population suppression model oscillation threshold sterile mosquitoes time delay

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Area of Science:

Mathematical biology
Ecology
Population dynamics

Background:

Mosquito population dynamics are complex and influenced by various factors.
Time delays in biological models can lead to oscillatory behaviors.
Sterile insect technique is a method for pest control.

Purpose of the Study:

To analyze a mathematical model of mosquito population suppression incorporating time delay.
To investigate the effect of sterile mosquito releases on population dynamics.
To determine the conditions under which population oscillations occur or cease.

Main Methods:

Mathematical modeling of mosquito population dynamics.
Analysis of time-delayed differential equations.
Bifurcation analysis to identify oscillation thresholds.
Numerical simulations to validate theoretical findings.

Main Results:

In the absence of sterile mosquito releases, the model exhibits oscillations around the non-zero equilibrium.
An oscillation threshold (b̂) for the sterile mosquito release rate was identified.
Population oscillations persist for release rates below b̂ and disappear above it.

Conclusions:

Sterile mosquito releases can be a critical factor in controlling population oscillations.
The identified threshold b̂ provides a quantitative measure for managing sterile insect releases.
Mathematical modeling offers valuable insights into pest control strategies.