scholarly journals Oscillation threshold for a mosquito population suppression model with time delay

2019 ◽  
Vol 16 (6) ◽  
pp. 7362-7374 ◽  
Author(s):  
Yuanxian Hui ◽  
◽  
Genghong Lin ◽  
Qiwen Sun ◽  
Keyword(s):  
Time Delay ◽  
Mosquito Population ◽  
Population Suppression ◽  
Oscillation Threshold

scholarly journals Stability and periodicity in a mosquito population suppression model composed of two sub-models

2021 ◽  
Author(s):  
Zhongcai Zhu ◽  
Bo Zheng ◽  
Yantao Shi ◽  
Rong Yan ◽  
Jianshe Yu
Keyword(s):  
Periodic Solution ◽  
Stable Equilibrium ◽  
Mosquito Population ◽  
Sexually Active ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Numerical Examples ◽  
Suppression Process ◽  
Population Suppression ◽  
Theoretical Results

AbstractIn this paper, we propose a mosquito population suppression model which is composed of two sub-models switching each other. We assume that the releases of sterile mosquitoes are periodic and impulsive, only sexually active sterile mosquitoes play a role in the mosquito population suppression process, and the survival probability is density-dependent. For the release waiting period T and the release amount c, we find three thresholds denoted by $$T^*$$ T ∗ , $$g^*$$ g ∗ , and $$c^*$$ c ∗ with $$c^*>g^*$$ c ∗ > g ∗ . We show that the origin is a globally or locally asymptotically stable equilibrium when $$c\ge c^*$$ c ≥ c ∗ and $$T\le T^*$$ T ≤ T ∗ , or $$c\in (g^*, c^*)$$ c ∈ ( g ∗ , c ∗ ) and $$T<T^*$$ T < T ∗ . We prove that the model generates a unique globally asymptotically stable T-periodic solution when either $$c\in (g^*, c^*)$$ c ∈ ( g ∗ , c ∗ ) and $$T=T^*$$ T = T ∗ , or $$c>g^*$$ c > g ∗ and $$T>T^*$$ T > T ∗ . Two numerical examples are provided to illustrate our theoretical results.

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