Journal
JOURNAL OF BIOLOGICAL DYNAMICS
Volume 13, Issue 1, Pages 606-620Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17513758.2019.1682201
Keywords
Sterile mosquitoes; mosquito population suppression; delay differential equation; global stability; bi-stability; semi-stability
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Funding
- National Natural Science Foundation of China [11631005]
- Program for Changjiang Scholars and Innovative Research Team in University [IRT16R16]
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We develop a delay differential equation model for the interactive wild and sterile mosquitoes. Different from the existing modelling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics. We consider the cases where the release amount is either constant or described by a given function of time. For the constant releases, we establish a threshold of releases to determine whether the wild mosquito suppression succeeds or fails. We study the existence and stability of the model equilibria. When the releases are described by given functions, the trivial equilibrium is no longer globally but locally uniformly asymptotically stable if the amount of releases is below the threshold whereas it is still globally uniformly asymptotically stable if the release amount is above the threshold. Numerical examples demonstrating the model dynamical features and brief discussions of our findings are also provided.
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