Abstract
ABSTRACTTo study the impact of the sterile insect technique and effects of the mosquitoes' metamorphic stage structure on the transmission dynamics of mosquito-borne diseases, we formulate stage-structured continuous-time mathematical models, based on systems of differential equations, for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for the releases of sterile mosquitoes in the models and investigate the model dynamics, including the existence of positive equilibria and their stability. Numerical examples are provided to demonstrate the dynamical features of the models.
Highlights
The sterile insect technique (SIT), as one of the mosquitoes control measures, has been applied to reducing or eradicating wild mosquitoes
We investigate the stability for the positive equilibria of Equation (4) as follows
Mosquitoes undergo complete metamorphosis through four distinct stages of development during a lifetime, and the effects of crowding, in the aquatic stages, could be an important factor and it is necessary to have the metamorphic stages be included in modelling population dynamics of mosquitoes
Summary
The sterile insect technique (SIT), as one of the mosquitoes control measures, has been applied to reducing or eradicating wild mosquitoes. Utilizing radical or other chemical or physical methods, male mosquitoes are genetically modified to be sterile which are incapable of producing offspring despite being sexually active These sterile mosquitoes are released into the environment to mate with wild mosquitoes that are present in the environment. Mathematical models have been formulated in the literature to study the interactive dynamics and control of the wild and sterile mosquito populations [2,3,4,5,6, 11, 12].
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