Dynamics of an impulsive reaction-diffusion mosquitoes model with multiple control measures

Yun Li; Hongyong Zhao; Kai Wang; Yun Li; Hongyong Zhao; Kai Wang

doi:10.3934/mbe.2023036

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 775-806. doi: 10.3934/mbe.2023036

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Dynamics of an impulsive reaction-diffusion mosquitoes model with multiple control measures

1.
College of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2.
Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing 211106, China

Academic Editor: Xiang-Sheng Wang

Received: 09 September 2022 Revised: 03 October 2022 Accepted: 06 October 2022 Published: 14 October 2022

It is well-known that mosquito control is one of the effective methods to reduce and prevent the transmission of mosquito-borne diseases. In this paper, we formulate a reaction-diffusion impulsive hybrid model incorporating Wolbachia, impulsively spraying of insecticides, spatial heterogeneity, and seasonality to investigate the control of mosquito population. The sufficient conditions for mosquito extinction or successful Wolbachia persistence in a population of natural mosquitoes are derived. More importantly, we give the estimations of the spraying times of insecticides during a period for achieving the mosquito extinction and population replacement in a special case. A global attractivity of the positive periodic solution is analyzed under appropriate conditions. Numerical simulations disclose that spatial heterogeneity and seasonality have significant impacts on the design of mosquitoes control strategies. It is suggested to combine biological control and chemical pulse control under certain situations to reduce the natural mosquitoes. Further, our results reveal that the establishment of a higher level of population replacement depends on the strain type of the Wolbachia and the high initial occupancy of the Wolbachia-infected mosquitoes.
- mosquito-borne diseases,
- Wolbachia,
- impulsive control of insecticides,
- spatial heterogeneity,
- seasonality
Citation: Yun Li, Hongyong Zhao, Kai Wang. Dynamics of an impulsive reaction-diffusion mosquitoes model with multiple control measures[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 775-806. doi: 10.3934/mbe.2023036

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Abstract

It is well-known that mosquito control is one of the effective methods to reduce and prevent the transmission of mosquito-borne diseases. In this paper, we formulate a reaction-diffusion impulsive hybrid model incorporating Wolbachia, impulsively spraying of insecticides, spatial heterogeneity, and seasonality to investigate the control of mosquito population. The sufficient conditions for mosquito extinction or successful Wolbachia persistence in a population of natural mosquitoes are derived. More importantly, we give the estimations of the spraying times of insecticides during a period for achieving the mosquito extinction and population replacement in a special case. A global attractivity of the positive periodic solution is analyzed under appropriate conditions. Numerical simulations disclose that spatial heterogeneity and seasonality have significant impacts on the design of mosquitoes control strategies. It is suggested to combine biological control and chemical pulse control under certain situations to reduce the natural mosquitoes. Further, our results reveal that the establishment of a higher level of population replacement depends on the strain type of the Wolbachia and the high initial occupancy of the Wolbachia-infected mosquitoes.

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