Diffusing wild type and sterile mosquitoes in an optimal control setting

•An optimal control approach to mosquito population reduction with diffusion.•It is possible, through optimal choices, to eliminate the wild mosquito population.•If larvicide is allowed, it should be used at a maximal level.•A combination of techniques leads to a rapid elimination of the wild mosqui...

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Bibliographic Details
Published in:Mathematical biosciences 2018-08, Vol.302, p.100-115
Main Authors: Fister, K. Renee, McCarthy, Maeve L., Oppenheimer, Seth F.
Format: Article
Language:English
Subjects:
Aquatic insects
Coccidioidomycosis
Computer simulation
Control theory
Culicidae
Dengue fever
Diffusion rate
Dispersion
Fecundity
Insect control
Insects
Malaria
Mathematical models
Mosquitoes
Optimal control
Partial differential equations
Protocol (computers)
Rift Valley fever
Sterile mosquitoes
Sterilization
Vector-borne diseases
Vectors
Viral diseases
Yellow fever
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Summary:•An optimal control approach to mosquito population reduction with diffusion.•It is possible, through optimal choices, to eliminate the wild mosquito population.•If larvicide is allowed, it should be used at a maximal level.•A combination of techniques leads to a rapid elimination of the wild mosquitos.•Numerical results suggest that a combination of both strategies is optimal. This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2018.05.015