An LMI Approach-Based Mathematical Model to Control Aedes aegypti Mosquitoes Population via Biological Control

In this paper, a novel age-structured delayed mathematical model to control Aedes aegypti mosquitoes via Wolbachia-infected mosquitoes is introduced. To eliminate the deadly mosquito-borne diseases such as dengue, chikungunya, yellow fever, and Zika virus, the Wolbachia infection is introduced into...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021, Vol.2021, p.1-18
Main Authors: Dianavinnarasi, J., Raja, R., Alzabut, J., Niezabitowski, M., Selvam, G., Bagdasar, O.
Format: Article
Language:English
Subjects:
Bacteria
Biological control
Dengue fever
Engineering
Laboratories
Linear matrix inequalities
Mathematical analysis
Mathematical models
Mosquitoes
Population
Stability analysis
Zika virus
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Summary:In this paper, a novel age-structured delayed mathematical model to control Aedes aegypti mosquitoes via Wolbachia-infected mosquitoes is introduced. To eliminate the deadly mosquito-borne diseases such as dengue, chikungunya, yellow fever, and Zika virus, the Wolbachia infection is introduced into the wild mosquito population at every stage. This method is one of the promising biological control strategies. To predict the optimal amount of Wolbachia release, the time varying delay is considered. Firstly, the positiveness of the solution and existence of both Wolbachia present and Wolbachia free equilibrium were discussed. Through linearization, construction of suitable Lyapunov–Krasovskii functional, and linear matrix inequality theory (LMI), the exponential stability is also analyzed. Finally, the simulation results are presented for the real-world data collected from the existing literature to show the effectiveness of the proposed model.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/5565949