Control analysis of Nilaparvata Lugens with Wolbachia using sterile‎ ‎ insect techniques

Volume 37, Issue 3, pp 261--273 https://dx.doi.org/10.22436/jmcs.037.03.01

Publication Date: October 04, 2024 Submission Date: June 13, 2024 Revision Date: July 10, 2024 Accteptance Date: July 29, 2024

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Authors

R. Chinnathambi - Department of Mathematics‎, ‎School of Advanced Sciences, ‎Vellore Institute of Technology, ‎Chennai‎, ‎Tamilnadu-600 127, India. F. A. Rihan - Department of Mathematical Sciences‎, ‎College of Science, United Arab Emirates University, ‎Al-Ain‎, ‎15551, UAE. G. P. Balakrishnan - Department of Mathematics, ‎Mepco Schlenk Engineering College, ‎Sivakasi‎, ‎Tamil Nadu 626 005, India. Ch. Pichani - Department of Mathematics‎, ‎School of Advanced Sciences, ‎Vellore Institute of Technology, ‎Chennai‎, ‎Tamilnadu-600 127, India.

Abstract

‎The ecologist and farmers have both greatly benefited from the modeling and control of {\it Nilaparvata Lugens} (N‎. ‎Lugens) populations in rice fields‎. ‎This work describes a sex-structured wild Lugens population and male Lugens infected with w-Stri (Wolbachia)‎. ‎The w-Stri type Wolbachia can naturally control wild Lugens‎, ‎as shown in a test done in the laboratory‎. ‎Male Lugens infected with w-Stri produce larger amounts of cytoplasmic incompatibility‎, ‎when they mate with wild female Lugens‎. ‎Using the time-dependent control parameter of the continuous releasing rate of male Lugens infected with w-Stri‎, ‎we create an optimal control problem‎. ‎By analyzing the necessary and sufficient conditions‎, ‎we investigate the optimality‎. ‎Furthermore‎, ‎we explore the sufficient conditions for the elimination of wild Lugens via periodic impulsive releases of male Lugens infected with w-Stri‎. ‎Numerical simulations validate the theoretical conclusions‎.

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Keywords

• Feedback control
• optimal control
• sterile insect technique
• Lugens
• Wolbachia

MSC

•  37N25
•  37N35
•  49N25
•  92B05

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