Control analysis of Nilaparvata Lugens with Wolbachia using sterile insect techniques

The ecologist and farmers have both greatly benefited from the modeling and control of 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.