MODELING AND ANALYSIS OF OPTIMAL IMPLEMENTATION OF STERILE INSECT TECHNIQUE TO SUPPRESS MOSQUITO POPULATION

Sterile Insect Technique (SIT) is a biological insect (or pest) control tool aiming to reduce or eliminate wild insect (or pest) populations by releasing sterile insects (or pests). In this paper, we propose and study a stage- and sex-structured entomological model describing the dynamics of wild-type mosquito population and observed that the extinction equilibrium of the model is globally asymptotically stable when the basic offspring number is less than unity. However, when the basic offspring number is greater than unity, the extinction equilibrium becomes unstable, followed by the emergence of the stable interior equilibrium. We extend the model by introducing sterile male mosquitoes as a biological control agent against wild-type mosquito species. We have considered the Allee effect in the fertile female mosquito population due to the presence of non-egg-laying females in the mosquito population. While the wild mosquito-free equilibrium of the SIT model is always locally asymptotically stable, there exists either no interior equilibrium or a pair of interior equilibria, among which one is always unstable, and the other is always locally asymptotically stable. We observed that the wild mosquito population of the SIT system goes to extinction, followed by a saddle-node bifurcation when the supply rate of sterile males increases through some critical threshold value. As an alternative to the eradication policy, we formulated an optimal control problem to suppress the wild mosquito population, which suggests increasing the investment in awareness campaigns to suppress the mosquito population.