On the Improvement of the Sterile Insect Technique by Entomopathogenic Fungi: Impact of Residual Fertility and Re-mating Behaviour.

This study investigates the use of the Sterile Insect Technique (SIT) combined with Entomopathogenic Fungi soil treatment (EPFS) to control two major pests: the Mediterranean fruit fly and the Oriental fruit fly. The SIT involves releasing sterile males to mate with wild females, but the challenge lies in female polyandry (re-mating) and residual fertility in sterile males. We develop a continuous release SIT model with single- and double-mated females, but with a novel approach to accounting the residual fertility parameter, $\epsilon$ . We also consider scenarios where the competitiveness of sterile males may decline between the first and the second mating. A key finding is that insect elimination, at least locally, with SIT can only occur when the product of the residual fertility parameter, $\epsilon$ , and the basic reproduction number of sterile mated females, $R_S$ , is less than 1. We also prove the existence of a sterile male release threshold, above which global elimination is possible. When $\epsilon R_S$ is greater than one, elimination is impossible regardless of the size of sterile male releases. We also extend our results to periodic releases. We illustrate our theoretical findings using numerical simulations, with parameters from the Mediterranean fruit fly (medfly), with and without ginger root oil (GRO) treatment, and the oriental fruit fly, with and without Methyl-Eugenol (ME) treatment. Both treatments are known to enhance sterile male competitiveness. We also show that combining SIT with EPFS can greatly improve SIT efficiency, and, in particular, reduce the constraint on residual fertility. We conclude that re-mating and residual fertility can have a significant impact on the effectiveness of SIT. However, this mainly depends on whether SIT is used in combination with EPFS or not, and also on the knowledge of the parameters of sterile-mated females which seem to have been superficially studied in many SIT programs so far.