Periodically Switched Shepherd-Type Survival Function Model: Unveiling Diverse Dynamics for Suppressing Nilaparvata lugens and Boosting Rice Production

The brown planthopper, Nilaparvata lugens (N. lugens hereinafter), is a devastating pest of rice—a dietary staple for over half of the global population. Given the world's growing population and limited arable land, suppressing wild N. lugens populations is critical for boosting rice yields. Recent decades, the sterile insect technique (SIT) and the incompatible insect technique (IIT) have gained significant attention from researchers and practitioners, as they are environmentally friendly, effective, and species-specific for pests control. This study utilizes SIT and IIT and follows the periodic pulsed release strategy for sexually active sterile male mosquitoes outlined in previous research. We then develop a periodically switched ODE model incorporating a complete, more flexible Shepherd-type survival function to capture suppression dynamics in wild N. lugens populations. Through identifying the upper and lower critical thresholds governing per-batch release amount and release period, introducing a Poincaré map, novelly constructing two unimodal auxiliary functions, and conducting rigorous qualitative analyses for the two functions, we derive the local/global asymptotic stability of the origin, as well as the model's unique stability and bistability. Specifically, wild N. lugens populations can be completely eliminated with minimal operational expenditure provided that the two release parameters stay within the thresholds-limited feasible region. Numerical examples are offered to elucidate and expand the theoretical results. This work validates and extends prior results, and can assist in designing cost-effective infertile N. lugens release strategies while addressing food security concerns.