Study on pest management SI epidemic model with instantaneous and non-instantaneous impulsive effects

In this study, we propose and analyze a Susceptible-Infected (SI) epidemic model applied to pest management, focusing on the nonlinear release of infected pests and an instantaneous pulse of pesticide spraying. Additionally, the mortality rates of both susceptible and infected pests following the pesticide application are modeled as non-instantaneous pulses. Utilizing the comparison theorem for pulse differential equations and Floquet theory, we derive a threshold condition for the eradication of susceptible pests. We also demonstrate that all solutions are uniformly ultimately bounded. Furthermore, we establish conditions for the globally asymptotic stability of the pest-free boundary periodic solution and the permanence of the system. Finally, numerical simulations are conducted to verify the theoretical findings, and the key parameters affecting the pest extinction threshold were obtained, thereby providing a solid theoretical basis for the development of effective pest management strategies.