Study on a delayed pest management model with pulse chemical control

Chemical control is crucial in pest management, but delayed responses to pesticide application can significantly affect its success. This study develops a type of novel mathematical models combining delayed impulse differential equations with pulse pesticide spraying to evaluate these delayed effects. The uniform stability of the pest eradication solution is analysed, and key parameters influencing pest control success are explored. Considering delays in both pest population growth reaching environmental capacity and pesticide response, a double delayed impulse differential equation is formulated. The asymptotic stability and exponential stability of the system are studied, and threshold conditions for pest extinction are identified. The findings help optimize pest control strategies under delayed pesticide responses.