Plant disease models with nonlinear impulsive cultural control strategies for vegetatively propagated plants

In present work, with aims to eradicate plant diseases or maintain the number of infected plants below the Economic Threshold, the plant disease models including nonlinear impulsive functions and cultural control strategies are proposed and analyzed. Firstly, the model with impulsive effects at fixed moments is considered. The existence and stability of the disease-free periodic solution of the model are investigated. Moreover, we establish conditions for the permanence of the system and obtain the sufficient conditions under which the positive periodic solution exists by bifurcation theory. Secondly, the impulsive model with Economic Threshold for the infected plants is analyzed. The existence and stability of the positive periodic solution are discussed. Further, the complete expression of the period of the periodic solution is obtained. Our main results imply that we can choose proper control frequency and intensity to either eradicate the plant disease or maintain the number of infected plants below the Economic Threshold. The modeling and analytic methods presented here extend the classical results for the systems with impulsive interventions, and the findings can serve as an integrating measure to design appropriate plant disease control strategies.