The dynamics of plant disease models with continuous and impulsive cultural control strategies

Plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are proposed and investigated. This novel theoretical framework could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Firstly, continuous replanting of healthy plants and removing of infected plants is taken. The existence and stability of disease-free equilibrium and positive equilibrium are studied and continuous cultural control strategy is given. Secondly, plant disease model with impulsive replanting of healthy plants and removing of infected plants is also considered. Using Floquetʹs theorem and small amplitude perturbation, the sufficient conditions under which the infected plant free periodic solution is locally stable are obtained. Moreover, permanence of the system is investigated. Under certain parameter spaces, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations. The modeling methods and analytical analysis presented can serve as an integrating measure to identify and design appropriate plant disease control strategies.