Stability and Sensitivity Analysis of a Plant Disease Model with Continuous Cultural Control Strategy

Abstract

In this paper, a plant disease model with continuous cultural control strategy and time delay is formulated. Then, how the time delay affects the overall disease progression and, mathematically, how the delay affects the dynamics of the model are investigated. By analyzing the transendental characteristic equation, stability conditions related to the time delay are derived for the disease-free equilibrium. Specially, when $R_0=1$, the Jacobi matrix of the model at the disease-free equilibrium always has a simple zero eigenvalue for all $\tau \ge 0$. The center manifold reduction and the normal form theory are used to discuss the stability and the steady-state bifurcations of the model near the nonhyperbolic disease-free equilibrium. Then, the sensitivity analysis of the threshold parameter $R_0$ and the positive equilibrium $E^{*}$ is carried out in order to determine the relative importance of different factors responsible for disease transmission. Finally, numerical simulations are employed to support the qualitative results.