Author(s)

Jianping Wang^1*, Xue Zhang², Juanjuan Wang¹, Quanben Sun¹

¹The Department of Basic Course Education, Ji’an College, Ji’an, China.
²College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China.

In this paper, for controlling the spread of plant diseases, a nonautonomous SEIS (Susceptible → Exposed → Infectious → Susceptible) epidemic model with a general nonlinear incidence rate and time-varying impulsive control strategy is proposed and investigated. This novel model could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Using the method of small amplitude perturbation, the sufficient conditions under which guarantee the globally attractive of the disease-free periodic solution and the permanence of the disease are obtained, that is, the disease dies out if R₁<1, otherwise, the disease persists if R₂>1.

Plant Disease, Nonautonomous Model, Time-Varying Impulse, General Nonlinear Incidence, Permanence

Wang, J. , Zhang, X. , Wang, J. and Sun, Q. (2019) Dynamics of a Nonautonomous Plant Disease Model with General Nonlinear Incidence Rate and Time-Varying Impulse. Journal of Applied Mathematics and Physics, 7, 2518-2530. doi: 10.4236/jamp.2019.710171.