Disease dynamics with curative and preventive treatments in a two-stage plant disease model

摘要

Due to an increase number of human population, food security becomes an important issue. In this situation, agriculture plays an important role. The staple foods are mostly extracted from plants. However, plant diseases can reduce the production and quality of food. Therefore, understanding plant disease dynamics is important as it can provide insightful knowledge on plant disease transmission. A mathematical model can be used to investigate plant disease dynamics and analyze the effect of disease control strategies. Most mathematical models have assumed that the plant population is divided into five compartments: Susceptible-, Exposed-, Infectious-, Post-Infectious-, and Protected-plant subpopulations. It also has been assumed that infection is only coming from the infectious class. However, in some cases, it is possible that an infection can be caused by the exposed class in a slightly lower rate. In this paper we consider these differential infection rates. We include preventive and curative treatments in the model and analyze their effects on plant disease transmission dynamics. We analytically determine the equilibrium points and epidemic threshold conditions. Several numerical simulations are given to support the analytical results and to compare the results to those in existing literature.