Stability Analysis of Tungro Disease Spread Model in Rice Plant Using Matrix Method

Abstract

Rice is one of the staple foods produced from the rice plant. Rice productivity is increased by carrying out efforts to control diseases that usually attack rice plants. Tungro is one of the most destructive diseases of rice plants. Mathematical models can help solve problems in the spread of plant diseases. In this paper, the development of a mathematical model for the spread of tungro disease in rice plants with 6 compartments is developed involving rice in the vegetative and generative phases. Furthermore, stability analysis is carried out on the obtained model by using the Basic Reproduction Number ( ) search through the matrix method, especially through the search for transition matrices and transmission matrices. The analytical results show that when 1 the non-endemic equilibrium point is stable and when >1 the endemic equilibrium point is stable. Numerical results showed that rice plants in the generative phase were more infected than rice plants in the vegetative phase.