Optimal Control The Use of Botanical Fungicides in The Spread of Plant Diseases
Rika Amelia (a*), Nursanti Anggriani (b), Maisyah Mardiyah (b), Asep Kuswandi Supriatna (b)
a) Master Program in Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, INDONESIA
*rika17003[at]mail.unpad.ac.id
b) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, INDONESIA
Abstract
One of the main obstacles in crop cultivation is the occurrence of fungal infections. Fungal spores can spread due to direct contact between susceptible hosts and infected hosts, which can be controlled using botanical fungicides. We constructed a mathematical model of the growth of logistics on the spread of plant diseases. From this model, we show the value of the Basic Reproduction Number (R0) of plant diseases transmission. The value of R0 is obtained by finding the largest eigenvalue of the next generation matrix. The results obtained show that when R0 is greater than one (R0>1), the endemic equilibrium point will be stable. However, if R0 is less than one (R0<1), the endemic equilibrium point is unstable. In addition, the results of this discussion indicate that by using botanical fungicides can reduce the infected host population. We provide numerical simulations to describe the results of the analysis obtained.
Keywords: Basic Reproduction Number; Local Stability Analysis; Optimal Control
Topic: Applied Mathematics