Stability Analysis of Mathematical Models for Controlling the Spread of Pests and Diseases in Shallot Plants (Allium ascalonicum L.)

Abstract

There is a pest of shallots (Allium ascalonicum L.) with the most common cases being onion caterpillars and purple spot which must be controlled to get good yields. This study aims to determine the properties of the stability of the model by examining the stability analysis by determining the model equation, equilibrium point, basic reproduction number, analysis of the equilibrium point by linearization of the Jacobian matrix to obtain eigenvalues ​​and stability properties. The simulation shows the effect of pesticide treatment using the fourth order Runge-Kutta method and the Matlab program. There are two equilibrium points: (1) Point (E0) free of pests and diseases is stable if R0 < 1. (2) Endemic point (E1) is stable if R0 > 1. The simulation shows that the greater the pesticide treatment, the faster the susceptible population and infected decreased, the faster the recovering population has increased.