STABILITY ANALYSIS OF DYNAMICAL MODEL INTERACTIONS TEA PLANTS, PESTS, AND DISEASES WITH FUNGICIDES AND INSECTICIDES CONTROLS

Abstract

Tea plants are one of the exports commodities in Indonesia. In their development, the plantation ecosystem is heavily influenced by several factors, both internal and external factors. In the field of applied mathematics, mathematical modelling can be used to analyze the development of tea plant growth and their interactions each other in their ecosystem. The mathematical model in this research is combining three main models, there are logistic model, epidemiological model, and predator prey model by adding fungicide and insecticide controls. Furthermore, local and global stability analysis is carried out and the optimal control problem is solved by Pontryagin maximum principle. The results of the analysis obtained five equilibrium points. Local stability analysis was carried out using the Routh Hurwitz criteria which showed the fifth equilibrium point is locally asymptotically stable. The basic reproduction number in the model is 0.99. Because 16R0<1" style="width: 28pt; height: 11pt;">, it can be concluded that there is no spread of disease in the tea plantation ecosystem after a period of 5 years. The control provided can reduce pest and disease attacks. After being given control, the population of infected tea plants decreased by 93.21%, Empoasca pests decreased by 99.47%, and leaf roller caterpillars decreased by 99.31% compared to the model that was not given control.