Analisis Kontrol Optimal Model Matematika Penyebaran Penyakit Mosaic pada Tanaman Jarak Pagar

Mosaic disease is an infectious disease that attacks Jatropha curcas caused by Begomoviruses. Mosaic disease can be transmitted through the bite of a whitefly as a vector. In this paper, we studied a mathematical model of mosaic disease spreading of Jatropha curcas with awareness effect. We also studied the effect of prevention and extermination strategies as optimal control variables. Based on the results of the model analysis, we found two equilibriums namely the mosaic-free equilibrium and the endemic equilibrium. The stability of equilibriums and the existence of endemic equilibrium depend on basic reproduction number ( ). When , the spread of mosaic disease does not occur in the population, while when , the spread of mosaic disease occurs in the population. Furthermore, we determined existence of the optimal control variable by Pontryagin's Maximum Principle method. Simulation results show that prevention and extermination have a significant effect in eliminating mosaic disease.