Dynamic Model of The Spread of Vascular Streak Dieback Disease (VSD) by Oncobasidium Theobromae on Cocoa Trees with Trichoderma Sp Control

Abstract

Disease Vascular Streak Dieback (VSD) is caused by the fungus Oncobasidium theobromae which produces basidiospores and grow on infected cacao branches. Biological control of VSD disease used Trichoderma sp. The mathematical model that represented the spread of this disease is adapted from the SIS and provided two existing critical points, namely the disease-free critical point and the endemic critical point . Analysis of system stability at the critical points using the Linearization method and the Routh-Hurwitz indicated that the is stable and appearing a threshold for the growth rate of Oncobasidium theobromae that must be less than 0.767. The is exist and stable with a threshold for spore growth rate of Oncobasidium theobromae is greater than 0.767. Simulations at the both critical points showed that the spore growth rate of Oncobasidium theobromae is very fluently in the spread of the disease. In this case, suppressing the growth rate of Oncobasidium theobromae could be used as a good treatment to control the disease.