Model of Two Infectious Diseases in Nettle Caterpillar Population

摘要

Palm oil is a vital commodity to the economy of Indonesia. The area of oil palm plantations in Indonesia has increased from year to year. However, the effectiveness of palm oil production is reduced by pest infestation. One of the pest which often infests oil palm plantations is nettle caterpillar. The pest control used in this study is biological control, viz. biological agents given to oil palm trees. This paper describes a mathematical model of two infectious diseases in nettle caterpillar population. The two infectious diseases arise due to two biological agents, namely Bacillus thuringiensis bacterium and parasite which usually attack nettle caterpillars. The derivation of the model constructed in this paper is obtained from ordinary differential equations without time delay. The equilibrium points are analyzed. Two of three equilibrium points are stable if the Routh-Hurwitz criteria are fulfilled. In addition, this paper also presents the numerical simulation of the model which has been constructed.