MODEL PENGENDALIAN ALAMI PENYAKIT EMBUN JELAGA OLEH JAMUR CAPNADIUM SP PADA TANAMAN CENGKEH MENGGUNAKAN KUMBANG HELM CYCLONEDA SPP SEBAGAI PREDATOR KUTU DAUN (COCCOUS VIRIDIS GREEN

Abstract

Soot dew disease is one of the clove plant diseases caused by fungi Capnadium sp. fungus Capnadium sp living on filth of aphids Coccous Viridis Green. The fungus is spread by vectors of black ants that exist on a clove vulnerable. To control the disease naturally, people utilize the helmet beetles Cycloneda spp as a pest predator of aphids Coccous Viridis Green. The mathematical models that represent the natural control of the disease was adapted from the SI model. The model provides 9 exiting critical points which describes the state of the system. The results of the stability analysis of the critical points using the method of Linearization and Routh-Hurwitz shows that there are 4 disease-free critical points such that the solution can be maintained in the neighbourhood of the critical points. All endemic critical points are unstable such that the solution will leave the critical points. Simulation at the endemic critical points indicates the existence of helmet beetles Cycloneda spp population that able to suppress the spread of this disease by preying aphids Coccus Viridis Green.

Keywords : Dew Soot, Helmet Beetles, Aphids, Mathematical Models.