Analisis Dinamika Populasi Tanaman Kopi (Coffea sp.) Akibat Infeksi Jamur Colletotrichum Kahawae

Abstract

Tanaman kopi (Coffea sp.) merupakan salah satu jenis komoditas perkebunan penting secara ekonomi di dunia. Infeksi jamur Colletotrichum kahawae pada tanaman kopi menyebabkan tanaman kopi terinfeksi penyakit coffee berry disease. Tujuan penelitian ini adalah merekontruksi model matematika, mengetahui titik tetap bebas penyakit, titik tetap endemik, dan bilangan reproduksi dasar serta sifat kestabilan titik tetap, mengetahui indeks sensitivitas parameter berdasarkan hasil analisis sensitivitas parameter terhadap bilangan reproduksi dasar pada model, serta melihat dinamika populasi terhadap perubahan parameter. Analisis kestabilan titik tetap ditentukan dengan kriteria Routh-Hurwitz dan Fungsi Lyapunov. Dari analisis sensitivitas diperoleh beberapa parameter yang berpengaruh terhadap dinamika populasi tanaman kopi. Hasil simulasi menunjukkan bahwa dengan menurunkan tingkat penanaman kembali dan meningkatkan laju kematian jamur Colletotrichum kahawae dapat menurunkan bilangan reproduksi dasar.

Coffee plants (Coffea sp.) are one of the most economically important plantation commodities in the world. Colletotrichum kahawae fungal infection in coffee plants causes coffee berry disease. The purposes of this study are to reconstruct a mathematical model, determine the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number, as well as the stability properties of these points. Additionally, the study aimed to determine the parameter sensitivity index based on the sensitivity analysis of the basic reproduction number in the model, and to observe the population dynamics in response to changes in parameters. The analysis of the stability of the equilibrium points was determined using the Routh-Hurwitz criteria and the Lyapunov Function. The sensitivity analysis identified several parameters that affect the dynamics of the coffee plant population. The simulation results showed that reducing the replanting rate and increasing the death rate of Colletotrichum kahawae fungi could reduce the basic reproduction number