Analisis Kestabilan Lokal Titik Ekuilibrium Model Dinamik Kebiasaan Merokok
DOI:
https://doi.org/10.15575/kubik.v5i2.9348Keywords:
stabil asimtotik lokal, bebas rokok, perokok beratAbstract
Dinamika kebiasaan merokok dalam artikel ini dianalisis dengan pendekatan model epidemiologi. Lingkungan perokok dibagi menjadi empat populasi, yaitu populasi  (Potential) menyatakan populasi dari individu-individu yang tidak merokok, populasi  (Light) menyatakan populasi dari perokok ringan, populasi (Smokers) menyatakan populasi dari perokok berat, populasi  menyatakan populasi dari individu-individu yang berhenti merokok sementara dan populasi  menyatakan populasi dari individu-individu yang berhenti merokok secara permanen. Model  tersebut dimodifikasi kemudian dianalisis titik ekuilibriumnya. Langkah pertama, ditentukan titik ekuilibrium bebas rokok. Langkah kedua, ditentukan titik ekuilibrium kebiasaan merokok. Langkah ketiga, ditentukan the Smoking Generation Number (R0 ) dengan menggunakan next generation matrix yang melibatkan radius spektral. Langkah terakhir, kestabilan lokal setiap titik ekuilibrium pada modelnya dianalisis. Hasil analisis menunjukkan bahwa titik ekuilibrium bebas rokok stabil asimtotik lokal saat nilai the Smoking Generation Number kurang dari satu. Sebaliknya, jika nilai the Smoking Generation Number lebih dari satu dan b1(m+g) lebih dari b2(b1-m), maka titik ekuilibrium perokok ringan stabil asimtotik lokal. Sedangkan titik ekuilibrium perokok berat stabil asimtotik lokal jika nilai the Heavy Smoking Generation Number lebih dari satu. Kemudian dilakukan simulasi numerik menggunakan Software Maple untuk mengecek hasil analisis kestabilan lokal titik ekuilibrium tersebut.
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