Model Klasik dan Model Fraksional untuk Dinamika Penyebaran Virus Covid-19 Berbasis Model Lotka-Volterra

Suparno Suparno; Sri Wahyuni Jamal; Riski Safitri

doi:10.21831/pythagoras.v19i2.76358

Model Klasik dan Model Fraksional untuk Dinamika Penyebaran Virus Covid-19 Berbasis Model Lotka-Volterra

Suparno Suparno, Alumni Departemen Matematika, Universitas Gadjah Mada, Indonesia, Indonesia
Sri Wahyuni Jamal, Fakultas Ekonomi Bisnis dan Politik, Universitas Muhammadiyah Kalimantan Timur, Indonesia, Indonesia
Riski Safitri, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Yogyakarta, Indonesia, Indonesia

10.21831/pythagoras.v19i2.76358

Abstract

Covid-19 telah menjadi pandemi global sejak pertama kali muncul pada akhir tahun 2019. Pandemi ini ditandai dengan penyebarannya yang cepat dan gejalanya yang tidak muncul dengan cepat. Penelitian ini bertujuan untuk menganalisis dinamika penyebaran virus Covid-19 menggunakan pendekatan model Lotka-Volterra. Model yang diusulkan melibatkan model turunan klasik yang memuat order bilangan bulat dan model turunan fraksional dengan order fraksional. Model matematika yang terbentuk memiliki dua titik ekuilibrium yang berbeda: titik ekuilibrium trivial dan titik ekuilibrium tak nol. Untuk model klasik, kestabilan titik ekuilibrium trivial adalah saddle, sedangkan titik ekuilibrium tak nol bersifat stabil asimptotik lokal. Selanjutnya, stabilitas lokal untuk model fraksional juga dibahas berdasarkan kondisi stabilitas Matignon. Karena melibatkan efek memori, model turunan fraksional memberikan gambaran yang lebih memadai dan realistis mengenai fenomena alam yang timbul dari model tersebut. Selain itu, hasil numerik menunjukkan bahwa parameter fraksional berpengaruh terhadap dinamika penyebaran Covid-19. Hasil ini mungkin dapat digunakan sebagai sebuah strategi bagi para pemangku jabatan dalam mengendalikan penyebaran pandemi.

Keywords

Covid-19; Lotka-Volterra; model turunan fraksional; model turunan klasik; stabilitas Matignon

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DOI: https://doi.org/10.21831/pythagoras.v19i2.76358