APPLICATION OF THE SEIPAHRF MODEL TO THE DYNAMICS OF COVID-19 TRANSMISSION: A CASE STUDY IN EAST JAVA

Coronavirus Disease 2019 (Covid-19) merupakan penyakit menular yang disebabkan oleh virus corona dari famili coronaviridae.  Penyebaran virus ini berlangsung dengan cepat di beberapa negara, salah satunya Indonesia. Penelitian ini bertujuan untuk menerapkan model dinamik SEIPAHRF   pada penularan Covid-19 di provinsi Jawa Timur, Indonesia, pada periode 6 Agustus-5 Oktober 2020 ketika sudah diberlakukan kebijakan Pembatasan Sosial Berskala Besar (PSBB) di provinsi Jawa Timur. Dalam penelitian ini dibahas juga tentang bilangan reproduksi dasar, titik ekuilibrium, kestabilan dan sensitivitas dari solusi model dinamik SEIPAHRF berdasarkan variasi nilai parameter. Simulasi numerik dari model dinamik SEIPAHRF diberikan dengan nilai parameter dan nilai awal dari Ndaïrou et al. (2020), kemudian hasilnya dibandingkan dengan data riil dari Satgas Covid-19 Jawa Timur. Berdasarkan hasil pembahasan, diperoleh bilangan reproduksi dasar   yang artinya Covid-19 telah menyebar dan menjadi wabah. Analisis stabilitas model SEIPAHRF berdasarkan titik ekuilibrium menunjukkan bahwa titik ekuilibrium bebas penyakit  adalah tidak stabil, namun titik ekuilibrium endemik  adalah stabil asimtotik. Hasil dari simulasi numerik, model SEIPAHRF sangat sesuai dengan data riil dari Satgas Covid-19 Jawa Timur, dan memperkuat hasil pengendalian pandemi Covid-19 di Wuhan, China dengan nilai parameter yang berbeda.  Penelitian lanjutan dapat dilakukan terhadap model SEIPAHRF dengan membandingkan perilaku solusinya dengan hasil dengan model dinamik lain maupun pada wabah atau wilayah pandemi lain.

Kata kunci: Bilangan reproduksi dasar, model matematika,  Covid-19, stabilitas, sensitivitas.

Coronavirus Disease 2019 (Covid-19) is an infectious disease caused by the corona virus from the coronaviridae family.  The spread of the virus is fast in several countries, as well as in Indonesia. The spread of this virus is taking place rapidly in a number of countries, including Indonesia. This study aims to implement the dynamic model of SEIPAHRF for the transmission of Covid-19 in the province of East Java, Indonesia, for the period 6 August-5 October 2020 when the regulation of the Large-Scale Social Restrictions (PSBB) were implemented in East Java province. This study discusses also basic reproduction numbers, equilibrium points, stability, and sensitivity of the dynamic model based on variations in parameter values. The numerical simulation of the SEIPAHRF model is given by using all parameter values ​​and initial values ​​which taken from Ndaïrou et al. (2020), then the result is compared to data from the Satgas Covid-19 Jawa Timur. Based on the results, this study obtaines the basic reproduction number , which means that Covid-19 has spread and had become an epidemic. The stability analysis of the SEIPAHRF’s model based on the equilibrium points concludes that the disease-free equilibrium point  is unstable, while the endemic equilibrium point is asymptotic stable. The numerical simulation results from the SEIPAHRF’s model are positively consistent with the real data from the Satgas Covid-19 Jawa Timur, and are supported to the handling of the pandemic Covid-19 in Wuhan with different parameter values. Furthermore, another researcher may implement the SEIPAHRF’s model and is to compare its solution behaviors with any result from another dynamical model, as well as for other epidemics or  other pandemic areas.

Keywords: Basic reproduction number, mathematical model, Covid-19, stability, sensitivity.