Analisis Kestabilan Model Matematika SEIR pada Penyakit Covid-19

Abstract

Penelitian ini menggunakan model matematika SEIR (Susceptible-Exposed Infected-Recovered) untuk menganalisis dinamika penyebaran Covid-19. Penelitian ini mencakup penentuan titik tetap bebas penyakit dan endemik, analisis kestabilan menggunakan kriteria Routh-Hurwitz, serta perhitungan bilangan reproduksi dasar (R0) melalui metode matriks next generation. Simulasi numerik digunakan untuk melihat bagaimana variabel seperti laju transmisi, vaksinasi, dan laju pemulihan memengaruhi dinamika penyebaran penyakit. Hasil analisis menunjukkan bahwa R0 < 1 menunjukkan bahwa penyakit akan hilang, sedangkan R0 >1 menunjukkan bahwa kondisi menjadi endemik. Simulasi menunjukkan bahwa pengurangan kontak, peningkatan laju vaksinasi, dan peningkatan pengobatan secara signifikan dapat mengurangi nilai R0, mengurangi jumlah kasus infeksi, dan mempercepat waktu pengendalian wabah

This study uses the SEIR (Susceptible-Exposed-Infected-Recovered) mathematical model to analyze the dynamics of the spread of Covid-19. The study includes the determination of disease-free and endemic fixed points, stability analysis using the Routh-Hurwitz criterion, and calculation of the basic reproduction number (R0) through the next generation matrix method. Numerical simulations are used to see how variables such as transmission rate, vaccination, and recovery rate affect the dynamics of disease spread. The analysis shows that R0 <1 indicates that the disease will disappear, while R0 > 1 indicates that the condition becomes endemic. Simulations show that reducing contacts, increasing the vaccination rate, and increasing treatment can significantly reduce the R0 value, reduce the number of infectious cases, and speed up the outbreak control time.