STABILITY ANALYSIS OF THE MODEL SVEI_a I_sR ON COVID-19 SPREAD - Tiara Adinda Permatasari; Redemtus Heru Tjahjana; Widowati Widowati (Journal of Fundamental Mathematics and Applications (JFMA), 2025)
The COVID-19 pandemic has presented a major challenge in understanding the dynamics of disease transmission in a region. DKI Jakarta is the province with the highest number of COVID-19 cases in Indonesia. In this article, the SVEIₐIₛR model (Susceptible, Vaccinated, Exposed, Asymptomatic, Symptomatic, and Recovered) is examined to model the spread of COVID-19 in DKI Jakarta Province. The basic reproduction number is obtained through the Next Generation Matrix (NGM) approach, whereas the local stability analysis is carried out using the Routh–Hurwitz criterion. Furthermore, there are two equilibrium points obtained, which are the disease-free equilibrium and the endemic equilibrium. The stability of the equilibrium point is analyzed based on the value of the basic reproduction number. The endemic equilibrium point is considered asymptotically stable if the basic reproduction number is less than one. To demonstrate the behavior of the COVID-19 transmission model, numerical simulations are conducted using data obtained from DKI Jakarta Province. The results of the analysis indicate that, the COVID-19 transmission model is asymptotically stable at the diseas-free equilibrium point with R0=0.001897843854. This indicates that, over time, the COVID-19 disease will eventually disappear from the population.