Analisis Kestabilan Model Matematika Pada Penyebaran Covid Varian Omicron Dengan Kontrol Vaksinasi

Abstract

Covid-19 pandemic has been going on for approximately two years in Indonesia. During the pandemic, COVID-19 virus has undergone many mutations. mutation process produces new variants, where the latest variant that has been discovered is known as the Omicron variant. This variant has a very rapid transmission rate. To overcome the problem of Omicron distribution, it is necessary to analyze the distribution through mathematical modeling. This research uses literature study method related to omicron, especially modeling using vaccination control. Study will analyze SLIR model of the spread of the omicron variant of covid with vaccination control. Formed model will be analyzed by determining equilibrium, stability and continued with the addition of controls and then numerically simulated. Model has four subpopulations, namely Susceptible, Latent, Infected, and Recovery with the addition of migration parameters in the Susceptible and Latent subpopulations to form a system of nonlinear differential equations. The results of the analysis of this model have two equilibrium points, namely the disease-free and endemic equilibrium points. Stability of the disease-free equilibrium point will be stable when . And the endemic stability meets and so that it is concluded that it is asymptotically stable. And with the addition of control in the form of vaccination, if vaccination can be carried out massively for at least 100 days, then the number of infected individuals can be controlled properly and the reduction in migration parameters obtained can minimize the number of latent and infected populations in Omicron sufferers so that the spread of disease can be controlled and the impact of the spread disease can be minimized.