Analysis of Stability Covid19 Spread Mathematical Model Type SV1V2EIR Regarding Both Vaccinated and Not Vaccinated Human Population

Abstract

The Covid19 case dated 11 November 2021 recorded that the human population died from Covid19 (143,595 people) with confirmed cases (4,249,323 cases) and active cases (9,537 cases). Based on these data, it can be concluded that COVID-19 is an acute and deadly disease. In addition to deaths, due to Covid-19, namely the increase in divorce cases, decreased income in the economy and tourism. In this study, the author made a mathematical modeling of Covid19 type SV1V2EIR as an effort to prevent the spread of Covid19. In the modeling there are human populations susceptible to Covid19 (S), human populations have been vaccinated (V1), human populations have not been vaccinated (V2), human populations are exposed (E), human populations are infected with Covid19 (I), and human populations recovered from Covid19 (R). The research objectives are 1) to build a mathematical model of Covid19, 2) to determine the fixed point and basic reproduction numbers, and 3) to analyze the stability of the fixed point. This type of research includes applied science research. The research procedure is 1) observing real phenomena, 2) searching literature, 3) determining variables, parameters, and assumptions in mathematical modeling, 4) building a mathematical model of Covid19, 5) analyzing the Covid19 mathematical model in the form of fixed points, basic reproduction numbers, and fixed point stability. The results of the analysis 1) the mathematical model type SV1V2EIR has a fixed point without disease and an endemic fixed point, 2) a fixed point without disease is stable for the condition, and the endemic fixed point is stable for the condition.