Mathematical Model for the Propagation of COVID-19 in the Brazilian Population with the Insertion of the Vaccine Against Disease

Abstract

The application of vaccination campaigns against epidemiological diseases is of immense importance for its control and eradication, mainly due to the high rate of infection and mortality from these diseases. This work aims to present two mathematical models of the transmission process of COVID-19, with and without the vaccine against the disease, for systematic analysis of the best scenario. In both models, only the temporal evolution of the process is considered, thus having a mathematical model described by a system of Ordinary Differential Equations (ODEs). To obtain the numerical results, the Finite Regressive Differences Method is used to determine the period of collective immunity and the impact of the vaccine on the Brazilian population. During the work, we emphasized the importance of investments in the manufacture of medicines and vaccines, and vaccination campaigns against the disease.