Análisis de la transferencia del coronavirus utilizando un modelo seir con efecto de vacunación

Abstract

The main issue lies in the lack of reference documents describing the dynamics of the spread of infectious diseases, including the effects of vaccination. The compartmental models SIR (susceptible-infected-recovered), SEIR (susceptible, exposed, infected, and recovered) do not include the effects of vaccination, which when compared with reality result in a considerable degree of error. The main objective of this work was to estimate the basic reproduction number using the Next Generation Matrix and to study the positivity, existence, and uniqueness of the solutions of the SEIRV model consisting of five compartments (susceptible-exposed-infected-recovered-vaccinated) through a mathematical language to describe the behavior of COVID-19. Using a documentary design methodology, with a qualitative and quantitative approach, the result obtained R0 = 1,68 × 10−11 < 1 reflects that the disease does not have the necessary epidemic potential to cause an epidemic over time. In addition, a bifurcation was also evidenced α = 3.5 × 10−4 in the vaccination rate. Therefore, it is concluded that the spread of COVID-19 can be controlled by increasing the vaccination rate in the population and that the Next Generation Matrix constitutes an efficient method for the calculation of the basic reproductive number in different epidemiological models