A Nonlinear Dynamical Map for COVID-19

Resumo

The new coronavirus disease (COVID-19) has rapidly spread around the world, being considered a
pandemic with serious consequences. In this regard, epidemic models became an essential tool to describe and
predict epidemic evolution. A classical approach is the compartmental models where different populations are
employed to describe the system evolution. Typically, four populations are considered: susceptible, exposed,
infected and recovered, giving rise to the SEIR model. This paper proposes a dynamical map to describe Covid-19
epidemic based on the classical SEIR model taking into consideration the effect of vaccination. This novel map
describes the evolution of currently infected, cumulative infected and vaccinated population using three coupled
nonlinear algebraic equations. Due to the simplicity of the novel model description, useful information to evaluate
the epidemic stage can be obtained analytically, allowing the support of decision making. In this regard, the
herd immunization and the estimation of the number of deaths should be pointed out. Real epidemic data from

Germany, Italy and Brazil are employed in order to verify the model capability to describe the evolution of Covid-
19 dynamics.