A dynamical map to describe COVID-19 epidemics

Abstract

Nonlinear dynamics perspective is an interesting approach to describe COVID-19 epidemics, providing information to support strategic decisions. This paper proposes a dynamical map to describe COVID-19 epidemics based on the classical susceptible-exposed-infected-recovered (SEIR) differential model, incorporating vaccinated population. On this basis, the novel map represents COVID-19 discretetime dynamics by adopting three populations: infected, cumulative infected and vaccinated. The map promotes a dynamical description based on algebraic equations with a reduced number of variables and, due to its simplicity, it is easier to perform parameter adjustments. In addition, the map description allows analytical calculations of useful information to evaluate the epidemic scenario, being important to support strategic decisions. In this regard, it should be pointed out the estimation of the number deaths, infection rate and the herd immunization point. Numerical simulations show the model capability to describe COVID-19 dynamics, capturing the main features of the epidemic evolution. Reported data from Germany, Italy and Brazil are of concern showing the map ability to describe different scenario patterns that include multi-wave pattern with bell shape and plateaus characteristics. The effect of vaccination is analyzed considering different campaign strategies, showing its importance to control the epidemics.

A Survey on the Applications of SIR Model in COVID-19

“…Linjunfeng [27] added 'invisible disseminator' on the traditional SEIR model and the results reflected the effective of nucleic acid detection and other technologies. Dos et al [28] proposed a dynamic map to describe the COVID-19 epidemic on the classical SEIR differential model with vaccinated population, which can describe three population dynamics: newly infected population, cumulative infected population and vaccinated population. The model has reduced the number of variables, made it easy to adjust parameters, and used analysis tools to define useful information.…”

Complex bio rhythms

“…Their results show that for a certain set of parameters can be related to chaos. dos Reis and Savi [ 14 ] present a dynamical map to explain Covid-19 epidemics based on the standard susceptible-exposed-infected-recovered (SEIR) differential equations and incorporating the vaccinated population. Finally, Borah et al [ 15 ] revisit the past plague epidemic (India) and compare with the Covid-19 pandemic based on fractional-order chaotic models and fuzzy logic control.…”

Response of vaccination on community transmission of COVID-19: a dynamical approach

“…[ 36 ] that in case roll out of vaccines are not upto speed, then permanent drug treatment should be focused on. Some other interesting models ([ 37 – 40 ]) on vaccination and prioritization have been reported in literature and it is concluded that vaccination is an efficient tool to stop the spread of infections.…”