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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 discrete-time 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. [ABSTRACT FROM AUTHOR]

Early warning tools are crucial for the timely application of intervention strategies and the mitigation of the adverse health, social and economic effects associated with outbreaks of epidemic potential such as COVID-19. This paper introduces, the Epidemic Volatility Index (EVI), a new, conceptually simple, early warning tool for oncoming epidemic waves. EVI is based on the volatility of newly reported cases per unit of time, ideally per day, and issues an early warning when the volatility change rate exceeds a threshold. Data on the daily confirmed cases of COVID-19 are used to demonstrate the use of EVI. Results from the COVID-19 epidemic in Italy and New York State are presented here, based on the number of confirmed cases of COVID-19, from January 22, 2020, until April 13, 2021. Live daily updated predictions for all world countries and each of the United States of America are publicly available online. For Italy, the overall sensitivity for EVI was 0.82 (95% Confidence Intervals: 0.75; 0.89) and the specificity was 0.91 (0.88; 0.94). For New York, the corresponding values were 0.55 (0.47; 0.64) and 0.88 (0.84; 0.91). Consecutive issuance of early warnings is a strong indicator of main epidemic waves in any country or state. EVI's application to data from the current COVID-19 pandemic revealed a consistent and stable performance in terms of detecting new waves. The application of EVI to other epidemics and syndromic surveillance tasks in combination with existing early warning systems will enhance our ability to act swiftly and thereby enhance containment of outbreaks. [ABSTRACT FROM AUTHOR]