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This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic currently ravaging the planet. There are two objectives to arrive at an appropriate model that captures the collected data faithfully and to use that as a basis to explore the nonlinear behavior. We use a nonlinear susceptible, exposed, infectious and removed transmission model with added behavioral and government policy dynamics. We develop a genetic algorithm technique to identify key model parameters employing COVID-19 data from South Korea. Stabili