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. Stability, bifurcations and dynamic behavior are analyzed. Parametric analysis reveals conditions for sustained epidemic equilibria to occur. This work points to the value of nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of social and government behavior on disease dynamics.

Background: In general, diagnostics can be defined as the procedure of mapping the information obtained in the measurement space to the presence and magnitude of faults in the fault space. These measurements, and especially their nonlinear features, have the potential to be exploited to detect changes in dynamics due to the faults.Purpose: We have been developing some interesting techniques for fault diagnostics with gratifying results.Methods: These techniques are fundamentally based on extracting appropriate features of nonlinear dynamical behavior of dynamic systems. In particular, this paper provides an overview of a technique we have developed called Phase Space Topology (PST), which has so far displayed remarkable effectiveness in unearthing faults in machinery. Applications to bearing, gear and crack diagnostics are briefly discussed.