A locally sequential refinement of the growth dynamics identification

The approach is developed to specify a reconstruction of complicated functions using samples of limited size with invariant properties regarding the desired parameters. The idea is based on solutions to inverse problems, which should identify various representations of unknown parameters of a mathematical model and do so in a series. The sequential solutions to inverse problems ensure the identifiability of desired parameters that belong to an invariant family. The locally sequential refinement restricts local spikes additionally to the general regularization under a scheme of separate matching with observations. A simulation with inverse problems is applied to refine the known features of population dynamics. The reconstruction shows that the parameters of the Verhulst equation should be introduced as oscillatory functions. Based on the novel functional representation of the Verhulst equation parameters, the patterns of the COVID-19 spread and its progression in a given region are determined. The results emphasize the Verhulst equation’s character as a generalized and fruitful model for an object growth simulation.