Before revision:  We compare the proposed method to an EnKF-based parameter drift algorithm, where periodicity is not guaranteed , using synthetic data generated from the  FitzHugh-Nagumo system which models the spiking dynamics of a neuron. We further demonstrate the proposed method by estimating the seasonal transmission parameterin an epidemic model for the spread of measles. Results are obtained using time-series data of measles case reports from three locations during the pre-vaccine era , in particular the weekly reported cases in England and Wales (1948-1967) and monthly reported cases in New York City (1945-1964) and Baltimore (1928-1960).
After revision:  We compare the proposed method to an EnKF-based parameter drift algorithm, where periodicity is not guaranteed , using synthetic data generated from the FitzHugh-Nagumo system , modeling the excitability of a nerve cell, to estimate the external voltage parameter, and a case study using reported measles incidence data from three locations during the pre-vaccine era , in particular the weekly reported cases in England and Wales (1948-1967) and monthly reported cases in New York City (1945-1964) and Baltimore (1928-1960).