Many important factors affect the spread of childhood infectious disease. To understand better the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients using discrete-time models. This research addresses several shortcomings of the discrete-time approaches, including removing the need for the reporting interval to match the serial interval of the disease using infectious disease data from three major cities: New York City, London, and Bangkok. Using a simultaneous approach for optimization of differential equation systems with a Radau collocation discretization scheme and total variation regularization for the transmission parameter profile, this research demonstrates that seasonal transmission parameters can be effectively estimated using continuous-time models. This research further correlates school holiday schedules with the transmission parameter for New York City and London where previous work has already been done, and demonstrates similar results for a relatively unstudied city in childhood infectious disease research, Bangkok, Thailand.