Estimation and Analysis of Time-dependent Transmission Rates Based on a Multi-population Reinfection Model

In this study, we establish a multi-population model that counting the number of reinfection and obtain the intrinsic relationship between the time-dependent transmission rates and reported case data. Using a Gaussian convolution-based approach on reported cases, we derive explicit expressions for first-infection and reinfection transmission rates and the compatibility conditions for parameters. Through computational analysis and numerical simulations, we compare the variations of these transmission rates over the same time period and explore the long-term transmissibility of COVID-19 in New York state. Our results indicate that the transmission pattern of COVID-19 is shifting from being primarily driven by initial infections to a "cyclical reinfection" pattern, a trend that became particularly evident after the spread of the Omicron variant. This study provides theoretical support for the estimation of time-dependent transmission rates and can contribute to long-term epidemic monitoring and control strategies.