Measles is a highly infectious, severe viral disease. The disease is targeted for global eradication; however, this result has proven challenging. In China, where countrywide vaccination coverage for the last decade has been above 95% (the threshold for measles elimination), measles continues to cause large epidemics. To diagnose factors contributing to the persistency of measles, here we develop a model-inference system to infer measles transmission dynamics in China. The model-inference system uses demographic and vaccination data for each year as model inputs to directly account for changing population dynamics (including births, deaths, migrations, and vaccination). In addition, it simultaneously estimates unobserved model variables and parameters based on incidence data. When fitted to yearly incidence data for the entire population, it is able to accurately estimate independent, out-of-sample age-specific incidence. Using this validated model-inference system, we are thus able to estimate epidemiological and demographical characteristics key to measles transmission during 1951-2004 for three key locations in China, including its capital Beijing. These characteristics include age-specific population susceptibility and incidence rates, the basic reproductive number (R0), reporting rate, population mixing intensity, and amplitude of seasonality. Key differences among the three sites reveal population and epidemiological characteristics crucial for understanding the current persistence of measles epidemics in China. We also discuss the implications our findings have for future elimination strategies.