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• An age-structured mathematical model on mumps outbreaks in Jiangsu, China is proposed and analyzed. • Three different stages of no vaccine, effectively controlled and resurgence stages are considered. • Patterns of mumps dynamics are simulated and compared based on data in Jiangsu from January 2005 to May 2019. • The time average basic reproduction number may be lower or over estimated the real one. • Changes in seasonal transmission patterns and demographic structures may be reasons of mumpsre-emerging. Measles, mumps and rubella (MMR) vaccine program was introduced in Jiangsu province of China in May 2008 and has been greatly contributed to decreasing of mumps cases. However, mumps has been resurging since May 2015. A number of studies have put forward that the resurgence of mumps is due to vaccine failure. In this paper, we investigated the other reasons for the resurging of mumps, such as the changes in seasonal transmission patterns and demographic structures, by using an age-structured mathematical model. We divided the history (January 2005 to May 2019) of mumps epidemics of Jiangsu province into three different stages: No vaccine stage (January 2005 to December 2008), effectively controlled stage (January 2009 to December 2014) and resurgence stage (January 2015 to May 2019). The features of mumps epidemics in three stages are compared under different demographic structures with same physical contact rate. The mumps transmission rate was increased in summer and dropped in November in stage III compared with that in stage I. The changes in demographic structures give a good explanation why the mumps outbreaked among children around 10 years old in stage I and around 5 years old in stage III. We have a conclusion that the vaccine failure, changes in seasonality and demographic structures were associated with the mumps outbreaks in recent years in Jiangsu province, China. We give the patterns of mumps dynamics considering age, vaccine, seasonality and demographic structures, which can help health program planners to implement more preventive interventions in mumps control during the period of higher risk of infection. [ABSTRACT FROM AUTHOR]