A mumps model with seasonality in China.

BACKGROUND: Mumps, an infectious viral disease, classically manifested by inflammation of salivary glands and is best known as a common childhood viral disease with no specific treatment. Although it can be protected by vaccine, there are more than 100,000 reported mumps cases according to the Chinese Center for Disease Control and Prevention. However, the factors and mechanisms behind the persistence and prevalence of mumps have not been well understood. METHODS: A mumps model with seasonal fluctuation is formulated and investigated. We evaluate the basic reproduction number ℛ(0) and analyze the dynamical behavior of the model. We also use the model to simulate the monthly data of mumps cases and carry out some sensitivity analysis of ℛ(0) in terms of various model parameters. RESULTS: It is shown that there exists only disease-free solution which is globally asymptotically stable if ℛ(0) < 1, and there exists a positive periodic solution if ℛ(0) > 1. ℛ(0) is a threshold parameter, and its magnitude determines the extinction or persistence of the disease. CONCLUSION: Our analysis shows that vaccination rate and invalid vaccination rate play important roles in the spread of mumps. Hence, Our study suggests to increase the vaccine coverage and make two doses of MMR (Measles, mumps and rubella vaccine) vaccine freely available in China.