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A mumps model with seasonality in China
Qianqian Qu1, Cong Fang2, Le Zhang1
1School of Information and Mathematics, Yangtze University, Jingzhou 434023, China.
Mumps remains prevalent despite vaccination. Mathematical modeling reveals that increasing vaccine coverage and ensuring access to two doses of the Measles, mumps, and rubella (MMR) vaccine are crucial for controlling mumps outbreaks.
Area of Science:
- Epidemiology
- Mathematical Modeling
- Infectious Diseases
Background:
- Mumps is a common childhood viral illness with no specific treatment.
- Despite vaccine availability, over 100,000 mumps cases are reported annually in China.
- The underlying factors and mechanisms driving mumps persistence are not fully understood.
Purpose of the Study:
- To investigate the factors influencing mumps persistence and prevalence.
- To analyze the dynamics of mumps transmission using a mathematical model.
- To evaluate the impact of vaccination strategies on mumps control.
Main Methods:
- Development of a mathematical model for mumps incorporating seasonal fluctuations.
- Calculation and analysis of the basic reproduction number (R0).
- Simulation of monthly mumps case data and sensitivity analysis of R0.
Main Results:
- The model demonstrates that R0 is a critical threshold parameter for mumps extinction or persistence.
- A disease-free state is globally stable when R0 < 1.
- A persistent disease state (positive periodic solution) occurs when R0 > 1.
Conclusions:
- Vaccination rates and the effectiveness of vaccination significantly impact mumps spread.
- Increasing overall vaccine coverage is recommended.
- Providing two doses of the Measles, mumps, and rubella (MMR) vaccine freely in China is suggested to enhance control.
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