Abstract: The dynamic characteristic of meningococcal meningitis SCIRS model with three age structures is studied. First, the basic reproduction number $\widetilde{R_0}$ is defined by using the regeneration matrix. It is proved that the disease-free equilibrium is globally asymptotically stable when $\widetilde{R_0}<1$. The disease-free equilibrium is unstable, there exists an endemic equilibrium and the system is uniformly persistent when $\widetilde{R_0}>1$. Second, using the data from the report of notifiable infectious diseases in China, the model is applied to describe the spread of meningococcal meningitis in China. For the uncertainty of many parameters in the model, we make sensitivity analysis about the parameters of the basic reproductive number. Finally, we consider the influence of seasonal factors to the incidence of meningococcal meningitis to modify the model, and predict the meningococcal meningitis in population development trend of China. The numerical simulation results show that the impact of seasonal factors on the rate of disease progression of meningococcal meningitis is greater than the effect on infection rate, this also provides advice to control the spread of meningococcal meningitis in our country.

Key words: discrete model, age structure, meningococcal meningitis, basic reproduction number, sensitivity analysis