Abstract: According to the epidemic characteristics of Meningococcal Meningitis in China and the influence of vaccination factors, we formulate a discrete-time SCIRS model with vaccination and therapy by using the backward Euler method and investigate its dynamic characteristics. We obtain sufficient conditions for the global behavior of the equilibrium points by constructing suitable Lyapunov functions. We further conclude that the disease is permanent by using the theory of persistence in dynamical systems.~Numerical simulations are carried out to illustrate the main theoretical results.

Key words: discrete Meningococcal Meningitis model, backward Euler, persistent, globally asymptotically stability, Lyapunov function, numerical simulation