带有免疫治疗的离散流脑模型的动力学性态

Threshold Dynamics of Discrete Meningococcal Meningitis Model with Vaccination and Therapy

根据流脑在我国的流行特点和疫苗因素的影响,文中采用隐式欧拉法建立了一类带有免疫治疗的离散SCIRS模型,并研究了模型的全局动力学特性.通过构造合适的Lyapunov函数得到了模型平衡点全局稳定的充分条件,利用动力系统的持久性理论进一步得出了疾病的持久性.最后,利用数值模拟对理论结果进行了验证与推广.

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.