具有一般复发现象的疾病模型的全局稳定性

Global Stability for Disease Model with General Relapse Phenomenon

本文研究了具有一般复发现象和非线性发生率的疾病模型的动力学性质,其中模型是具有无穷分布时滞的微积分方程.该模型描述了包含疱疹等传染病的—般复发现象.利用一致持久性理论和李雅普诺夫函数,我们证明了基本再生数R_0决定的系统的全局动力学性质:当R_0≤1时,疾病灭绝;当R_0>1时,疾病持久生存,并且正平衡点是全局吸引的.

The dynamics of a disease model with general relapse phenomenon and nonlinear incidence rate are investigated, where the model takes the forms of integro-differential equations with infinite-distributed delay. The model can describe a general relapse phenomenon in infectious diseases including herpes. By applying the uniform persistence theory and using the method of Lyapunov functionals, it is shown that that the global dynamics are completely determined by the basic reproduction number R0： the disease dies out if R0 ≤1 and that the disease becomes endemic permanently and globally attractively if R0 〉 1.