具有分布时滞的SIR离散模型的全局稳定性

Global stability of discrete SIR modle with distributed delays

研究一类具有分布时滞和非线性发生项的SIR模型。首先运用欧拉向后差分法提出模型的离散形式;然后证明离散的SIR流行病模型的全局动态是由阈值R0确定的:当且仅当R0≤1时,无疾病平衡点E0=(Λ/μS,0)是全局渐近吸引的。

A class of discrete SIR epidemic model derived from SIR model with distributed delay and general nonlinear incidence by using a variation of the backward Euler method is proposed. It shows that the global dynamics of each discrete SIR model is fully determined by a single threshold parameter and that on the condition that, the unique disease-free equilibrium E0 =（∧/μxs,0）is globally asymptotically stable.