基于脉冲接种扰动下随机传染病模型的稳定性分析

Stability Analysis Based on Random Infectious Disease Model under Pulse Vaccination Disturbance

摘要: 脉冲接种是一种有效控制疾病传播的方式，对传染病研究有重要意义。本文建立了一个具有标准发生率和垂直传播的噪声干扰脉冲接种随机SIR传染病模型，并研究了其在理论分析和数值模拟两个方面的动力学性质。首先构造辅助函数证明系统等价于一个不含脉冲的随机模型，并证明其正解的存在唯一性，其次利用伊藤公式给出疾病灭绝的充分条件，然后通过随机比较原理证明边界周期解的全局稳定性，最后用Matlab数值模拟来验证理论结果的正确性。

Abstract: Pulse vaccination is an effective way to control the spread of diseases and is of great significance for infectious disease research. In this paper, a random SIR infectious disease model of noise interfer-ence pulse inoculation with standard incidence and vertical propagation is established, and its ki-netic properties in both theoretical analysis and numerical simulation are studied. First, the auxil-iary function is constructed to prove that the system is equivalent to a random model without puls-es, and proves the existence uniqueness of its positive solution, and then uses Ito’s formula to give sufficient conditions for disease extinction, then proves the global stability of the boundary-periodic solution through the principle of random comparison, and finally uses Matlab numerical simulation to verify the correctness of the theoretical results.