一类带有脉冲疫苗接种的分数阶SIS传染病模型的稳定性分析  

Stability Analysis of a Class of Fractional-Order Sis Models with Pulse Vaccination

作　　者：刘娜[1] 方洁[1] 邓玮[1] LIU Na;FANG Jie;DENG Wei(School of Electric and Information Engineering,Zhengzhou University of Light Industry,Zhengzhou 450002,China)

机构地区：[1]郑州轻工业学院电气信息工程学院

出　　处：《数学的实践与认识》2019年第22期254-259,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61775198,61603348);河南省自然科学基金(162300410323);河南省科技攻关项目(192102210083,182102210160,182102210609);河南省高等学校青年骨干教师基金(2016GGJS090);郑州轻工业学院博士科研基金(2014BSJJ047)

摘　　要：分析了一类定时脉冲疫苗接种的分数阶SIS传染病模型的稳定性.基于分数阶比较定理,推导出脉冲分数阶SIS系统的平凡解是一致渐近稳定的.也就是说,疾病将会最终消亡.最后,通过仿真实例验证了理论结果的正确性,同时也仿真出分数阶参数和疫苗接种比例对疾病衰减速度的影响.这对预防和控制传染病的传播具有一定的理论指导作用.The stability of a class of fractional-order SIS models with pulse vaccination is analyzed in this paper.Based on the fractional-order comparison theorem,the trivial solutions of the impulsive fractional-order SIS systems axe uniformly asymptotically stable.That is,the disease will eventually die out.Finally,the theoretical results axe verified by simulation examples,and the effects of fractional-order parameter and vaccination ratio on the rate of disease attenuation are also simulated.This study has certain theoretical guiding function to prevent and control the spread of infectious diseases.

关 键 词：分数阶 SIS 稳定性 脉冲疫苗接种 

分 类 号：S85[农业科学—兽医学]