概率二分模式下随机传染病模型的平稳性与控制研究
Stability and control of stochastic infectious disease model under probability dichotomy model
李举 1张靖文 1王浩华1
作者信息
- 1. 海南大学理学院,海南海口 570228;海南大学海南省工程建模与统计计算重点实验室,海南海口 570228
- 折叠
摘要
提出了具有概率分流模式下的随机传染病模型,考察隔离个体诊断率(也包括疫苗功效)和环境扰动(噪声)的生物功效.首先,证明了随机模型正解的存在性和唯一性,然后确立了疾病灭绝和持续存在的充分条件.当噪声强度固定和疫苗效力增加时,(R)s0会变大并且灭绝时间会呈现负指数衰减.数值结果表明噪声的引入可以加快疾病的灭绝,从而达到对疾病的最优控制,其不仅能有效地降低感染人数,而且能加快疾病的灭绝.
Abstract
In the report,a stochastic infectious model with probability shunting was constructed,and the effects of the diagnostic rate of isolated individuals(vaccine efficacy)and the fluctuation environment(noise)on dis-ease transmission and control were investigated.The existence and uniqueness of the solution were proved,and the sufficient condition for the extinction and persistence of the disease were validated.If the noise is fixed and the vaccine efficacy increases,becomes bigger and the extinction time demonstrates a negative exponential de-cay.The numeric results indicated that the noise can accelerate the extinction of the disease and achieve the sto-chastic optimal control,which not only reduce effectively the number of infected people,but also accelerate the disease extinction.
关键词
传染病模型/环境扰动/稳态分布/疾病灭绝/最优控制Key words
infectious disease model/fluctuation environment/stationary distribution/disease extinction/opti-mal control引用本文复制引用
基金项目
国家自然科学基金(12261028)
国家自然科学基金(11961018)
海南省自然科学基金(120RC451)
海南省自然科学基金(2019RC168)
海南省重点研发项目(ZDYF2021SHFZ231)
海南省研究生创新创业项目(Qhys2021-208)
出版年
2024
国家科技期刊平台
NSTL
万方数据