考虑疫苗有效性的传染病渗流模型  

Infectious Disease Percolation Model Considering Vaccine Effectiveness

作　　者：高杰[1] 李毅红[1] 罗晓峰[1] GAO Jie;LI Yihong;LUO Xiaofeng(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报(自然科学版)》2025年第2期254-260,共7页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金项目(12101573)。

摘　　要：疫苗接种是当前公认的防控传染病传播时成本效益最高的公共卫生干预措施之一,对预防和控制传染病的暴发至关重要。在针对复杂网络中带有疫苗接种的传染病传播的点-边渗流模型基础上,根据存在的实际因素,考虑了疫苗有效性对人群中传染病传播的影响。分析并计算出传染病传播的流行阈值以及平均暴发规模的精确理论结果,并通过数值模拟研究了度分布分别为泊松、指数、幂律分布的情况下,疫苗有效性对传染病在人群中传播的流行阈值以及传播最终规模的影响。研究结果表明,提高疫苗有效性、合理均匀化接触网络能有效防止传染病的暴发。Vaccination is currently recognized as one of the most cost-effective public health interventions for preventing and controlling the spread of infectious disease,and it is essential for preventing and controlling outbreaks.Utilizing the site-bond percolation model,which simulated infectious disease spread with vaccination in complex networks,we innovatively considered the impact of vaccine effectiveness on the spread of the infectious disease in the population,taking into account practical factors.We analyzed and calculated precise theoretical results for the epidemic threshold of infectious disease transmission and average outbreak size.Furthermore,through numerical simulations,we explored the influence of vaccine effectiveness on both the epidemic threshold and the final scale of disease spread,under various degree distributions including Poisson,exponential,and power-law.The results show that enhancing vaccine effectiveness and reasonably homog-enizing contact network can effectively prevent outbreaks of infectious diseases.

关 键 词：生成函数 流行阈值 最终暴发规模 点-边渗流模型 疫苗有效性 

分 类 号：O175[理学—数学]