基于偶对逼近对SIS传染病模型中治疗阈值的研究  

Research on Treatment Threshold in Sis Infectious Disease Model Based on Even Pair Approximation

作　　者：刘森 高之茵 李维德[1] LIU SEN;GAO ZHIYIN;LI WEIDE(School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,China)

机构地区：[1]兰州大学数学与统计学院,兰州730000

出　　处：《应用数学学报》2023年第4期635-648,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(42130113)资助项目。

摘　　要：有效控制传染病的理论研究以往有很多,但是由于地区发展不均衡导致的医疗资源分布不均匀情况却很少被考虑到,因此如何有效地分配医疗资源来控制传染病的爆发是一个非常有意义的研究课题.采用偶对近似的方法,对SIS传染病模型下如何有效控制传染所需的最低医疗资源(治疗阈值)进行探究.结果表明,对致死率越低,传染性越强的疾病,疾病的治疗阈值就越高;控制个体的相互接触率并且对疾病进行早期监控,做到“早发现早治疗”可以有效地降低治疗阈值;另外,医疗资源的分散也可以小幅度地降低治疗阈值.本文的研究结果对传染病的控制有一定的指导意义,尤其是在医疗资源有限的情况下,其提供的策略对防止医疗资源挤兑有一定的参考价值.There have been many theoretical studies on effective control of infectious diseases in the past,but the uneven distribution of medical resources caused by unbal-anced regional development is rarely considered.Therefore,how to effectively allocate medical resources to control the outbreak of infectious diseases is a very meaningful research topic.Using the pair approximation method,we explore how to effectively control the minimum medical resources(treatment threshold)required for infection un-der SIS infectious disease model.The results showed that the lower the fatality rate and the stronger the infectious disease,the higher the treatment threshold of the disease;controlling the contact rate of individuals and early monitoring of diseases can effec-tively reduce the treatment threshold;in addition,the dispersion of medical resources can also reduce the treatment threshold slightly.The research results of this study have a certain guiding significance for the control of infectious diseases,especially in the case of limited medical resources,and the strategies provided by this study have a certain reference value for preventing the run-on medical resources.

关 键 词：SIS模型 偶对逼近(PA) 治疗阈值 有限医疗资源 空间分布 

分 类 号：O175[理学—数学]