Abstract：The management of emerging infectious diseases has always been given a high priority in public health. Identification of the epidemiological characteristics and transmission patterns of emerging infectious diseases is of great significance to contain the disease transmission and reduce the damages to public health and socioeconomic developments. Currently, infectious disease dynamics models are mainly established based on infectious disease surveillance data to predict the epidemiological patterns and trends of emerging infectious diseases; however, many model-based predictions fail to achieve the expected results due to the presence of multiple uncertain factors during the integrated management of infectious diseases. This review describes the basic principles and variables of common infectious disease dynamics models, including the susceptible-infected-recovered ( SIR ) model, susceptible-infected-removed-susceptible ( SIRS ) model, susceptible-exposed-infected-removed ( SEIR ) model and improved SEIR model, compares the advantages and disadvantages of these models, and summarizes the advances of the infectious disease dynamics models in the prediction of trends in incidence of emerging infectious diseases, so as to provide insights into the effective application of infectious disease dynamics models in the management of infectious diseases.
[1] 向蕾. 两类离散传染病模型的动力学分析[D]. 武汉:华中师范大学,2020. XIANG L.Dynamical analysis of two classes of discrete epidemic models[D]. Wuhan:Central China Normal University,2020. [2] UNKEL S,FARRINGTON C P,GARTHWAITE P H,et al.Statistical methods for the prospective detection of infectious disease outbreaks:a review[J].J R Stat Soc A Stat,2012,175(1):49-82. [3] DIETZ K,HEESTERBEEK J A P.Daniel Bernoulli's epidemiological model revisited[J].Math Biosci,2002,180:1-21. [4] 李静,王靖飞. 传染病动力学模型简介[C]//中国畜牧兽医学会.中国畜牧兽医学会信息技术分会成立大会暨首届学术研讨会论文集.北京:中国畜牧兽医学会信息技术分会,2005:121-124. LI J,WANG J F.Introduction to the dynamic model of infectious diseases[C]//Chinese Association of Animal Science and Veterinary Medicine. The first academic seminar of the Information Technology Branch of Chinese Association of Animal Science and Veterinary Medicine. Beijing:Information Technology Branch of Chinese Association of Animal Science and Veterinary Medicine,2005:121-124. [5] KERMACK W O,MCKENDRICK A G.A contribution to the mathematical theory of epidemics[J]. Proc Royal Soc A Math Phys Eng Sci,1927,115(772):700-721. [6] KERMACK W O,MCKENDRICK A G.Contributions to the mathematical theory of epidemics II. The problem of endemicity[J]. Proc Royal Soc A Math Phys Eng Sci,1932,138(834):55-83. [7] 马知恩,周义仓,王稳地,等.传染病动力学的数学建模与研究[M].北京:科学出版社,2004. MA Z E,ZHOU Y C,WANG W D,et al.Mathematical modeling and research of infectious disease dynamics[M]. Beijing:Science Press,2004. [8] 曹宇. 传染病动力学模型研究[D]. 沈阳:东北大学,2014. CAO Y.Research on infectious diseases modeling[D]. Shenyang:Northeast University,2014. [9] 徐涵,张庆.复杂网络上传播动力学模型研究综述[J]. 情报科学,2020,38(10):159-167. XU H,ZHANG Q.A?review?of?epidemic?dynamics?on?complex networks[J]. Inf Sci,2020,38(10):159-167. [10] 严薇荣. 传染病预警指标体系及三种预测模型的研究[D].武汉:华中科技大学,2008. YAN W R.Study on the early warning indicators system and three types of forecasting models for infectious diseases[D]. Wuhan:Huazhong University of Science and Technology,2008. [11] 杜志成,郝元涛,魏永越,等.基于马尔科夫链蒙特卡罗模拟方法的COVID-19年龄别病死率估计[J]. 中华流行病学杂志,2020,41(11):1777-1781. DU Z C,HAO Y T,WEI Y Y,et al.Using Markov Chain Monte Carlo methods to estimate the age-specific case fatality rate of COVID-19[J]. Chin J Epidemiol,2020,41(11):1777-1781. [12] HE S,BANERJEE S.Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection[J]. Physica A,2018,501:408-417. [13] 尹楠. 基于SIR模型的有限区域内新冠肺炎疫情传播仿真模拟[J].统计与决策,2020,36(5):15-20. YIN N.A?Simulation?of?COVID-19?epidemic?propagation?in limited?area?based?on?SIR?model[J]. Stat Decis,2020,36(5):15-20. [14] 梅文娟,刘震,朱静怡,等.新冠肺炎疫情极限IR实时预测模型[J].电子科技大学学报,2020,49(3):362-368. MEI W J,LIU Z,ZHU J Y,et al.Extreme IR model for COVID -19 real-time forecasting[J]. J Univ Elec Sci Technol China,2020,49(3):362-368. [15] 喻孜,张贵清,刘庆珍,等.基于时变参数SIR模型的COVID-19疫情评估和预测[J].电子科技大学学报,2020,49(3):357-361. YU Z,ZHANG G Q,LIU Q Z,et al.The outbreak assessment and prediction of COVID-19 based on time-varying SIR Model[J]. J Univ Elec Sci Technol China,2020,49(3):357-361. [16] 盛华雄,吴琳,肖长亮.新冠肺炎疫情传播建模分析与预测[J].系统仿真学报,2020,32(5):759-766. SHENG H X,WU L,XIAO C L.Modeling analysis and prediction on NCP epidemic transmission[J]. J Sys Simul,2020,32(5):759-766. [17] 凡友荣,杨涛,孔华锋.基于阶段式SIR-F模型的新冠肺炎疫情评估及预测[J].计算机应用与软件,2020,37(11):51-62. FAN Y R,YANG T,KONG H F.Assessment and prediction of COVID-19 based on staged SIR-F model[J]. Comput Appl Softw,2020,37(11):51-62. [18] 沈思鹏,魏永越,赵杨,等.全球新型冠状病毒肺炎疫情对我国的输入风险评估[J].中华流行病学杂志,2020,41(10):1582-1587. SHEN S P,WEI Y Y,ZHAO Y,et al.Risk assesment of global COVID-19 imported cases into China[J]. Chin J Epidemiol,2020,41(10):1582-1587. [19] 王旭艳,喻勇,胡樱,等.基于指数平滑模型的湖北省新冠肺炎疫情预测分析[J].公共卫生与预防医学,2020,31(1):1-4. WANG X Y,YU Y,HU Y,et al.COVID-19 analysis and forecast based on Exponential Smoothing Model in Hubei Province[J]. J Public Health Prev Med,2020,31(1):1-4. [20] 范如国,王奕博,罗明,等.基于SEIR的新冠肺炎传播模型及拐点预测分析[J].电子科技大学学报,2020,49(3):369-374. FAN R G,WANG Y B,LUO M,et al.SEIR-based COVID-19 transmission model and inflection point prediction analysis[J]. J Univ Elec Sci Technol China,2020,49(3):369-374. [21] 吉兆华,陆振华,刘昆,等. 全国新型冠状病毒肺炎发病情况室模型分析及疫情进展短期预测[J]. 热带医学杂志,2020,20(3):279-282. JI Z H,LU Z H,LIU K,et al.SIR model analysis and short-term prediction of epidemic progress of corona virus disease 2019 in China[J]. J Trop Med,2020,20(3):279-282. [22] KUZNETSOV Y A,PICCARDI C.Bifurcation analysis of periodic SEIR and SIR epidemic models[J]. J Math Biol,2020,32(2):109-121. [23] 林俊锋. 基于引入隐形传播者的SEIR模型的COVID-19疫情分析和预测[J].电子科技大学学报,2020,49(3):375-382. LIN J F.Assessment and prediction of COVID-19 based on SEIR model with undiscovered people[J]. J Univ Elec Sci Technol China,2020,49(3):375-382. [24] 徐丽君,刘文辉,刘远,等.SEIQCR传染病模型的构建及在广州市新型冠状病毒肺炎公共卫生防控效果评估中的应用[J].山东大学学报(医学版),2020,58(10):20-24. XU L J,LIU W H,LIU Y,et al.Construction of SEIQCR epidemic model and its application in the evaluation of public health interventions on COVID-19 in Guangzhou[J]. J Shandong Univ(Health Sci),2020,58(10):20-24. [25] HE S,PENG Y,SUN K.SEIR modeling of the COVID-19 and its dynamics[J]. Nonlinear Dyn,2020,101:1667-1680. [26] LUO D,HUANG S,LIU C,et al.Evaluation of COVID-19 control strategies in different countries and periods based on an adaptive PSO-SEIR model[J].Chin Sci Bull,2020,66(4/5):453-464. [27] DIN R U,ALGEHYNE E A.Mathematical analysis of COVID-19 by using SIR model with convex incidence rate[J/OL]. Results Phys(2021-02-19)[2021-10-04].https://doi.org/10.1016/j.rinp.2021.103970. [28] KOZIO K,STANISAWSKI R,BIALIC G.Fractional-order SIR epidemic model for transmission prediction of COVID-19 disease[J/OL].Appl Sci,2020[2021-10-04].https://www.researchgate.net/publication/347149402.DOI:10.3390/app10238316. [29] LIU L Y,JIANG D Q,HAYAT T.Dynamics of an SIR epidemic model with varying population sizes and regime switching 30 in a two patch setting[J/OL].Physica A,2021,574(1)(2021-04-01)[2021-10-04]. https://www.researchgate.net/publication/350951681.DOI:10.1016/j.physa.2021.125992. [30] VENNELA G S,KUMAR P.Covid-19 pandemic spread as growth factor using forecasting and SIR models[J].J Phys,2021,1767(1):11-12. [31] PRODANOV D.Analytical parameter estimation of the SIR epidemic model. Applications to the COVID-19 pandemic [J/OL].Entropy,2020[2021-10-04].https://www.researchgate.net/publication/348139133.DOI:10.3390/e23010059. [32] KUDRYASHOV N A,CHMYKHOV M A,VIGDOROWITSCH M.Analytical features of the SIR model and their applications to COVID-19[J].Appl Math Model,2021,90(2):466-473. [33] ALENEZI M N,AL-ANZI,ALABDULRAZZAQ H.Building a sensible SIR estimation model for COVID-19 outspread in Kuwait[J].AEJ,2021,60(3):3161-3175. [34] 朱仁杰,唐仕浩,刘彤彤,等.基于改进SIR模型的新型冠状病毒肺炎疫情预测及防控对疫情发展的影响[J].陕西师范大学学报,2020,48(3):33-38. ZHU R J,TANG S H,LIU T T,et al.COVID-19 epidemic prediction based on improved SIR model and the impact of prevention and control on epidemic development[J].J Shaanxi Norm Univ,2020,48(3):33-38. [35] DE LA SEN M,ALONSO-QUESADA S,IBEAS A,et al. On a discrete SEIR epidemic model with two-doses delayed feedback vaccination control on the susceptible[J/OL].Vaccines,2021,9(4)(2021-04-18)[2021-10-04].https://doi.org/10.3390/vaccines9040398. [36] KUNDU S,JANA D,MAITRA S.Study of a multidelayed SEIR epidemic model with immunity period and treatment function in deterministic and stochastic environment[J/OL].Differ Equ Dyn Syst(2021-05-30)[2021-10-04]. https://www.researchgate.net/publication/353258873. DOI:10.1007/s12591-021-00568-6. [37] LI Y,ZHANG X,CAO H.Large time behavior in a diffusive SEIR epidemic model with general incidence[J/OL].Appl Math Lett,2021,120[2021-10-04]. https://doi.org/10.1016/j.aml.2021.107322. [38] YOUSSEF H,ALGHAMDI N,EZZAT M A,et al.Study on the SEIQR model and applying the epidemiological rates of COVID-19 epidemic spread in Saudi Arabia[J].Infect Dis Model,2021,6:678-692. [39] 魏永越,卢珍珍,杜志成,等.基于改进的SEIR+CAQ传染病动力学模型进行新型冠状病毒肺炎疫情趋势分析[J].中华流行病学杂志,2020,41(4):470-475. WEI Y Y,LU Z Z,DU Z C,et al.Fitting and forecasting the trend of COVID-19 by SEIR+CAQ dynamic model[J]. Chin J Epidemiol,2020,41(4):470-475. [40] 丁中兴,宋文煜,方欣玉,等.基于SEIAQR动力学模型预测湖北省武汉市新型冠状病毒肺炎疫情趋势[J].中国卫生统计,2020,37(3):327-334. DING Z X,SONG W Y,FANG X Y,et al.Using SEIAQR dynamic model to predict the epidemic trend of novel coronavirus pneumonia in Wuhan,Hubei Province[J]. Chin J Health Stat,2020,37(3):327-334.
