JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (1): 56-68.doi: 10.6040/j.issn.1671-9352.0.2021.054

Previous Articles    

An SEAIR model with relapse effect and its application in COVID-19 transmission

ZHANG Yu-qian, ZHANG Tai-lei*   

  1. School of Science, Changan University, Xian 710064, Shaanxi, China
  • Published:2021-12-21

PDF (PC)

447

Abstract: In this paper, an SEAIR epidemic model with relapse and asymptomatic infection is established, and the basic reproduction number R0 is given. It is proved that the disease-free equilibrium is globally asymptotically stable when R0<1, the disease-free equilibrium is unstable and the disease is uniformly persistent when R0>1. As an application of the model, the cumulative number of COVID-19 cases reported in Hubei province is selected in this study. The model is fitted with reported data and simulated the development trend of the disease. Finally, the sensitivity of the parameters is analyzed, and the effect of different relapse rates on the COVID-19 is studied. The results show that the higher the relapse rates, the more serious the COVID-19 will be. The findings suggest that strict quarantine measures and wearing masks are recommended to reduce the infection rates of the disease and reduce the relapse rates of the disease.

Key words: relapse, an SEAIR infectious disease model, stability, partial rank correlation coefficients, COVID-19

CLC Number: 

  • O175
[1] 陈田木, 陈水连, 谢知, 等. 不同隐性感染和传播能力条件下的流感暴发防控措施效果模拟[J]. 中国热带医学, 2017, 17(5):470-476. CHEN Tianmu, CHEN Shuilian, XIE Zhi, et al. Simulated effectiveness of control countermeasures for influenza outbreaks based on different asymptomatic infections and transmissibility[J]. China Trop Med, 2017, 17(5):470-476.
[2] LEE J, KIM J, KWON H D. Optimal control of an influenza model with seasonal forcing and age-dependent transmission rate[J]. J Theor Biol, 2013, 317(1):310-320.
[3] TANG Yilei, XIAO Dongmei, ZHANG Weinian, et al. Dynamics of epidemic models with asymptomatic infection and seasonal succession[J]. Math Biosci Eng, 2017, 14(5/6):1407-1424.
[4] MARTIN M L M, MBANG J, LUBUMA J, et al. Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers[J]. Math Biosci Eng, 2016, 13(4):813-840.
[5] 王生福, 聂麟飞. 具有随机干扰和无症状感染者的疟疾模型研究[J]. 四川师范大学学报(自然科学版), 2020, 43(5):601-607. WANG Shengfu, NIE Linfei. Study of malaria model with random disturbance and asymptomatic infection[J]. Journal of Sichuan Normal University(Natural Science), 2020, 43(5):601-607.
[6] DOBROVOLNY H M. Modeling the role of asymptomatics in infection spreadwith application to SARS-CoV-2[J]. PLoS ONE, 2020, 15(8):e0236976.
[7] CHEN Xingguang. Infectious disease modeling and epidemic response measures analysis considering asymptomatic infection[J]. IEEE Access, 2020, 8(1):149652-149660.
[8] TANG Biao, BRAGAZZI N L, LI Qian, et al. An updated estimation of the risk of transmission of the novel coronavirus(2019-nCov)[J]. Infect Dis Model, 2020, 5(1):248-255.
[9] VANLANDINGHAM K E. Relapse of herpes simplex encephalitis after conventional acyclovir therapy[J]. JAMA, 1988, 259(7):1051-1053.
[10] DRIESSCHE P V D, ZOU Xingfu. Modeling relapse in infectious diseases[J]. Math Bio, 2007, 207(1):89-103.
[11] 朱承澄. 具有复发的SIR扩散流行病模型的动力学行为[D]. 兰州:兰州大学, 2018. ZHU Chengcheng. Dynamic behaviour of a relapse SIR diffusion epidemic model[D]. Lanzhou: Lanzhou University, 2018.
[12] 穆宇光, 徐瑞. 一类具有饱和发生率和复发的随机SIRI模型的稳定性[J]. 应用数学, 2019, 32(3):570-580. MU Yuguang, XU Rui. Stability of a stochastic SIRI model with saturated incidence and relapse[J]. Math Appl, 2019, 32(3):570-580.
[13] YAN Dongxue, ZOU Xingfu. Dynamics of an epidemic model with relapse over a two-patch environment[J]. Math Biosci Eng, 2020, 17(5):6098-6127.
[14] FENG Xiaomei, TENG Zhidong, ZHANG Fengqin. Global dynamics of a general class of multi-group epidemic models with latency and relapse[J]. Math Biosci Eng, 2015, 12(1):99-115.
[15] ZOU Xingfu, WANG Lin, DRIESSCHE P V D. Modeling disease with latencecy and relapse[J]. Math Biosci Eng, 2007, 4(2):205-219.
[16] DING Qian, LIU Yunfeng, CHEN Yuming, et al. Dynamics of a reaction-diffusion SIRI model with relapse and free boundary[J]. Math Bio Eng, 2020, 17(2):1659-1676.
[17] LIU Fang, CAI Zhaobin, HUANG Jinsong, et al. Repeated COVID-19 relapse during post-discharge surveillance with viral shedding lasting for 67 days in a recovered patient infected with SARS-CoV-2-ScienceDirect[J]. J Microbiol Immunol, 2020, 54(1):101-104.
[18] MUTLU E, YACOLU A. Relapse in patients with serious mental disorders during the COVID-19 outbreak: a retrospective chart review from a community mental health center[J]. Eur Arch Psy Clin N, 2020, 271(4):381-383.
[19] ZHANG Tailei, TENG Zhidong. On a nonautonomous SEIRS model in epidemiology[J]. B Math Biol, 2007, 69(8):2537-2559.
[20] DRIESSCHE P V D, WATMOUGH J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Math Bio, 2002, 180(1/2):29-48.
[21] THIEME, HORST R. Persistence under relaxed point-dissipativity(with application to an endemic model)[J]. Siam J Math Anal, 1993, 24(2):407-435.
[22] ZHAO Xiaoqiang. Uniform persistence and periodic coexistence states in infinite-dimensional periodic semiflows with applications[J]. Can Appl Math Q, 1995, 3(3):473-495.
[23] 中国疾病预防控制中心.截至1月11日—1月25日24时新型冠状病毒肺炎疫情最新情况[EB/OL].(2020-01-12—2020-01-26)[2020-10-14]. https://www.chinacdc.cn/jkzt/crb/zl/szkb_11803/jszl_11809/.
[24] 国家卫生健康委员会.武汉市卫生健康委员会关于新型冠状病毒感染的肺炎情况通报[EB/OL].(2020-01-12—2020-01-26)[2020-10-14]. http://www.nhc.gov.cn/xcs/yqtb/list_gzbd_26.shtml.
[25] YAN Qinling, TANG Yingling, YAN Dingding, et al. Impact of media reports on the early spread of COVID-19 epidemic[J]. J Theor Biol, 2020, 502(1):1-13.
[26] World Health Organization(WHO). Statement on the first meeting of the International Health Regulations(2005)Emergency Committee regarding the outbreak of novel coronavirus(2019-nCoV)[EB/OL].(2020-01-23)[2020-10-15]. https://www.who.int/news/item/23-01-2020-statement-on-the-meeting-of-the-international-health-regulations-(2005)-emergency-committee-regarding-the-outbreak-of-novel-coronavirus-(2019-ncov).
[27] TANG Biao, WANG Xia, LI Qian, et al. Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions[J]. J Clin Med, 2020, 9(2):462.
[28] 武汉市统计局. 2019年武汉市国民经济和社会发展统计公报[EB/OL].(2020-03-29)[2020-10-15]. http://tjj.wuhan.gov.cn/tjfw/tjgb/202004/t20200429_1191417.shtml.
[1] SHEN Wei, ZHANG Cun-hua. Multiple stability switches and Hopf bifurcation in a time-delay predator-prey system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(1): 42-49.
[2] ZHU Yan-lan, ZHOU Wei, CHU Tong, LI Wen-na. Complex dynamic analysis of the duopoly game under management delegation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(7): 32-45.
[3] ZHOU Yan, ZHANG Cun-hua. Stability and Turing instability of a predator-prey reaction-diffusion system with schooling behavior [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(7): 73-81.
[4] GUO Hui-ying, YANG Fu-xia, ZHANG Cui-ping. Stability of modules with finite Ext-strongly Ding projective dimensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 31-38.
[5] LU Chang-na, CHANG Sheng-xiang. Finite element method of Cahn-Hilliard equation based on adaptive moving mesh method [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 17-25.
[6] Jie TANG,Ling WEI,Rui-si REN,Si-yu ZHAO. Granule description using possible attribute analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 75-82.
[7] YANG Zhong-liang, GUO Gai-hui. Bifurcation analysis of positive solutions for a predator-prey model with B-D functional response [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 9-15.
[8] YANG Yang, WU Bao-wei, WANG Yue-e. Input-output finite time stability of asynchronous switched systems with event-triggered [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 118-126.
[9] WEN Xiao, LIU Qi, GAO Zhen, DON Wai-sun, LYU Xian-qing. Application of local non-intrusive reduced basis method in Rayleigh-Taylor instability [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 109-117.
[10] CHEN Lu, ZHANG Xiao-guang. Research of an epidemic model on adaptive networks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(9): 76-82.
[11] WANG Zhan-ping, YUAN Kai-ying. Strongly Gorenstein injective modules with respect to a cotorsion pair [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 102-107.
[12] FENG Na-na, WU Bao-wei. Input-output finite time stability for event-triggered control of switched singular systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(3): 75-84.
[13] ZHANG Yu, ZHAO Ren-yu. Gorenstein FP-projective modules and its stability [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 79-85.
[14] DAI Li-hua, HUI Yuan-xian. Almost automorphic solutions for shunting inhibitory cellular neural networks with leakage delays on time scales [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 97-108.
[15] LIU Hua, YE Yong, WEI Yu-mei, YANG Peng, MA Ming, YE Jian-hua, MA Ya-lei. Study of dynamic of a discrete host-parasitoid model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 30-38.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd