Effect of travel restrictions, contact tracing and vaccination on control of emerging infectious diseases: transmission of COVID-19 as a case study

Fen-fen Zhang; Zhen Jin; Fen-fen Zhang; Zhen Jin

doi:10.3934/mbe.2022147

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 3: 3177-3201. doi: 10.3934/mbe.2022147

Previous Article Next Article

Research article

Effect of travel restrictions, contact tracing and vaccination on control of emerging infectious diseases: transmission of COVID-19 as a case study

Fen-fen Zhang ^1,2,3,
Zhen Jin ^{3
,
,}

1.
School of Data Science and Technology, North University of China, Taiyuan 030051, China
2.
Shanxi College of Technology, Shuozhou 036000, China
3.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, China

Academic Editor: Masaki Ogura

Received: 24 November 2021 Revised: 05 January 2022 Accepted: 13 January 2022 Published: 20 January 2022

Patch models can better reflect the impact of spatial heterogeneity and population mobility on disease transmission. While, there is relatively little work on using patch models to study the role of travel restrictions, contact tracing and vaccination in COVID-19 epidemic. In this paper, based on COVID-19 epidemic propagation and diffusion mechanism, we establish a dynamic model of disease spread among two patches in which Wuhan is regarded as one patch and the rest of Mainland China (outside Wuhan) as the other patch. The existence of the final size is proved theoretically and some model parameters are estimated by using the reported confirmed cases. The results show that travel restrictions greatly reduce the number of confirmed cases in Mainland China, and the earlier enforced, the fewer confirmed cases. However, it is impossible to bring the COVID-19 epidemic under control and lift travel restrictions on April 8, 2020 by imposing travel restrictions alone, the same is true for contact tracing. While, the disease can always be controlled if the protection rate of herd immunity is high enough and the corresponding critical threshold is given. Therefore, in order to quickly control the spread of the emerging infectious disease (such as COVID-19), it is necessary to combine a variety of control measures and develop vaccines and therapeutic drugs as soon as possible.
- COVID-19,
- two patches,
- population movement,
- travel restrictions,
- contact tracing,
- vaccination
Citation: Fen-fen Zhang, Zhen Jin. Effect of travel restrictions, contact tracing and vaccination on control of emerging infectious diseases: transmission of COVID-19 as a case study[J]. Mathematical Biosciences and Engineering, 2022, 19(3): 3177-3201. doi: 10.3934/mbe.2022147

Related Papers:

Abstract

Patch models can better reflect the impact of spatial heterogeneity and population mobility on disease transmission. While, there is relatively little work on using patch models to study the role of travel restrictions, contact tracing and vaccination in COVID-19 epidemic. In this paper, based on COVID-19 epidemic propagation and diffusion mechanism, we establish a dynamic model of disease spread among two patches in which Wuhan is regarded as one patch and the rest of Mainland China (outside Wuhan) as the other patch. The existence of the final size is proved theoretically and some model parameters are estimated by using the reported confirmed cases. The results show that travel restrictions greatly reduce the number of confirmed cases in Mainland China, and the earlier enforced, the fewer confirmed cases. However, it is impossible to bring the COVID-19 epidemic under control and lift travel restrictions on April 8, 2020 by imposing travel restrictions alone, the same is true for contact tracing. While, the disease can always be controlled if the protection rate of herd immunity is high enough and the corresponding critical threshold is given. Therefore, in order to quickly control the spread of the emerging infectious disease (such as COVID-19), it is necessary to combine a variety of control measures and develop vaccines and therapeutic drugs as soon as possible.

References

[1]	Wuhan Municipal Statistial Buerau, Wuhan Statistical Yearbook, Beijing: China Statistical Press, 2020.
[2]	National Health Commission of the People's Republic of China, Entire Nation Mobilizes to Help Wuhan, 2020. Available from: http://en.nhc.gov.cn/2020-02/27/c_77008.htm.
[3]	Sina Finance and Economics, Huo Shen Shan and Lei Shen Shan Hospital were Built in More Than Ten Days. How do Prefabricated Buildings Create Chinese Speed?, 2020. Available from: https://baijiahao.baidu.com/s?id=1660426738336170285&wfr=spider&for=pc.
[4]	Health Commission of Hubei Province, The 67th Press Conference on "The Prevention and Control of Pneumonia Infected by Novel Coronavirus", 2020. Available from: https://wjw.hubei.gov.cn/bmdt/ztzl/fkxxgzbdgrfyyq/xxfb/202004/t20200409_2213253.shtml.
[5]	Xinhua Net, China Focus: Work Resumes After Extended Spring Festival Holiday, 2020. Available from: http://www.xinhuanet.com/english/2020-02/03/c_138753176.htm.
[6]	World Health Organization, Timeline: WHO's COVID-19 Response, 2020. Available from: https://www.who.int/zh/news/item/29-06-2020-Covidtimeline.
[7]	World Health Organization, WHO Coronavirus (COVID-19) Dashboard, 2022. Available from: https://covid19.who.int/.
[8]	National Health Commission of the People's Republic of China, As of 24: 00 on November 15th, the Latest Situation of COVID-19's Epidemic Situation, 2021. Available from: http://www.nhc.gov.cn/xcs/yqtb/202111/df263e648ec84a4796d199d414d084cc.shtml.
[9]	X. He, E. H. Lau, P. Wu, X. Deng, J. Wang, X. Hao, et al., Temporal dynamics in viral shedding and transmissibility of covid-19, Nat. Med., 26 (2020), 672–675. https://doi.org/10.1038/s41591-020-1016-z doi: 10.1038/s41591-020-1016-z
[10]	Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, et al., Early transmission dynamics in wuhan, china, of novel coronavirus infected pneumonia, N. Engl. J. Med., 2020 (2020). https://doi.org/10.1056/NEJMoa2001316 doi: 10.1056/NEJMoa2001316
[11]	W. Guan, Z. Ni, Y. Hu, W. Liang, C. Ou, J. He, et al., Clinical characteristics of coronavirus disease 2019 in china, N. Engl. J. Med., 382 (2020), 1708–1720. https://doi.org/10.1056/NEJMoa2002032 doi: 10.1056/NEJMoa2002032
[12]	B. Tang, N. L. Bragazzi, Q. Li, S. Tang, Y. Xiao, J. Wu, An updated estimation of the risk of transmission of the novel coronavirus (2019-ncov), Infect. Dis. Model., 5 (2020), 248–255. https://doi.org/10.1016/j.idm.2020.02.001 doi: 10.1016/j.idm.2020.02.001
[13]	J. Dehning, J. Zierenberg, F. P. Spitzner, M. Wibral, J. P. Neto, M. Wilczek, et al., Inferring change points in the spread of covid-19 reveals the effectiveness of interventions, Science, 369 (2020), 1–9. https://doi.org/10.1126/science.abb9789 doi: 10.1126/science.abb9789
[14]	S. M. Moghadas, A. Shoukat, M. C. Fitzpatrick, C. R. Wells, P. Sah, A. Pandey, et al., Projecting hospital utilization during the covid-19 outbreaks in the united states, Proc. Natl. Acad. Sci., 117 (2020), 9122–9126. https://doi.org/10.1073/pnas.2004064117 doi: 10.1073/pnas.2004064117
[15]	A. Shoukat, C. R. Wells, J. M. Langley, B. H. Singer, A. P. Galvani, S. M. Moghadas, Projecting demand for critical care beds during covid-19 outbreaks in canada, Cmaj, 192 (2020), E489–E496. https://doi.org/10.1503/cmaj.200457 doi: 10.1503/cmaj.200457
[16]	J. Zhang, M. Litvinova, Y. Liang, Y. Wang, W. Wang, S. Zhao, et al., Changes in contact patterns shape the dynamics of the covid-19 outbreak in china, Science, 368 (2020), 1481–1486. https://doi.org/10.1126/science.abb8001 doi: 10.1126/science.abb8001
[17]	Z. F. Yang, Z. Q. Zeng, K. Wang, S. S. Wong, W. Liang, M. Zanin, et al., Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions, J. Thorac. Dis., 12 (2020), 165–174. https://doi.org/10.21037/jtd.2020.02.64 doi: 10.21037/jtd.2020.02.64
[18]	H. Tian, Y. Liu, Y. Li, C. Wu, B. Chen, M. U. Kraemer, et al., An investigation of transmission control measures during the first 50 days of the covid-19 epidemic in china, Science, 368 (2020), 638–642. https://doi.org/10.1126/science.abb6105 doi: 10.1126/science.abb6105
[19]	J. Zhang, G. Q. Sun, M. T. Li, R. Gao, H. Ren, X. Pei, et al., COVID-19 reverse prediction and assessment on the diamond princess cruise ship, Front. Phys., 8 (2020).
[20]	M. Li, J. Cui, J. Zhang, G. Sun, Transmission analysis of covid-19 with discrete time imported cases: Tianjin and chongqing as cases, Infect. Dis. Model., 6 (2021), 618–631. https://doi.org/10.1016/j.idm.2021.03.007 doi: 10.1016/j.idm.2021.03.007
[21]	J. H. Buckner, G. Chowell, M. R. Springborn, Dynamic prioritization of covid-19 vaccines when social distancing is limited for essential workers, Proc. Natl. Acad. Sci., 118 (2021). https://doi.org/10.1073/pnas.2025786118 doi: 10.1073/pnas.2025786118
[22]	S. Moore, E. M. Hill, M. J. Tildesley, L. Dyson, M. J. Keeling, Vaccination and non-pharmaceutical interventions for covid-19: a mathematical modelling study, Lancet Infect. Dis., 21 (2021), 793–802. https://doi.org/10.1016/S1473-3099(21)00143-2 doi: 10.1016/S1473-3099(21)00143-2
[23]	P. C. Jentsch, M. Anand, C. T. Bauch, Prioritising covid-19 vaccination in changing social and epidemiological landscapes: a mathematical modelling study, Lancet Infect. Dis., 21 (2021), 1097–1106. https://doi.org/10.1016/S1473-3099(21)00057-8 doi: 10.1016/S1473-3099(21)00057-8
[24]	J. Chen, S. Hoops, A. Marathe, H. Mortveit, B. Lewis, S. V. enkatramanan, et al., Prioritizing allocation of covid-19 vaccines based on social contacts, preprint, medRxiv: 2021.02.04.21251012. https://doi.org/10.1101/2021.02.04.21251012
[25]	D. Gao, C. Cosner, R. S. Cantrell, J. C. Beier, S. Ruan, Modeling the spatial spread of Rift Valley fever in Egypt, Bull. Math. Biol., 75 (2013), 523–542. https://doi.org/10.1007/s11538-013-9818-5 doi: 10.1007/s11538-013-9818-5
[26]	J. Zhang, C. Cosner, H. Zhu, Two-patch model for the spread of west nile virus, Bull. Math. Biol., 80 (2018), 840–863. https://doi.org/10.1007/s11538-018-0404-8 doi: 10.1007/s11538-018-0404-8
[27]	A. Y. A. Mukhtar, J. B. Munyakazi, R. Ouifki, Assessing the role of human mobility on malaria transmission, Math. Biosci., 320 (2020). https://doi.org/10.1016/j.mbs.2019.108304 doi: 10.1016/j.mbs.2019.108304
[28]	X. Sun, Y. Xiao, X. Ji, When to lift the lockdown in Hubei province during COVID-19 epidemic? An insight from a patch model and multiple source data, J. Theor. Biol., 507 (2020). https://doi.org/10.1016/j.jtbi.2020.110469 doi: 10.1016/j.jtbi.2020.110469
[29]	J. Li, Z. Jin, Y. Yuan, G. Sun, A non-Markovian SIR network model with fixed infectious period and preventive rewiring, Comput. Math. Appl., 75 (2018), 3884–3902. https://doi.org/10.1016/j.camwa.2018.02.035 doi: 10.1016/j.camwa.2018.02.035
[30]	H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Com- petitive and Cooperative Systems, American Mathematical Soc., 2008.
[31]	W. Hirsch, H. Hanisch, J. Gabriel, Differential equation models of some parasitic infections: methods for the study of asymptotic behavior, Commun. Pure Appl. Math., 38 (1985), 733–753. https://doi.org/10.1002/cpa.3160380607 doi: 10.1002/cpa.3160380607
[32]	C. Yuan, A simple model to assess wuhan lock-down effect and region efforts during covid-19 epidemic in china mainland, preprint, medRxiv: 2020.02.29.20029561. https://doi.org/10.1101/2020.02.29.20029561
[33]	National Health Commission of the People's Republic of China, Epidemic Situation Report, 2022. Available from: http://www.nhc.gov.cn/xcs/yqtb/list_gzbd.shtml.
[34]	S. Tang, Y. Xiao, J. Liang, X. Wang, Mathematical Biology, Beijing: Science press, 2019.
[35]	Bureau of Disease Control and Prevention, Protocol on Prevention and Control of Novel Coronavirus Pneumonia (Version 2), 2020. Available from: http://www.nhc.gov.cn/jkj/s3577/202001/c67cfe29ecf1470e8c7fc47d3b751e88.shtml.
[36]	National Health Commission of the People's Republic of China, Protocol on Prevention and Control of Novel Coronavirus Pneumonia (Version 3), 2020. Available from: http://www.nhc.gov.cn/jkj/s7923/202001/470b128513fe46f086d79667db9f76a5/files/8faa1b85841f42e8a0febbea3d8b9cb2.pdf.
[37]	National Health Commission of the People's Republic of China, Protocol on Prevention and Control of Novel Coronavirus Pneumonia (Version 5), 2020. Available from: http://www.nhc.gov.cn/xcs/zhengcwj/202002/a5d6f7b8c48c451c87dba14889b30147/files/3514cb996ae24e2faf65953b4ecd0df4.pdf.
[38]	Y. Chen, Y. Wang, Y. Zhou, Z. Lu, M. Peng, F. Sun, et al., Epidemiological characteristics of COVID-19 in Wuchang district of Wuhan, Chin. J. Epidemiol., 41 (2020), 1616–1622. https://doi.org/10.3760/cma.j.cn112338-20200412-00565 doi: 10.3760/cma.j.cn112338-20200412-00565
[39]	National Bureau of Statistics, Statistical $Communiqu\acute{e}$ of the People's Republic of China on the 2019 National Economic and Social Development, 2020. Available from: http://www.stats.gov.cn/tjsj/zxfb/202002/t20200228_1728913.html.
[40]	G. Sun, S. Wang, M. Li, L. Li, G. Feng, Transmission dynamics of COVID-19 in Wuhan, China: effects of lockdown and medical resources, Nonlinear Dyn., 101 (2020), 1981–1993. https://doi.org/10.1007/s11071-020-05770-9 doi: 10.1007/s11071-020-05770-9
[41]	M. Colomer, A. Margalida, F. Alòs, P. Oliva-Vidal, A. Vilella, L. Fraile, Modeling of Vaccination and Contact Tracing as Tools to Control the COVID-19 Outbreak in Spain, Vaccines, 9 (2021). https://doi.org/10.3390/vaccines9040386 doi: 10.3390/vaccines9040386

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)