Patch model for border reopening and control to prevent new outbreaks of COVID-19

Tingting Zheng; Huaiping Zhu; Zhidong Teng; Linfei Nie; Yantao Luo; Tingting Zheng; Huaiping Zhu; Zhidong Teng; Linfei Nie; Yantao Luo

doi:10.3934/mbe.2023310

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 7171-7192. doi: 10.3934/mbe.2023310

Previous Article Next Article

Research article

Patch model for border reopening and control to prevent new outbreaks of COVID-19

1.
College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, PR China
2.
College of Mathematics and Systems Science, Xinjiang University, Urumqi, PR China
3.
Department of Mathematics and Statistics, York University, Toronto, Canada

Received: 08 December 2022 Revised: 20 January 2023 Accepted: 02 February 2023 Published: 10 February 2023

In this paper, we propose a two-patch model with border control to investigate the effect of border control measures and local non-pharmacological interventions (NPIs) on the transmission of COVID-19. The basic reproduction number of the model is calculated, and the existence and stability of the boundary equilibria and the existence of the coexistence equilibrium of the model are obtained. Through numerical simulation, when there are no unquarantined virus carriers in the patch-2, it can be concluded that the reopening of the border with strict border control measures to allow people in patch-1 to move into patch-2 will not lead to disease outbreaks. Also, when there are unquarantined virus carriers in patch-2 (or lax border control causes people carrying the virus to flow into patch-2), the border control is more strict, and the slower the growth of number of new infectious in patch-2, but the strength of border control does not affect the final state of the disease, which is still dependent on local NPIs. Finally, when the border reopens during an outbreak of disease in patch-2, then a second outbreak will happen.
- COVID-19,
- Patch model,
- Border control,
- reopen border
Citation: Tingting Zheng, Huaiping Zhu, Zhidong Teng, Linfei Nie, Yantao Luo. Patch model for border reopening and control to prevent new outbreaks of COVID-19[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 7171-7192. doi: 10.3934/mbe.2023310

Related Papers:

Abstract

In this paper, we propose a two-patch model with border control to investigate the effect of border control measures and local non-pharmacological interventions (NPIs) on the transmission of COVID-19. The basic reproduction number of the model is calculated, and the existence and stability of the boundary equilibria and the existence of the coexistence equilibrium of the model are obtained. Through numerical simulation, when there are no unquarantined virus carriers in the patch-2, it can be concluded that the reopening of the border with strict border control measures to allow people in patch-1 to move into patch-2 will not lead to disease outbreaks. Also, when there are unquarantined virus carriers in patch-2 (or lax border control causes people carrying the virus to flow into patch-2), the border control is more strict, and the slower the growth of number of new infectious in patch-2, but the strength of border control does not affect the final state of the disease, which is still dependent on local NPIs. Finally, when the border reopens during an outbreak of disease in patch-2, then a second outbreak will happen.

References

[1]	COVID-19 Coronavirus Pandemic. Available from: https://www.worldometers.info/coronavirus
[2]	Coronavirus disease (COVID-19): Vaccines. Available from: https://www.who.int/news-room/questions-and-answers/item/coronavirus-disease-(covid-19)-vaccines
[3]	J. Seungpil, K. Jong-Hoon, H. Seung-Sik, C. Junyoung, L. Woojoo, Modified susceptible-exposed-infectious-recovered model for assessing the effectiveness of non-pharmaceutical interventions during the COVID-19 pandemic in Seoul, J. Theor. Biol., 557 (2023), 111329. https://doi.org/10.1016/j.jtbi.2022.111329 doi: 10.1016/j.jtbi.2022.111329
[4]	M. Chinazzi, J. T. Davis, M. Ajelli, C. Gioannini, M. Litvinova, S. Merler, et al., The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak, Science, 368 (2020), 395–400. https://doi.org/10.1126/science.aba9757 doi: 10.1126/science.aba9757
[5]	S. Chang, E. Pierson, P. W. Koh, J. Gerardin, B. Redbird, D. Grusky, et al., Mobility network models of COVID-19 explain inequities and inform reopening, Nature, 589 (2021), 82–87. https://doi.org/10.1038/s41586-020-2923-3 doi: 10.1038/s41586-020-2923-3
[6]	K. Ousmane, D. Abou Bakari, S. Boureima, Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19, Math. Comput. Simul., 205 (2023), 600–618. https://doi.org/10.1016/j.matcom.2022.10.017 doi: 10.1016/j.matcom.2022.10.017
[7]	H. Tu, X. Wang, S. Tang, Exploring COVID-19 transmission patterns and key factors during epidemics caused by three major strains in Asia, J. Theor. Biol., 557 (2023), 111336. https://doi.org/10.1016/j.jtbi.2022.111336 doi: 10.1016/j.jtbi.2022.111336
[8]	Z. Yang, Z. 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. Thoracic Dis., 12 (2020), 165–174. https://doi.org/10.21037/jtd.2020.02.64 doi: 10.21037/jtd.2020.02.64
[9]	D. Glass, European and US lockdowns and second waves during the COVID-19 pandemic, Math. Biosci., 330 (2020), 108472. https://doi.org/10.1016/j.mbs.2020.108472 doi: 10.1016/j.mbs.2020.108472
[10]	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), 110469. https://doi.org/10.1016/j.jtbi.2020.110469 doi: 10.1016/j.jtbi.2020.110469
[11]	L. Hu, S. Wang, T. Zheng, Z. Hu, Y. Kang, L. Nie, et al., The effects of migration and limited medical resources of the transmission of SARS-CoV-2 model with two patches, Bull. Math. Biol., 84 (2022), 55. https://doi.org/10.1007/s11538-022-01010-w doi: 10.1007/s11538-022-01010-w
[12]	L. Zou, S. Ruan, A patch model of COVID-19: The effects of containment on Chongqing, Acta Math. Appl. Sin., 43 (2020), 310–323. https://doi.org/10.12387/C2020025 doi: 10.12387/C2020025
[13]	S. Zhao, C. T. Bauch, D. H. He, Strategic decision making about travel during disease outbreaks: A game theoretical approach, J. R. Soc. Interface, 15 (2020), 20180515. http://dx.doi.org/10.1098/rsif.2018.0515 doi: 10.1098/rsif.2018.0515
[14]	R. S. Quilliam, P. Cross, A. P. Williams, G. Edwards-Jones, R. L. Salmon, et al., Subclinical infection and asymptomatic carriage of gastrointestinal zoonoses: Occupational exposure, environmental pathways, and the anonymous spread of disease, Epidemiol. Infect., 141 (2013), 2011-2021. https://doi.org/10.1017/S0950268813001131 doi: 10.1017/S0950268813001131
[15]	B. Tang, F. Xia, S. Tang, L. B. Nicola, Q. Li, X. Sun, et al., The effectiveness of quarantine and isolation determine the trend of the COVID-19 epidemic in the final phase of the current outbreak in China, Int. J. Infect. Dis., 96 (2020), 636–647. https://doi.org/10.1016/j.ijid.2020.05.113 doi: 10.1016/j.ijid.2020.05.113
[16]	P. Yuan, J. Li, E. Aruffo, E. Gatov, Q. Li, T. Zheng, et al., Efficacy of 'Stay-at-Home' Policy and Transmission of COVID-19 in Toronto, Canada: A Mathematical Modeling Study, CMAJ OPEN, 10 (2022), E367–E378. https://doi.org/10.9778/cmajo.20200242 doi: 10.9778/cmajo.20200242
[17]	J. Li, P. Yuan, J. Heffernan, T. Zheng, N. Ogden, B. Sander, et al., Observation wards and control of the transmission of COVID-19 in Wuhan, Bull. World Health Organ., 98 (2020). http://dx.doi.org/10.2471/BLT.20.258152 doi: 10.2471/BLT.20.258152
[18]	X. Wang, H. Wu, S. Tang, Assessing age-specific vaccination strategies and post-vaccination reopening policies for COVID-19 control using SEIR modeling approach, Bull. Math. Biol., 84 (2022), 108. https://doi.org/10.1007/s11538-022-01064-w doi: 10.1007/s11538-022-01064-w
[19]	Y. Luo, L. Zhang, Z. Teng, D.L. DeAngelis, A parasitism-mutualism-predation model consisting of crows, cuckoos and cats with stage-structure and maturation delays on crows and cuckoos, J. Theor. Biol., 446 (2018), 212–228. https://doi.org/10.1016/j.jtbi.2018.02.028 doi: 10.1016/j.jtbi.2018.02.028
[20]	D. Gao, How does dispersal affect the infection size, SIAM J. Appl. Math., 80 (2020), 2144–2169. https://doi.org/10.1137/19M130652X doi: 10.1137/19M130652X
[21]	L. Liu, D. Jiang, T. Hayat, Dynamics of an SIR epidemic model with varying population sizes and regime switching in a two patch setting, Phys. A, 574 (2021), 125992. https://doi.org/10.1016/j.physa.2021.125992 doi: 10.1016/j.physa.2021.125992
[22]	D. Yan, X. Zou, Dynamics of an epidemic model with relapse over a two-patch environment, Math. Biosci. Eng., 17 (2020), 6098–6127. https://doi.org/10.3934/mbe.2020324 doi: 10.3934/mbe.2020324
[23]	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
[24]	Y. Luo, S. Tang, Z. Teng, L. Zhang, Global dynamics in a reaction-diffusion multi-group SIR epidemic model with nonlinear incidence, Nonlinear Anal-Real., 50 (2019), 365–385. https://doi.org/10.1016/j.nonrwa.2019.05.008 doi: 10.1016/j.nonrwa.2019.05.008
[25]	N. Firouzabadi, P. Ghasemiyeh, S. Mohammadi-Samani, A focused review on technologies, mechanisms, safety, and efficacy of available COVID-19 vaccines, Int. Immunopharmacol., 100 (2021), 108162. https://doi.org/10.1016/j.intimp.2021.108162 doi: 10.1016/j.intimp.2021.108162
[26]	F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemics, Springer-Verlag, New York, 2000. https://doi.org/10.1007/978-1-4757-3516-1
[27]	S. Busenberg, K. Cooke, Vertically Transmitted Diseases, Springer-Verlag, New York, 1993. https://doi.org/10.1016/B978-0-12-434170-8.50029-7
[28]	J. M. Heffernan, R. J. Smith, L. M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface, 2 (2005), 281–293. https://doi.org/10.1098/rsif.2005.0042 doi: 10.1098/rsif.2005.0042
[29]	G. F. Webb, M. J. Blaser, H. Zhu, S. Ardal, J. Wu, Critical role of nosocomial transmission in the Toronto SARS outbreak, Math. Biosci. Eng., 1 (2004), 1–13. https://doi.org/10.3934/mbe.2004.1.1 doi: 10.3934/mbe.2004.1.1

Reader Comments

Your name:*

Email:*
© 2023 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)