Lifting mobility restrictions and the effect of superspreading events on the short-term dynamics of COVID-19

Mario Santana-Cibrian; Manuel A. Acuña-Zegarra; Jorge X. Velasco-Hernandez; Mario Santana-Cibrian; Manuel A. Acuña-Zegarra; Jorge X. Velasco-Hernandez

doi:10.3934/mbe.2020330

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 6240-6258. doi: 10.3934/mbe.2020330

Previous Article Next Article

Research article Special Issues

Lifting mobility restrictions and the effect of superspreading events on the short-term dynamics of COVID-19

1.
Instituto de Matemáticas UNAM-Juriquilla, Juriquilla, Querétaro, México
2.
CONACyT-Instituto de Matemáticas, UNAM-Juriquilla, Juriquilla, Querétaro, México
3.
Departamento de Matemáticas, Universidad de Sonora, Hermosillo, Sonora, México
4.
Nodo Multidisciplinario de Matemáticas Aplicadas, Instituto de Matemáticas UNAM-Juriquilla, Juriquilla, Querétaro, M éxico

Received: 24 July 2020 Accepted: 10 September 2020 Published: 18 September 2020

SARS-CoV-2 has now infected 15 million people and produced more than six hundred thousand deaths around the world. Due to high transmission levels, many governments implemented social distancing and confinement measures with different levels of required compliance to mitigate the COVID-19 epidemic. In several countries, these measures were effective, and it was possible to flatten the epidemic curve and control it. In others, this objective was not or has not been achieved. In far too many cities around the world, rebounds of the epidemic are occurring or, in others, plateaulike states have appeared, where high incidence rates remain constant for relatively long periods of time. Nonetheless, faced with the challenge of urgent social need to reactivate their economies, many countries have decided to lift mitigation measures at times of high incidence. In this paper, we use a mathematical model to characterize the impact of short duration transmission events within the confinement period previous but close to the epidemic peak. The model also describes the possible consequences on the disease dynamics after mitigation measures are lifted. We use Mexico City as a case study. The results show that events of high mobility may produce either a later higher peak, a long plateau with relatively constant but high incidence or the same peak as in the original baseline epidemic curve, but with a post-peak interval of slower decay. Finally, we also show the importance of carefully timing the lifting of mitigation measures. If this occurs during a period of high incidence, then the disease transmission will rapidly increase, unless the effective contact rate keeps decreasing, which will be very difficult to achieve once the population is released.
- COVID-19,
- SARS-CoV-2,
- superspreading events,
- lifting restrictions,
- epidemic plateau
Citation: Mario Santana-Cibrian, Manuel A. Acuña-Zegarra, Jorge X. Velasco-Hernandez. Lifting mobility restrictions and the effect of superspreading events on the short-term dynamics of COVID-19[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 6240-6258. doi: 10.3934/mbe.2020330

Related Papers:

Abstract

SARS-CoV-2 has now infected 15 million people and produced more than six hundred thousand deaths around the world. Due to high transmission levels, many governments implemented social distancing and confinement measures with different levels of required compliance to mitigate the COVID-19 epidemic. In several countries, these measures were effective, and it was possible to flatten the epidemic curve and control it. In others, this objective was not or has not been achieved. In far too many cities around the world, rebounds of the epidemic are occurring or, in others, plateaulike states have appeared, where high incidence rates remain constant for relatively long periods of time. Nonetheless, faced with the challenge of urgent social need to reactivate their economies, many countries have decided to lift mitigation measures at times of high incidence. In this paper, we use a mathematical model to characterize the impact of short duration transmission events within the confinement period previous but close to the epidemic peak. The model also describes the possible consequences on the disease dynamics after mitigation measures are lifted. We use Mexico City as a case study. The results show that events of high mobility may produce either a later higher peak, a long plateau with relatively constant but high incidence or the same peak as in the original baseline epidemic curve, but with a post-peak interval of slower decay. Finally, we also show the importance of carefully timing the lifting of mitigation measures. If this occurs during a period of high incidence, then the disease transmission will rapidly increase, unless the effective contact rate keeps decreasing, which will be very difficult to achieve once the population is released.

References

[1]	J. Dehning, J. Zierenberg, F. P. Spitzner, M. Wibral, J. P. Neto, M. Wilczekand, et al., Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions, Science, 369 (2020), eabb9789. doi: 10.1126/science.abb9789
[2]	T. Sardar, S. S. Nadim, S. Rana, J. Chattopadhyay, Assessment of Lockdown Effect in Some States and Overall India: A Predictive Mathematical Study on COVID-19 Outbreak, Chaos Solitons Fractals, 139 (2020), 110078. doi: 10.1016/j.chaos.2020.110078
[3]	A. L. Bertozzi, E. Franco, G. Mohler, M. B. Short, D. Sledge, The challenges of modeling and forecasting the spread of COVID-19, Proc. Natl. Acad. U S A, 117 (2020), 16732-16738. doi: 10.1073/pnas.1914072117
[4]	H. S. Badr, H. Du, M. Marshall, E. Dong, M. M. Squire, L. M. Gardner, Association between mobility patterns and COVID-19 transmission in the USA: a mathematical modelling study, Lancet Infect. Dis., DOI: 10.1016/S1473-3099(20)30553-3.
[5]	C. N. Ngonghala, E. Iboi, S. Eikenberry, M. Scotch, C. R. MacIntyre, M. H. Bonds, et al., Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus, Math. Biosci., 325 (2020), 108364. doi: 10.1016/j.mbs.2020.108364
[6]	M. A. Acuña-Zegarra, M. Santana-Cibrian, J. X. Velasco-Hernandez, Modeling behavioral change and COVID-19 containment in Mexico: A trade-off between lockdown and compliance, Math. Biosci., 325 (2020), 108370. doi: 10.1016/j.mbs.2020.108370
[7]	M. Santana-Cibrian, M. A. Acuna-Zegarra, J. X. Velasco-Hernandez, Flattening the curve and the effect of atypical events on mitigation measures in Mexico: a modeling perspective, preprint, May 2020, medRxiv: 10.1101/2020.05.21.20109678.
[8]	S. Lee, T. Kim, E. Lee, C. Lee, H. Kim, H. Rhee, et al., Clinical course and molecular viral shedding among asymptomatic and symptomatic patients with SARS-CoV-2 infection in a community treatment center in the Republic of Korea, JAMA Intern. Med., DOI: 10.1001/jamainternmed.2020.3862.
[9]	L. Zou, F. Ruan, M. Huang, L. Liang, H. Huang, Z. Hong, et al., SARS-CoV-2 viral load in upper respiratory specimens of infected patients, N. Engl. J. Med., 382 (2020), 1177-1179. doi: 10.1056/NEJMc2001737
[10]	N. Lozano, Ssa estima pico máximo de casos por covid-19 entre 8 y 10 de mayo, 2020. Available from: https://www.politico.mx/minuta-politica/minuta-politica-gobierno-federal/ssa-estima-pico-m%C3%A1ximo-de-casos-por-covid-19-entre-8-y-10-de-mayo/, Político.mx.
[11]	E. Castillo, En valle de méxico se prevé fin de epidemia por coronavirus el 25 de junio: López-gatell, 2020. Available from: https://www.milenio.com/politica/coronavirus-valle-mexico-preven-epidemia-25-junio, Milenio.
[12]	R. H. Mena, J. X. Velasco-Hernandez, N. B. Mantilla-Beniers, G. A. Carranco-Sapiéns, L. Benet, D. Boyer, et al., Using posterior predictive distributions to analyse epidemic models: COVID-19 in Mexico City, Phys. Biol., (2020). DOI: 10.1088/1478-3975/abb115.
[13]	Gobierno de la Ciudad de México, Datos abiertos, 2020. Available from: https://datos.cdmx.gob.mx/explore/dataset/base-covid-sinave/table/.
[14]	K. Roosa, Y. Lee, R. Luo, A. Kirpich, R. Rothenberg, J. Hyman, et al., Real-time forecasts of the covid-19 epidemic in China from February 5th to February 24th, 2020, Infect. Disease Model., 5 (2020), 256-263. doi: 10.1016/j.idm.2020.02.002
[15]	C. P. Robert, G. Casella, Monte Carlo Statistical Methods, 2nd edition, Springer Texts in Statistics, Springer New York, 2004.
[16]	J. P. Kaipio, E. Somersalo, Statistical and Computational Inverse Problems, vol. 160 of Applied Mathematical Sciences, Springer-Verlag, New York, 2005.
[17]	Gobierno de la Ciudad de México, Información laboral, 2020. Available from: http://www.stps.gob.mx/gobmx/estadisticas/pdf/perfiles/perfil%20distrito%20federal.pdf,
[18]	R. N. Thompson, J. E. Stockwin, R. D. van Gaalen, J. A. Polonsky, Z. N. Kamvar, P. A. Demarsh, et al., Improved inference of time-varying reproduction numbers during infectious disease outbreaks, Epidemics, 29 (2019), 100356. doi: 10.1016/j.epidem.2019.100356
[19]	A. Cori, N. M. Ferguson, C. Fraser, S. Cauchemez, A New Framework and Software to Estimate Time-Varying Reproduction Numbers During Epidemics, Am. J. Epidemiol., 178 (2013), 1505-1512. doi: 10.1093/aje/kwt133
[20]	H. Nishiura, N. M. Linton, A. R. Akhmetzhanov, Serial interval of novel coronavirus (COVID-19) infections, Int. J. Infect. Dis., 93 (2020), 284-286. doi: 10.1016/j.ijid.2020.02.060
[21]	Gobierno de la Ciudad de México, Sem áforo epidemiológico COVID-19, 2020. Available from: https://semaforo.covid19.cdmx.gob.mx/tablero/, 2020.
[22]	X. Rong, L. Yang, H. Chu, M. Fan, Effect of delay in diagnosis on transmission of COVID-19, Math. Biosci. Eng., 17 (2020), 2725-2740. doi: 10.3934/mbe.2020149
[23]	C. Yang, J. Wang, A mathematical model for the novel coronavirus epidemic in Wuhan, China, Math. Biosci. Eng., 17 (2020), 2708-2724. doi: 10.3934/mbe.2020148
[24]	L. Wang, J. Wang, H. Zhao, Y. Shi, K. Wang, P. Wu, et al., Modelling and assessing the effects of medical resources on transmission of novel coronavirus (COVID-19) in Wuhan, China, Math. Biosci. Eng., 17 (2020), 2936-2949. doi: 10.3934/mbe.2020165
[25]	G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo, et al., Modelling the covid-19 epidemic and implementation of population-wide interventions in Italy, Nat. Med., 26 (2020), 855-860. doi: 10.1038/s41591-020-0883-7
[26]	H. Zhao, Z. Feng, Staggered release policies for covid-19 control: Costs and benefits of relaxing restrictions by age and risk, Math. Biosci., 326 (2020), 108405. doi: 10.1016/j.mbs.2020.108405
[27]	E. Estrada, COVID-19 and SARS-CoV-2. Modeling the present, looking at the future, Phys. Rep., 869 (2020), 1-51. doi: 10.1016/j.physrep.2020.07.005
[28]	J. A. Christen, C. Fox, A general purpose sampling algorithm for continuous distributions (the t-walk), Bayesian Anal., 5 (2010), 263-281. doi: 10.1214/10-BA603

Reader Comments

Your name:*

Email:*
© 2020 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)