A Model of Social Distancing for Interacting Age-Distributed Multi-Populations: An Analysis of Students’ In-Person Return to Schools
DOI:
https://doi.org/10.5540/tcam.2022.023.04.00655Keywords:
COVID-19, SIRQ model, multi-populationAbstract
Because of the current scenario of the SARS-CoV-2 (COVID-19) pandemic in Brazil, whose vaccination campaign is in the initial stage, government authorities have pointed out towards the complete reopening of the economy. And recently for the in-personal return of classroom teaching in schools. Given the family relationship, one of the questions that remained without an answer is: What are the consequences of the schools reopening on the dissemination of COVID-19? The purpose of this work is to analyze a variant of the compartmental SIRD (Susceptible, Infected, Recovered, social distancing) model within a structured interacting age population representing six age groups from the basic education age to the elders. We present a complete analysis of the well-posedness of the proposed mathematical model. Moreover, we discuss distinct disease spreading scenarios based on observations of the mathematical behavior of the proposed dynamics. We also present a result of existence for the stationary points in terms of the parameters of the model and the number of infected age groups. Finally, we present different numerical simulations of predicted scenarios by the model. Those numerical realizations collaborate with the conclusion that an early school reopening - that implies the departure of the youngster from social isolation - causes the infection curve to grow considerably, even for other age groups.
References
W. H. Organization, “Who coronavirus disease (covid-19) dashboard,”
https://covid19.who.int 2020/7/29, 2020.
D.Wang, B. Hu, C. Hu, F. Zhu, X. Liu, J. Zhang, B.Wang, H. Xiang, Z. Cheng, Y. Xiong, et al., “Clinical characteristics of 138 hospitalized patients with 2019 novel coronavirus–infected pneumonia in wuhan, china,” Jama, vol. 323, no. 11, pp. 1061–1069, 2020.
Z. Khan, Y. Karatas, and H. Rahman, “Anti covid-19 drugs: need for more clinical evidence and global action,” Advances in therapy, vol. 37, no. 6, pp. 2575– 2579, 2020.
D. Bernoulli, “Essai d’une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l’inoculation pour la prévenir,” Histoire de l’Acad., Roy. Sci.(Paris) avec Mem, pp. 1–45, 1760.
R. Anderson and R. May, “Vaccination against rubella and measles: quantitative investigations of different policies,” Epidemiology & Infection, vol. 90, no. 2, pp. 259–325, 1983.
P. G.Walker, C. Whittaker, O. J.Watson, M. Baguelin, P. Winskill, A. Hamlet, B. A. Djafaara, Z. Cucunubá, D. O. Mesa, W. Green, et al., “The impact of covid-19 and strategies for mitigation and suppression in low-and middle-income countries,” Science, vol. 369, no. 6502, pp. 413–422, 2020.
O. T. Ranzani, L. S. Bastos, J. G. M. Gelli, J. F. Marchesi, F. Baião,
S. Hamacher, and F. A. Bozza, “Characterisation of the first 250 000 hospital admissions for covid-19 in brazil: a retrospective analysis of nationwide data,” The Lancet Respiratory Medicine, 2021.
A. Aleta, D. Martin-Corral, A. P. y Piontti, M. Ajelli, M. Litvinova, M. Chinazzi, N. E. Dean, M. E. Halloran, I. M. Longini Jr, S. Merler, et al., “Modelling the impact of testing, contact tracing and household quarantine on second waves of covid-19,” Nature Human Behaviour, vol. 4, no. 9, pp. 964–971, 2020.
D. K. Chu, E. A. Akl, S. Duda, K. Solo, S. Yaacoub, H. J. Schünemann,
A. El-harakeh, A. Bognanni, T. Lotfi, M. Loeb, et al., “Physical distancing,
face masks, and eye protection to prevent person-to-person transmission of sars-cov-2 and covid-19: a systematic review and meta-analysis,” The Lancet, vol. 395, no. 10242, pp. 1973–1987, 2020.
[
J. M. Brauner, S. Mindermann, M. Sharma, D. Johnston, J. Salvatier,
T. Gavenciak, A. B. Stephenson, G. Leech, G. Altman, V. Mikulik, et al.,
“Inferring the effectiveness of government interventions against covid-19,” Science, vol. 371, no. 6531, 2021.
J. Panovska-Griffiths, C. C. Kerr, R. M. Stuart, D. Mistry, D. J. Klein, R. M. Viner, and C. Bonell, “Determining the optimal strategy for reopening schools, the impact of test and trace interventions, and the risk of occurrence of a second covid-19 epidemic wave in the uk: a modelling study,” The Lancet Child & Adolescent Health, vol. 4, no. 11, pp. 817–827, 2020.
M. J. Lazo and A. De Cezaro, “Why can we observe a plateau even in an out of control epidemic outbreak? a seir model with the interaction of n distinct populations for covid-19 in brazil.,” TEMA, to appear 2021.
J. K. Hale, Ordinary Differential Equations (2nd ed.), vol. 1. Malabar: Robert E. Krieger Publishing Company, 1980.
H. W. Hethcote, “Three basic epidemiological models,” in Applied mathematical ecology, pp. 119–144, Springer, 1989.
H. W. Hethcote, “The mathematics of infectious diseases,” SIAM review, vol. 42, no. 4, pp. 599–653, 2000.
M. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2007.
O. P. Neto, D. M. Kennedy, J. C. Reis, Y. Wang, A. C. B. Brizzi,
G. J. Zambrano, J. M. de Souza, W. Pedroso, R. C. de Mello Pedreiro,
B. de Matos Brizzi, et al., “Mathematical model of covid-19 intervention scenarios for são paulo—brazil,” Nature Communications, vol. 12, no. 1, pp. 1–13, 2021.
A. J. Barros, C. G. Victora, A. Menezes, B. L. Horta, F. Hartwig, G. Victora, L. C. Pellanda, O. A. Dellagostin, C. J. Struchiner, M. N. Burattini,
et al., “Padrões de distanciamento social em nove cidades gaúchas: estudo epicovid19/ rs,” Revista de Saúde Pública, vol. 54, p. 75, 2020.
U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, vol. 1. SIAM, 1998.
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.
