A Logistic Fractional Model with Control Measures for Cumulative Cases of COVID-19
DOI:
https://doi.org/10.5540/tcam.2023.024.02.00275Keywords:
Logistic model with removal, fractional differential equations, social isolation.Abstract
The curve of cumulative cases of individuals infected by COVID-19 shows similar growth to the logistic curve in the period referring to each epidemic "wave'', as each peak of active cases is called. Considering that in pandemic scenarios it is common to seek control measures based on previous experiences. In this paper, we model the curve of cumulative cases through a logistic model with infected removal to include the control measures in the dynamics. This model is based on fractional differential equations to also include the memory effect. We study the scenario of the first two "waves'' in the analyzed countries: Brazil, China, Italy, and Switzerland. Scenarios with and without control measures are compared, proving the importance of control measures such as isolation. Moreover, this model makes it possible to determine the portion of the population that did not participate in the dynamics of the spread of the disease, as well as to analyze how the number of infected people reduced in each country.References
World Health Organization, "Director-General's remarks at the media briefing on 2019-nCoV on 11 February 2020." Available at: {https://www.who.int/dg/speeches/detail/who-director-general-s-remarks-at-the-media-briefing-on-2019- ncov-on-11-february-2020}. Accessed on March 2020.
Fundação Oswaldo Cruz, "Covid-19: que vírus é esse?." Available at: {https://portal.fiocruz.br/noticia/covid-19-que-virus-e-esse}. Accessed on March 2020.
N. Van Doremalen, T. Bushmaker, D. H. Morris, M. G. Holbrook, A. Gamble, B. N. Williamson, A. Tamin, J. L. Harcourt, N. J. Thornburg, S. I. Gerber, et al., “Aerosol and surface stability of sars-cov-2 as compared with sars-cov-1,” New England journal of medicine, vol. 382, no. 16, pp. 1564–1567, 2020.
L. Zou, F. Ruan, M. Huang, L. Liang, H. Huang, Z. Hong, J. Yu, M. Kang, Y. Song, J. Xia, et al., “Sars-cov-2 viral load in upper respiratory specimens of infected patients,” New England Journal of Medicine, vol. 382, no. 12, pp. 1177–1179, 2020.
L. Bao, W. Deng, H. Gao, C. Xiao, J. Liu, J. Xue, Q. Lv, J. Liu, P. Yu, Y. Xu, et al., “Reinfection could not occur in sars-cov-2 infected rhesus macaques,” BioRxiv, 2020.
World Health Organization, “Novel coronavirus situation report -2. January 22, 2020.” Available at: https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200122-sitrep-2-2019-ncov.pdf.
Accessed on March 2020, 2020.
European Centre for Disease Prevention and Control, “Threat Assessment Brief: Implications of the emergence and spread of the SARSCoV-2 B.1.1. 529 variant of concern (Omicron) for the EU/EEA..” Available at: https://www.ecdc.europa.eu/en/publications-data/threat-assessment-brief-emergence-sars-cov-2-variant-b.1.1.529. Accessed on January 2022, 2021.
Centers for Disease Control and Prevention, “New SARS-CoV-2 Variant
of Concern Identified: Omicron (B.1.1.529) Variant.” Available at: https://emergency.cdc.gov/han/2021/han00459.asp?ACSTrackingID=
USCDC_511-DM71221&ACSTrackingLabel=HAN%20459%20-%20General% 20Public&deliveryName=USCDC_511-DM71221. Accessed on January 2022, 2021.
L. Edelstein-Keshet, Mathematical models in biology. SIAM, 2005.
M. Saeedian, M. Khalighi, N. Azimi-Tafreshi, G. Jafari, and M. Ausloos, “Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model,” Physical Review E, vol. 95, no. 2, p. 022409, 2017.
L. C. Barros, M. M. Lopes, F. Santo Pedro, E. Esmi, J. P. C. dos Santos, and D. E. Sánchez, “The memory effect on fractional calculus: an application in the spread of covid-19,” Computational and Applied Mathematics, vol. 40, no. 3, pp. 1–21, 2021.
A. N. Góis, E. E. Laureano, D. d. S. Santos, D. E. Sánchez, L. F. Souza, R. d. C. A. Vieira, J. C. Oliveira, and E. Santana-Santos, “Lockdown as an intervention measure to mitigate the spread of covid-19: a modeling study,” Revista da Sociedade Brasileira de Medicina Tropical, vol. 53, 2020.
K. Diethelm, “A fractional calculus based model for the simulation of an outbreak of dengue fever,” Nonlinear Dynamics, vol. 71, no. 4, pp. 613–619, 2013.
Worldometers, “Covid-19 coronavirus pandemic.” Available at: https://www.worldometers.info/coronavirus/country/brazil/. Accessed on March 2021, 2021.
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.
