A Logistic Fractional Model with Control Measures for Cumulative Cases of COVID-19

Authors

  • M. M. Lopes University of Campinas
  • F. S. Pedro Federal University of São Paulo
  • D. E. Sánchez University Austral of Chile
  • V. F. Wasques São Paulo State University and Brazilian Center for Research in Energy and Materials
  • E. Esmi University of Campinas
  • L. C. De Barros University of Campinas

DOI:

https://doi.org/10.5540/tcam.2023.024.02.00275

Keywords:

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.

Author Biographies

M. M. Lopes, University of Campinas

Department of Applied Mathematics

F. S. Pedro, Federal University of São Paulo

Multidisciplinary Department

D. E. Sánchez, University Austral of Chile

Center of Basic Science Teaching for Engineering

V. F. Wasques, São Paulo State University and Brazilian Center for Research in Energy and Materials

Department of Mathematics and Ilum School of Science

E. Esmi, University of Campinas

Department of Applied Mathematics

L. C. De Barros, University of Campinas

Department of Applied Mathematics

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.

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Published

2023-05-24

How to Cite

Lopes, M. M., Pedro, F. S., Sánchez, D. E., Wasques, V. F., Esmi, E., & De Barros, L. C. (2023). A Logistic Fractional Model with Control Measures for Cumulative Cases of COVID-19. Trends in Computational and Applied Mathematics, 24(2), 275–291. https://doi.org/10.5540/tcam.2023.024.02.00275

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Section

Original Article