The Impact of Staying at Home on Controlling the Spread of COVID -19: Strategy of Control

  • Omar Zakary Faculty of sciences Ben M'Sik, Universiry Hassan II of Casablanca
  • Sara Bidah Faculty of sciences Ben M'Sik, University Hassan II of Casablanca
  • Mostafa Rachik Faculty of sciences Ben M'Sik, University Hassan II of Casablanca
Keywords: SARS-CoV-2, COVID-19, Mathematical model, Optimal control, Parameters estimation

Abstract

In this paper, we present a new mathematical model to describe the evolution of the COVID-19 in a population. We aim to investigate an optimal strategy of control to bring the situation under control in Italy and Morocco, where the COVID-19 pandemic is sweeping country after country. The Italian and Moroccan authorities have declared a state of emergency in response to the growing threat of this novel coronavirus (COVID-19) outbreak by March 09 and 20, respectively. The state of emergency means that citizens cannot go out to public spaces without special authorization from local authorities. But after all these efforts exerted by these authorities, the number of new cases of the COVID-19 continues to rise significantly, which confirms the lack of commitment of some citizens. The first objective of this article is to estimate the number of these people who underestimate the lives and safety of citizens and put them at risk. To do this, we use real data of the COVID-19 in Italy and Morocco to estimate the parameters of the model, and then we predict the number of these populations. After that, we investigate an optimal control strategy that could be the optimal and efficient way for the Moroccan authorities and other countries to control the spread of the COVID-19 based on the Italian experience. Numerical examples are provided to illustrate the efficiency of the strategy of control that we propose.

References

Rothan HA, Byrareddy SN. The epidemiology and pathogenesis of coronavirus disease (COVID-19) outbreak. Journal of Autoimmunity [Internet]. 2020;109: 102433. Available from: https://doi.org/10.1016/j.jaut.2020.102433

World Health Organization. Health-topics. WHO [Internet]. 2020; Available from: https://www.who.int/health-topics/

Weinkove R, McQuilten Z, Blyth E, Cheng AC, Conyers R, Crane M, et al. Managing haematology and oncology patients during the COVID-19 pandemic: Interim consensus guidance. The Medical Journal of Australia [Internet]. 2020;212(10):481-489. Available from: https://doi.org/10.5694/mja2.50607

World Health Organization. Rolling updates on coronavirus disease (COVID-19). WHO [Internet]. 2020; Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/events-as-they-happen

Ellyantt H. Italy passes 10,000 coronavirus cases as national quarantine moves closer to total shutdown. CNBC [Internet]. 2020; Available from: https://www.cnbc.com/2020/03/11/italy-passes-10000-coronavirus-cases.html

Chen H, Xu W, Paris C, Reeson A, Li X. Social distance and SARS memory: impact on the public awareness of 2019 novel coronavirus (COVID-19) outbreak. medRxiv [Preprint]. 2020. https://doi.org/10.1101/2020.03.11.20033688

Mackay J. Under coronavirus lockdown, Italy is finding a fragile sense of solidarity. The Guardian [Internet]. 2020; Available from: https://www.theguardian.com/commentisfree/2020/mar/10/coronavirus-lockdown-italy-florence-panic

ITV News. Panic buying in Italy as nationwide coronavirus lockdown gets underway [Internet]. 2020; Available from: https://www.itv.com/news/2020-03-09/whole-of-italy-now-subject-to-coronavirus-quarantine-restrictions/

Zhou W, Wang A, Xia F, Xiao Y, Tang S. Effects of media reporting on mitigating spread of COVID-19 in the early phase of the outbreak. Mathematical Biosciences and Engineering [Internet]. 2020;17(3): 2693-2707. Available from: http://dx.doi.org/10.3934/mbe.2020147

The Center for Systems Science, at Johns Hopkins University (JHU) EC. Novel Coronavirus (COVID-19) Cases [Internet]. 2020; Available from: https://github.com/CSSEGISandData/COVID-19

The Center for Systems Science, at Johns Hopkins University (JHU) EC. Coronavirus COVID-19 Global Cases [Internet]. 2020;Available from: https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6

DXY. COVID-19 Global pandemic real time report [Internet]. 2020;Available from: https://ncov.dxy.cn/ncovh5/view/en_pneumonia?from=dxy

CCDC. COVID-19 Tracking the Epidemic [Internet]. 2020;Available from: http://weekly.chinacdc.cn/news/TrackingtheEpidemic.htm

Government of the Hong Kong special administrative region T. COVID-19 Tracking the Epidemic [Internet]. 2020;Available from: https://www.coronavirus.gov.hk/eng/index.html

Macau Government. Daily reports for Tracking the Epidemic of COVID-19 [Internet]. 2020;Available from: https://www.ssm.gov.mo/portal/

Taiwan CDC. COVID-19 Tracking the Epidemic [Internet]. 2020; Available from: https://sites.google.com/cdc.gov.tw/2019ncov/taiwan?authuser=0

European Centre for Disease Prevention and Control. COVID-19 situation update worldwide [Internet]. 2020; Available from: https://www.ecdc.europa.eu/en/geographical-distribution-2019-ncov-cases

Pontryagin. Mathematical theory of optimal processes. London: Routledge. 1987. 360p. https://doi.org/10.1201/9780203749319

Sethi SP, Thompson GL. Applications to management science and economics. Boston: Kluwer Academic Publishers. 2000. 524p.

Zakary O, Rachik M, Elmouki I. On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach. International Journal of Dynamics and Control [Internet]. 2017;5(3):917–930. Available from: https://doi.org/10.1007/s40435-016-0233-2

Zakary O, Rachik M, Elmouki I. A new epidemic modeling approach: Multi-regions discrete-time model with travel-blocking vicinity optimal control strategy. Infectious Disease Modelling [Internet]. 2017;2(3):304–322. Available from: https://doi.org/10.1016/j.idm.2017.06.003

Boutayeb H, Bidah S, Zakary O, Rachik M. A New Simple Epidemic Discrete-Time Model Describing the Dissemination of Information with Optimal Control Strategy. Discrete Dynamics in Nature and Society [Internet]. 2020;2020:7465761. Available from: https://doi.org/10.1155/2020/7465761

Einian M, Tabarraei HR. Modeling of COVID-19 Pandemic and Scenarios for Containment. medRxiv. [Preprint]. 2020. https://doi.org/10.1101/2020.03.27.20045849

Tian J, Wu J, Bao Y, Weng X, Shi L, Liu B, Yu X, Qi L, Liu Z. Modeling analysis of COVID-19 based on morbidity data in Anhui, China. Mathematical Biosciences and Engineering [Internet]. 2020;17(4):2842-52. Available from: http://dx.doi.org/10.3934/mbe.2020158

Kingdom of Morocco Ministry of National Education HE Vocational Training. Press release–March 16, 2020 [Internet]. 2020; Available from: https://www.men.gov.ma/Ar/Pages/Publication.aspx?IDPublication=5938

Kingdom of Morocco Ministry of National Education HE Vocational Training. Newsletter no. 3- March 16, 2020 [Internet]. 2020;Available from: https://www.men.gov.ma/Ar/Pages/Publication.aspx?IDPublication=5941

D’Antiga L. Coronaviruses and Immunosuppressed Patients: The Facts During the Third Epidemic. Liver Transplantation [Internet]. 2020; 26(6):832-834. Available from: https://doi.org/10.1002/lt.25756

Published
2020-09-23
How to Cite
Zakary, O., Bidah, S., & Rachik, M. (2020). The Impact of Staying at Home on Controlling the Spread of COVID -19: Strategy of Control. Mexican Journal of Biomedical Engineering, 42(1), 10-26. Retrieved from http://rmib.com.mx/index.php/rmib/article/view/1051
Section
Special Issue