Abstract

The highly contagious infectious disease COVID-19 virus has spread around the world infecting millions of people with high number of deaths, causing profound health, social and economic distress around the world. Mathematical models can provide new insights into the transmission dynamics of the virus and suggest criteria for the design of efficient control strategies. In this work, we use epidemiological modelling to assess the effect of physical distancing measures on the spread of the virus. The mathematical model describing the epidemic progression includes COVID-19 treatment and vaccination. The numerical resolution of the model shows its suitability for describing the Tunisian COVID-19 outbreak. We show the impact of application of social distancing measures with and without vaccination on the epidemic peak. We found that vaccination against COVID-19 is crucial in controlling the virus, but it is important to back this up with social control measures.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 2
Year: 2022

DOI: 10.12732/ijam.v35i2.11

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References

1. [1] A. Rachah, A mathematical model with isolation for the dynamics of Ebola virus, Journal of Physics: Conference Series, 1132 (2018), 12-58.
2. [2] A. Rachah, D. FM. Torres, Dynamics and optimal control of Ebola transmission, Mathematics in Computer Science, 10 (2016), 331-342.
3. [3] A. Rachah, D. FM. Torres, Predicting and controlling the Ebola infection, Mathematical Methods in the Applied Sciences, 40 (2017), 6155-6164.
4. [4] A. Rachah, D. FM. Torres, Analysis, simulation and optimal control of a SEIR model for Ebola virus with demographic effects, Communications Fac. of Sci. Univ. of Ankara Ser. A1: Math. and Stat., 67 (2018), 179-197.
5. [5] AR. McLean, SM. Blower, Modelling HIV vaccination, Trends in Microbiology, 3 (1995), 458-463.
6. [6] D. Fisman, E. Khoo, A. Tuite, Early epidemic dynamics of the West African 2014 Ebola outbreak: estimates derived with a simple twoparameter model, PLoS Currents, 6 (2014).
7. [7] F. Brauer, C. Castillo-Chavez, Z. Feng, Mathematical Models in Epidemiology, Springer (2019).
8. [8] FP. Polack, SJ. Thomas, N. Kitchin, J. Absalon, Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine, New England J. of Medicine, 383 (2020), 2603-2615.
9. [9] G. Evensen, J. Amezcua, M. Bocquet, A. Carrassi, A. Farchi, A. Fowler, PL. Houtekamer, CK. Jones, RJ. de Moraes, M. Pulido, C. Sampson, FC. Vossepoel, An international assessment of the COVID-19 pandemic using ensemble data assimilation, medRxiv, 2020.
10. [10] HR. Thieme, Mathematics in Population Biology, Princeton University Press (2018).
11. [11] I. Cooper, A. Mondal, CG. Antonopoulos, A SIR model assumption for the spread of COVID-19 in different communities, Chaos, Solitons and Fractals, 139 (2020), Art. 110057.
12. [12] JFW. Chan, S. Yuan, KH. Kok, KKW. To, H. Chu, J. Yang, A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster, The Lancet, 395 (2020), 514-523.
13. [13] KJ. Stehl ́, N. Voirin, A. Barrat, C. Cattuto, V. Colizza, L. Isella, C. Régis, JF. Pinton, N. Khanafer, W. Van den Broeck, Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees, Environmental Sci. & Technology Letters, 9 (2011), 1-15.
14. [14] KM. Andersson, AD. Paltiel, DK. Owens, The potential impact of an HIV vaccine with rapidly waning protection on the epidemic in Southern Africa: examining the RV144 trial results, Vaccine, 29 (2011), 6107-6112.
15. [15] K. Thomas, New Pfizer results: Coronavirus vaccine is safe and 95% effective, The New York Times, 2020.
16. [16] M. Dhafer, Covid19data. Website, medRxiv, 2020.
17. [17] M. Dhafer, World Statistics, URL: https://covid19data.website, 2020.
18. [18] M. Ivanova, L. Dospatliev, Data analitics and SIR modeling of Covid-19 in Bulgaria, International Journal of Applied Mathematics, 33, No 6, 2020, 1099-1114; DOI: 10.12732/ijam.v33i6.10.
19. [19] P. Van den Driessche, Reproduction numbers of infectious disease models, Infectious Disease Modelling, 2 (2017), 288-303.
20. [20] P. Van den Driessche, J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
21. [21] R. Ghostine, M. Gharamti, S. Hassrouny, I. Hoteit, An extended seir model with vaccination for forecasting the covid-19 pandemic in saudi arabia using an ensemble Kalman filter, Mathematics, 9 (2021), Art. 636.
22. [22] S. Zhao, H. Chen, Modeling the epidemic dynamics and control of COVID19 outbreak in China, Quantitative Biology, 2020, 1-9.
23. [23] SA. Madhi, V. Baillie, CL. Cutland, M. Voysey, AL. Koen, L. Fairlie, SD. Padayachee, K. Dheda, SL. Barnabas, QE. Bhorat, Efficacy of the ChAdOx1 nCoV-19 Covid-19 vaccine against the B. 1.351 variant, New England J. of Medicine, 2011.
24. [24] SM. Blower, AR. McLean, Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco, Science, 265 (1994), 1451-1454.
25. [25] TC. Reluga, Game theory of social distancing in response to an epidemic, PLoS Computational Biology, 6 (2010).
26. [26] WC. Koff, SF. Berkley, A universal coronavirus vaccine, Science (2021).
27. [27] WHO, Novel coronavirus (2019 nCoV): situation report, World Health Organization, 2020.
28. [28] X. Ma, S. Li, S. Yu, Y. Ouyang, L. Zeng, X. Li, H. Li, Emergency management of the prevention and control of novel coronavirus pneumonia in specialized branches of hospitals, Academic Emergency Medicine, 27 (2020), 312-316.
29. [29] ZJ. Cheng, J. Shan, 2019 Novel coronavirus: where we are and what we know, Infection, 48 (2020), 155-163.