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Parameter estimation and prediction for coronavirus disease outbreak 2019 (COVID-19) in Algeria

1 Department of Mathematics and Informatics, University center of Ain Temouchent, Algeria
2 Laboratoire d’Analyse Nonlinéaire et Mathématiques Appliquées, University of Tlemcen, Tlemcen 13000, Algeria
3 Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan

Special Issues: Coronavirus disease 2019: Modeling, Control and Prediction

Background: The wave of the coronavirus disease outbreak in 2019 (COVID-19) has spread all over the world. In Algeria, the first case of COVID-19 was reported on 25 February, 2020, and the number of confirmed cases of it has increased day after day. To overcome this difficult period and a catastrophic scenario, a model-based prediction of the possible epidemic peak and size of COVID-19 in Algeria is required. Methods: We are concerned with a classical epidemic model of susceptible, exposed, infected and removed (SEIR) population dynamics. By using the method of least squares and the best fit curve that minimizes the sum of squared residuals, we estimate the epidemic parameter and the basic reproduction number ${\cal R}_0$. Moreover, we discuss the effect of intervention in a certain period by numerical simulation. Results: We find that ${\cal R}_0$= 4.1, which implies that the epidemic in Algeria could occur in a strong way. Moreover, we obtain the following epidemiological insights: the intervention has a positive effect on the time delay of the epidemic peak; the epidemic size is almost the same for a short intervention; a large epidemic can occur even if the intervention is long and sufficiently effective. Conclusion: Algeria must implement the strict measures as shown in this study, which could be similar to the one that China has finally adopted.
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Keywords COVID-19; SEIR epidemic model; basic reproduction number

Citation: Soufiane Bentout, Abdennasser Chekroun, Toshikazu Kuniya. Parameter estimation and prediction for coronavirus disease outbreak 2019 (COVID-19) in Algeria. AIMS Public Health , 2020, 7(2): 306-318. doi: 10.3934/publichealth.2020026


  • 1. Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc London Ser A 115: 700–721.    
  • 2. Bentout S, Touaoula TM (2016) Global analysis of an infection age model with a class of nonlinear incidence rates. J Math Anal Appl 434: 1211–1239.    
  • 3. Chekroun A, Frioui MN, Kuniya T, et al. (2020) Mathematical analysis of an age structured heroin-cocaine epidemic model. Discrete Contin Dyn Syst Ser B 25: 1–13.
  • 4. Diekmann O, Heesterbeek J (2000) Mathematical Epidemiology of Infective Diseases: Model Building, Analysis and Interpretation. Wiley, New York.
  • 5. Hattaf K, Yang Y (2018) Global dynamics of an age-structured viral infection model with general incidence function and absorption. Int J Biomath 11: 1–18.
  • 6. Liu L, Wanga J, Liu X (2015) Global stability of an SEIR epidemic model with age-dependent latency and relapse. Nonlinear Anal Real World Appl 24: 18–35.    
  • 7. Magal P, McCluskey CC, Webb GF (2010) Lyapunov functional and global asymptotic stability for an infection-age model. Appl Anal 89: 1109–1140.    
  • 8. Korobeinikov A (2004) Lyapunov functions and global properties for SEIR and SEIS epidemic models. Math Med Biol 21: 75–83.    
  • 9. Korobeinikov A, Maini PK (2004) A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Math Biosci Eng 1: 57–60.    
  • 10. Li MY, Graef JR, Wang L, et al. (1999) Global dynamics of a SEIR model with varying total population size. Math Biosci 160: 191–213.    
  • 11. Li G, Jin Z (2005) Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period. Chaos Solitons Fractals 25: 1177–1184.    
  • 12. Li MY, Muldowney JS (1995) Global stability for the SEIR model in epidemiology. Math Biosci 12: 155–164.
  • 13. Zhang J, Ma Z (2003) Global dynamics of an SEIR epidemic model with saturating contact rate. Math Biosci 185: 15–32.    
  • 14. WHO (2020) Coronavirus disease (COVID-2019) situation reports. Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports.
  • 15. Rothe C, Schunk M, Sothmann P, et al. (2020) Transmission of 2019-nCoV Infection from an Asymptomatic Contact in Germany. New Eng J 382: 970–971.    
  • 16. African Future (2020) Algerian health minister confirms first COVID-19 case. Available from: https://africatimes.com/2020/02/25/algerian-health-minister-confirms-first-covid-19-case/.
  • 17. COVID-19 pandemic in Algeria (2020). Available from: https://fr.wikipedia.org/wiki/Pand%C3%A9mie_de_Covid-19_en_Alg%C3%A9rie.
  • 18. Epidemiological map (in Arabic and French) (2020) COVID-19- Alg ´ erie - Evolution de la situation(in Arabic and French). Available from: http://covid19.sante.gov.dz/carte/.
  • 19. Jia J, Ding J, Liu S, et al. (2020) Modeling the Control of COVID-19: Impact of Policy Interventions and Meteorological Factors. Electron J Differ Equations 23: 1–24.
  • 20. Kuniya T (2020) Prediction of the Epidemic Peak of Coronavirus Disease in Japan, 2020. J Clin Med 9: 1–7.
  • 21. Liu Y, Gayle A, Wilder Smith A, et al. (2020) The reproductive number of COVID-19 is higher compared to SARS coronavirus. J Travel Med 27: 1–4.
  • 22. Liu Z, Magal P, Seydi O, et al. (2020) Understanding Unreported Cases in the COVID-19 Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions. Biology 9: 1–22.
  • 23. Volpert V, Banerjee M, Petrovskii S (2020) On a quarantine model of coronavirus infection and data analysis. Math Model Nat Phenom 15: 1–6.    
  • 24. Diekmann O, Heesterbeek JAP, Metz JAJ (1990) On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J Math Biol 28: 365–382.
  • 25. Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180: 29–48.    
  • 26. Sanche S, Lin YT, Xu C, et al. (2020) High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerg Infect Diseases 26: 1–4.    
  • 27. Liu Y, Gayle AA, Wilder-Smith A, et al. (2020) The reproductive number of COVID-19 is higher compared to SARS coronavirus. J Travel Med 27: 1–4.
  • 28. Anderson RM, Heesterbeek H, Klinkenberg D, et al. (2020) How will country-based mitigation measures influence the course of the COVID-19 epidemic? Lancet 395: 931–934.    
  • 29. Zou L, Ruan F, Huang M, et al. (2020) SARS-CoV-2 viral load in upper respiratory specimens of infected patients. N Engl J Med.
  • 30. Li Q, Guan X, Wu P, et al. (2020) Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia. N Engl J Med.
  • 31. Office National des Statistiques (in French) (2020). Available from: http://www.ons.dz/-Demographie-.html.


This article has been cited by

  • 1. Ahmed A Mohsen, Hassan Fadhil AL-Husseiny, Xueyong Zhou, Khalid Hattaf, Global stability of COVID-19 model involving the quarantine strategy and media coverage effects, AIMS Public Health, 2020, 7, 3, 587, 10.3934/publichealth.2020047

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