Pinaki Pal,Asish Mitra,



Cumulative Case,Daily Infection Rate,Double Sigmoidal Boltzmann Equation,Multi-wave Covid-19 Pandemic,Simulation,


The world is facing multi-wave transmission of COVID-19 pandemics, and investigations are rigorously carried out on modeling the dynamics of the pandemic. Multi-wave transmission during infectious disease epidemics is a big challenge to public health. Here we introduce a simple mathematical model, the double sigmoidal-Boltzmann equation (DSBE), for analyzing the multi-wave Covid-19 spread in Iceland in terms of the number of cumulative cases. Simulation results and the main parameters that characterize multi waves are derived, yielding important information about the behavior of the multi-wave pandemics over time. The result of the current examination reveals the effectiveness and efficacy of DSBE for exploring the Covid 19 dynamics in Iceland and can be employed to examine the pandemic situation in different countries undergoing multi-waves.


I. Asish Mitra. : ‘COVID-19 IN INDIA AND SIR MODEL.’ J. Mech. Cont.& Math. Sci., Vol.-15, No.-7, July (2020) pp 1-8. DOI : 10.26782/jmcms.2020.07.00001
II. Asish Mitra. : ‘MODIFIED SIRD MODEL OF EPIDEMIC DISEASE DYNAMICS: A CASE STUDY OF THE COVID-19 CORONAVIRUS’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-2, February (2021) pp 1-8. DOI : 10.26782/jmcms.2021.02.00001
III. Castro, R.D.; Marraccini, P. Cytology, biochemistry and molecular changes during coffee fruit development. Brazilian Journal of Plant Physiology, v.18, n.1 p.175-199, 2006. Available from: <>. Accessed: Aug. 24, 2016.

IV. Centers for Disease Control and Prevention, “Cases of coronavirus disease (COVID-19) in the U.S.,” 2020. [cited 2020, Apr 7]. Available from:

V. Chowell, G., Hincapie-Palacio, D, Ospina, J, Pell, B, Tariq, A, Dahal, S, Moghadas, S, Smirnova, A, Simonsen, L, Viboud, C, “Using phenomenological models to characterize transmissibility and forecast patterns and final Burden of Zika epidemics,” PLoS Curr. (2016).

VI. Chowell, G, “Fitting dynamic models to epidemic outbreaks with quantified uncertainty: a primer for parameter uncertainty, identifiability, and forecasts,” Infect. Dis. Model. 2(3), 379–398 (2017).

VII. Chowell, G, Tariq, A, Hyman, J M, “A novel sub-epidemic modeling framework for short-term forecasting epidemic waves,” BMC Med. 17(1), 1–18 (2019).

VIII. Chowell, G, Luo, R, Sun, K, Roosa, K, Tariq, A, Viboud, C, “Real-time forecasting of epidemic trajectories using computational dynamic ensembles,” Epidemics. 30, 100379 (2020).

IX. Dingyu Xue, “Solving applied mathematical problems with MATLAB,” Chapman & Hall/CRC.

X. Elliott Sober, The Principle of Parsimony, Brit. J. Phil. Sci. 32 (1981), 145-156 DOI: 10.1093/bjps/32.2.145 • Source: OAI

XI. Fernandes TJ, Pereira AA, Muniz JA (2017) Double sigmoidal models describing the growth of coffee berries. Ciência Rural 47:1–7.


XIII. Laviola, B.G. et al. Nutrient accumulation in coffee fruits at four plantations altitude: calcium, magnesium and sulfur. Revista Brasileira de Ciência do Solo, v.31, n.6, p.1451- 1462, 2007. Available from: < 06832007000600022>. Accessed: Aug. 24, 2016.

XIV. Mendes, P.N. et al. Difasics logistic model in the study of the growth of Hereford breed females. Ciência Rural, v.38, n.7, p.1984-1990, 2008. Available from: < S0103-84782008000700029>. Accessed: Aug. 24, 2016.

XV. Mischan, M.M. et al. Inflection and stability points of diphasic logistic analysis of growth. Scientia Agricola, v.72, n.3, p.215- 220, 2015. Available from: < 2014-0212>. Accessed: Aug. 24, 2016.

XVI. Morais, H. et al. Detailed phenological scale of the reproductive phase of Coffea arabica. Bragantia, v.67, n.1, p.693-699, 2008. Available from: < 87052008000100031>. Accessed: Aug. 24, 2016.

XVII. Pinaki Pal, Asish Mitra, The Five Parameter Logistic (5PL) Function and COVID-19 Epidemic in Iceland, J. Mech.Cont. & Math. Sci., 16, 1-12, 2021.

XVIII. Santoro, K.R. et al. Growth curve parameters for Zebu breeds raised at Pernambuco State, Northeastern Brazil. Revista Brasileira de Zootecnia, v.34, n.6, p.2262-2279, 2005. Available from: <>. Accessed: Aug. 24, 2016.

XIX. Vasquez, J.A. et al. Evaluation of non-linear equations to model different animal growths with mono and bisigmoid profiles. Journal of Theoretical Biology, v.314, p.95-105, 2012. Available from: <http://>. Accessed: Aug. 24, 2016.

XX. Viboud, C, Simonsen, L, Chowell, G, “A generalized growth model to characterize the early ascending phase of infectious disease outbreaks,” Epidemics 15, 27–37 (2016).

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