Pinaki Pal,Asish Mitra,



5PL Function,Covid-19 Pandemic,Daily Growth Rate,Iceland,Simulation,Tipping Point,


Right now, investigations are rigorously carried out on modeling the dynamic progress of (Covid-19) pandemic around the globe. Here we introduce a simple mathematical model for analyzing the dynamics of the Covid-19, considering only the number of cumulative cases. In the present work, the 5PL function is applied to study the Covid-19 spread in Iceland. The cumulative number of infected persons C(t) has been accurately fitted with the 5PL equation, giving rise to different epidemiological parameters. The result of the current examination reveals the effectiveness and efficacy of the 5PL function for exploring the Covid 19 dynamics in Iceland. The mathematical model is simple enough such that practitioners knowing algebra and non-linear regression analysis can employ it to examining the pandemic situation in different countries.


I. Anton H, Herr A, “Calculus with analytic geometry,” Wiley New York; 1988.
II. 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
III. 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
IV. Birch C P, “A new generalized logistic sigmoid growth equation compared with the Richards growth equation,” Annals of Botany. 1999; 83(6):713–723.
V. Cao L, Shi P J, Li L, Chen G, “A New Flexible Sigmoidal Growth Model,” Symmetry. 2019; 11(2):204.
VI. Causton D A, “Computer program for fitting the Richards function,” Biometrics. 1969; p. 401–409.
VII. Centers for Disease Control and Prevention, “Cases of coronavirus disease (COVID-19) in the U.S.,” 2020. [cited 2020, Apr 7]. Available from:
VIII. 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).
IX. 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).
X. 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).
XI. 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).

XII. D Rodbard, P J Munson, A DeLean, “Improved Curve Fitting, Parallelism Testing, Characterization of Sensitivity and Specificity, Validation, and Optimization for Radioimmunoassays 1977,” Radioimmunoassay and Related Procedures in Medicine 1, Vienna: Int Atomic Energy Agency (1978) 469–504.
XIII. Dingyu Xue, “Solving applied mathematical problems with MATLAB,” Chapman & Hall/CRC.
XIV. Hsieh Y H, Lee J Y, Chang H L, “SARS epidemiology modeling. Emerging infectious diseases,” 2004; 10(6):1165. PMID: 15224675.
XV. Hsieh Y H, “Richards model: a simple procedure for real-time prediction of outbreak severity. In: Modelingand dynamics of infectious diseases,” World Scientific; 2009. p. 216–236.
XVI. Hsieh Y H, Ma S, “Intervention measures, turning point, and reproduction number for dengue, Singapore, 2005,” The American journal of tropical medicine and hygiene. 2009; 80(1):66–71. PMID: 19141842.
XVII. Hsieh Y H, Chen C, “Turning points, reproduction number, and impact of climatological events for multiwave dengue outbreaks,” Tropical Medicine & International Health. 2009, 14(6):628–638.
XVIII. Hsieh Y H, “Pandemic influenza A (H1N1) during winter influenza season in the southern hemisphere,” Influenza and Other Respiratory Viruses. 2010; 4(4):187–197. PMID: 20629772.
XX. Kahm M, Hasenbrink G, Lichtenberg-Frate´ H, Ludwig J, Kschischo M grofit, “Fitting biological growth curves with R,” J Stat. Softw. 33: 1–21; 2010.
XXI. Lee Se Yoon, Lei Bowen, Mallick Bani, “Estimation of COVID-19 spread curves integrating global data and borrowing information.” PLOS ONE. 15 (7), 2020: e0236860. arXiv:2005.00662 ( PMC7390340).
XXII. M Straume, J D Veldhuis, M L Johnson, “Model-independent quantification of measurement error: empirical estimation of discrete variance function profiles based on standard curves,” Methods Enzymol. 240 (1994) 121–150.
XXIII. R L A Prentice, “A generalization of the probit and logit methods for dose–response curves,” Biometrics 32 (1976) 761–768.
XXIV. R A Dudley, P Edwards, R P Ekins, D J Finney, I G M McKenzie, G M Raab, D Rodbard, R P C Rodgers, “Guidelines for immunoassay data processing,” Clin. Chem. 31 (1985) 1264–1271.
XXV. Seber G A, Wild C J, “Nonlinear Regression,” Hoboken. New Jersey: John Wiley & Sons. 2003; 62:63.
XXVI. Werker A, Jaggard K, “Modelling asymmetrical growth curves that rise and then fall: applications to foliage dynamics of sugar beet (Beta vulgaris L.),” Annals of Botany. 1997; 79(6):657–665.
XXVII. Wu K, Darcet D, Wang Q, Sornette D, “Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world,” arXiv preprint arXiv:200305681. 2020.
XXVIII. 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).

View Download