The Effect of Swabs on Modeling the First Wave of the COVID-19 Pandemic in Italy

Claudia Furlan, Cinzia Mortarino


The daily fluctuations in the released number of Covid-19 cases played a big role at the beginning of the pandemic, when local authorities in Italy had to decide whether imposing restrictive policies. When an increase/decrease was communicated, especially a large one, it was difficult to understand if it was due to a change in the epidemic evolution or if it was a fluctuation due to other reasons, such as an increase in the number of swabs or a delay in the swab processing. The aim of this paper is both to model the main trend of the outbreak evolution in the number of confirmed cases and to describe the daily fluctuations strongly dependent on the daily number of swabs. For our analysis, we propose a nonlinear asymmetric diffusion model, which includes information on the daily number of swabs, to describe daily fluctuations in the number of confirmed cases in addition to the main trend of the outbreak evolution. The proposed model is found to be the more efficient for prediction, as compared to 6 already existing models, including the SIRD and the logistic models. The new model combines the properties of innovation diffusion models with a parsimonious way to exploit information about swabs.


Doi: 10.28991/esj-2021-SPER-04

Full Text: PDF


Nonlinear Models; Generalized Bass Model; Logistic; SIRD Model; Compartmental Model; Diffusion; Epidemic.


Lavezzo, Enrico, Elisa Franchin, Constanze Ciavarella, Gina Cuomo-Dannenburg, Luisa Barzon, Claudia Del Vecchio, et al. “Suppression of a SARS-CoV-2 Outbreak in the Italian Municipality of Vo’.” Nature 584 (June 30, 2020): 425–429. doi:10.1038/s41586-020-2488-1.

Indolfi, Ciro, and Carmen Spaccarotella. “The Outbreak of COVID-19 in Italy.” JACC: Case Reports 2, no. 9 (July 2020): 1414–1418. doi:10.1016/j.jaccas.2020.03.012.

Gregori, Dario, Danila Azzolina, Corrado Lanera, Ilaria Prosepe, Nicolas Destro, Giulia Lorenzoni, and Paola Berchialla. “A First Estimation of the Impact of Public Health Actions against COVID-19 in Veneto (Italy).” Journal of Epidemiology and Community Health 74, no. 10 (May 4, 2020): 858–860. doi:10.1136/jech-2020-214209.

Farcomeni, Alessio, Antonello Maruotti, Fabio Divino, Giovanna Jona Lasinio, and Gianfranco Lovison. “An Ensemble Approach to Short-term Forecast of COVID-19 Intensive Care Occupancy in Italian Regions.” Biometrical Journal 63, no. 3 (November 30, 2021): 503–513. doi:10.1002/bimj.202000189.

Remuzzi, Andrea, and Giuseppe Remuzzi. “COVID-19 and Italy: What Next?” The Lancet 395, no. 10231 (April 2020): 1225–1228. doi:10.1016/s0140-6736(20)30627-9.

Batista, Milan. “Estimation of the Final Size of the Second Phase of the Coronavirus COVID 19 Epidemic by the Logistic Model” MedRxiv (March 16, 2020). doi:10.1101/2020.03.11.20024901.

Shen, Christopher Y. “Logistic Growth Modelling of COVID-19 Proliferation in China and Its International Implications.” International Journal of Infectious Diseases 96 (July 2020): 582–589. doi:10.1016/j.ijid.2020.04.085.

Anastassopoulou, Cleo, Lucia Russo, Athanasios Tsakris, and Constantinos Siettos. “Data-Based Analysis, Modelling and Forecasting of the COVID-19 Outbreak.” PLOS ONE 15, no. 3 (March 31, 2020): e0230405. doi:10.1371/journal.pone.0230405.

Batista, Milan. “Estimation of the Final Size of the COVID-19 Epidemic” MedRxiv (February 18, 2020). doi:10.1101/2020.02.16.20023606.

Caccavo, Diego. “Chinese and Italian COVID-19 Outbreaks Can Be Correctly Described by a Modified SIRD Model.” MedRxiv (March 23, 2020). doi:10.1101/2020.03.19.20039388.

Fanelli, Duccio, and Francesco Piazza. “Analysis and Forecast of COVID-19 Spreading in China, Italy and France.” Chaos, Solitons & Fractals 134 (May 2020): 109761. doi:10.1016/j.chaos.2020.109761.

Ivorra, B., M.R. Ferrández, M. Vela-Pérez, and A.M. Ramos. “Mathematical Modeling of the Spread of the Coronavirus Disease 2019 (COVID-19) Taking into Account the Undetected Infections. The Case of China.” Communications in Nonlinear Science and Numerical Simulation 88 (September 2020): 105303. doi:10.1016/j.cnsns.2020.105303.

Iwata, Kentaro, and Chisato Miyakoshi. “A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model.” Journal of Clinical Medicine 9, no. 4 (March 30, 2020): 944. doi:10.3390/jcm9040944.

Liu, M., J. Ning, Y. Du, J. Cao, D. Zhang, J. Wang, and M. Chen. “Modelling the Evolution Trajectory of COVID-19 in Wuhan, China: Experience and Suggestions.” Public Health 183 (June 2020): 76–80. doi:10.1016/j.puhe.2020.05.001.

Postnikov, Eugene B. “Estimation of COVID-19 Dynamics ‘on a Back-of-Envelope’: Does the Simplest SIR Model Provide Quantitative Parameters and Predictions?” Chaos, Solitons & Fractals 135 (June 2020): 109841. doi:10.1016/j.chaos.2020.109841.

Wangping, Jia, Han Ke, Song Yang, Cao Wenzhe, Wang Shengshu, Yang Shanshan, Wang Jianwei, et al. “Extended SIR Prediction of the Epidemics Trend of COVID-19 in Italy and Compared With Hunan, China.” Frontiers in Medicine 7 (May 6, 2020): 169. doi:10.3389/fmed.2020.00169.

Xiang, Yue, Yonghong Jia, Linlin Chen, Lei Guo, Bizhen Shu, and Enshen Long. “COVID-19 Epidemic Prediction and the Impact of Public Health Interventions: A Review of COVID-19 Epidemic Models.” Infectious Disease Modelling 6 (2021): 324–342. doi:10.1016/j.idm.2021.01.001.

Guliyev, Hasraddin. “Determining the Spatial Effects of COVID-19 Using the Spatial Panel Data Model.” Spatial Statistics 38 (August 2020): 100443. doi:10.1016/j.spasta.2020.100443.

Bartolucci, Francesco, and Alessio Farcomeni. “A Spatio-Temporal Model Based on Discrete Latent Variables for the Analysis of COVID-19 Incidence.” Spatial Statistics (March 2021): 100504. doi:10.1016/j.spasta.2021.100504.

Benvenuto, Domenico, Marta Giovanetti, Lazzaro Vassallo, Silvia Angeletti, and Massimo Ciccozzi. “Application of the ARIMA Model on the COVID-2019 Epidemic Dataset.” Data in Brief 29 (April 2020): 105340. doi:10.1016/j.dib.2020.105340.

Chintalapudi, Nalini, Gopi Battineni, and Francesco Amenta. “COVID-19 Virus Outbreak Forecasting of Registered and Recovered Cases after Sixty Day Lockdown in Italy: A Data Driven Model Approach.” Journal of Microbiology, Immunology and Infection 53, no. 3 (June 2020): 396–403. doi:10.1016/j.jmii.2020.04.004.

Triacca, Marco, and Umberto Triacca. “Forecasting the Number of Confirmed New Cases of COVID-19 in Italy for the Period from 19 May to 2 June 2020.” Infectious Disease Modelling 6 (2021): 362–369. doi:10.1016/j.idm.2021.01.003.

Guseo, Renato, and Mariangela Guidolin. “Modelling a Dynamic Market Potential: A Class of Automata Networks for Diffusion of Innovations.” Technological Forecasting and Social Change 76, no. 6 (July 2009): 806–820. doi:10.1016/j.techfore.2008.10.005.

Bass, Frank M., Trichy V. Krishnan, and Dipak C. Jain. “Why the Bass Model Fits Without Decision Variables.” Marketing Science 13, no. 3 (August 1994): 203–223. doi:10.1287/mksc.13.3.203.

Bemmaor, Albert C. “Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect Versus Consumer Heterogeneity.” In: Laurent G., Lilien G.L., Pras B. (eds). Research Traditions in Marketing (1992): 201–229. Springer. doi:10.1007/978-94-011-1402-8_6.

Guidolin, Mariangela, and Renato Guseo. “Modelling Seasonality in Innovation Diffusion.” Technological Forecasting and Social Change 86 (July 2014): 33–40. doi:10.1016/j.techfore.2013.08.017.

Civil Protection Department website - Presidency of the Council of Ministers. Data Repository (2020). Available online: (accessed on 02 May 2020).

Regione Lombardia. Coronavirus in Lombardia, aggiornamento delle ore 19 (February 2020). Available online: (accessed on 05 May 2020).

L’eco di Bergamo. Coronavirus, 118 casi e tre vittime. Regione: “Limitare gli assembramenti” (February 2020). Available online: (accessed on 05 May 2020).

Regione Emilia-Romagna. Aggiornamento Coronavirus, 115 casi positivi in Emilia-Romagna, 1.224 tamponi refertati (February 2020). Available online: (accessed on 05 May 2020).

ModenaToday. Coronavirus. Oggi 412 casi in più in regione, ma pochi tamponi: il calo va verificato domani (March 2020). Available online: (accessed on 05 May 2020).

Guseo, Renato, and Alessandra Dalla Valle. “Oil and Gas Depletion: Diffusion Models and Forecasting Under Strategic Intervention.” Statistical Methods and Applications 14, no. 3 (December 2005): 375–387. doi:10.1007/s10260-005-0118-6.

Ben Bolker and R Development Core Team. “bbmle: Tools for General Maximum Likelihood Estimation, 2020.” R package version Available online: (accessed on 15 May 2021).

Guseo, Renato, and Cinzia Mortarino. “Modeling Competition Between Two Pharmaceutical Drugs Using Innovation Diffusion Models.” The Annals of Applied Statistics 9, no. 4 (December 1, 2015): 2073–2089. doi:10.1214/15-aoas868.

Guseo, Renato, Alessandra Dalla Valle, Claudia Furlan, Mariangela Guidolin, and Cinzia Mortarino. “Pre-Launch Forecasting of a Pharmaceutical Drug.” International Journal of Pharmaceutical and Healthcare Marketing 11, no. 4 (November 6, 2017): 412–438. doi:10.1108/ijphm-07-2016-0036.

Full Text: PDF

DOI: 10.28991/esj-2021-SPER-04


  • There are currently no refbacks.

Copyright (c) 2021 Cinzia Mortarino, Claudia Furlan