Abstract
We propose a pipeline for the stochastic analysis of a SIR model for COVID-19 through the stochastic model checker PRISM. The pipeline consists in: (i) the definition of a modified SIR model, able to include governmental restriction and prevention measures through an additional time-dependent coefficient; (ii) parameter estimation based on real epidemic data; (iii) translation of the modified SIR model into a Continuous Time Markov Chain (CTMC) expressed using the PRISM input language; and (iv) stochastic analysis (simulation and model checking) with PRISM.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Agenzia Regionale di Sanita (ARS), https://www.ars.toscana.it/.
- 2.
Freely available at http://dati.toscana.it/dataset/open-data-covid19.
- 3.
GitHub repository: https://github.com/Unipisa/SIR-covid.
References
PRISM Probabilistic Model Checker. https://www.prismmodelchecker.org/
Acemoglu, D., et al.: A multi-risk SIR model with optimally targeted lockdown. Tech. rep., National Bureau of Economic Research (2020)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61474-5_75
Barbuti, R., Levi, F., Milazzo, P., Scatena, G.: Probabilistic model checking of biological systems with uncertain kinetic rates. Theor. Comput. Sci. 419, 2–16 (2012)
Calafiore, G.C., Novara, C., Possieri, C.: A modified SIR model for the COVID-19 contagion in Italy. arXiv preprint arXiv:2003.14391 (2020)
Chen, Y.C., Lu, P.E., Chang, C.S.: A time-dependent SIR model for COVID-19. arXiv preprint arXiv:2003.00122 (2020)
D’Arienzo, M., Coniglio, A.: Assessment of the SARS-CoV-2 basic reproduction number, R0, based on the early phase of COVID-19 outbreak in Italy. Biosaf. Health 2, 57–59 (2020)
Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Character 115(772), 700–721 (1927)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_47
Acknowledgements
This work is supported by the Università di Pisa under the “PRA – Progetti di Ricerca di Ateneo” (Institutional Research Grants) - Project no. PRA_2020-2021_26 “Metodi Informatici Integrati per la Biomedica”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Milazzo, P. (2021). Analysis of COVID-19 Data with PRISM: Parameter Estimation and SIR Modelling. In: Bowles, J., Broccia, G., Nanni, M. (eds) From Data to Models and Back. DataMod 2020. Lecture Notes in Computer Science(), vol 12611. Springer, Cham. https://doi.org/10.1007/978-3-030-70650-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-70650-0_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-70649-4
Online ISBN: 978-3-030-70650-0
eBook Packages: Computer ScienceComputer Science (R0)