Publications

Preprints and submitted manuscripts

Diekmann, O., and Scarabel F. Size-Structured Population Dynamics, arXiv:2506.03413
Diekmann, O., and Scarabel F. Age-Structured Population Dynamics, arXiv:2506.03405
De Reggi, S., Scarabel, F., and Vermiglio, R. (2025) On the convergence of the pseudospectral approximation of reproduction numbers for age-structured models. Available on arXiv.
Scarabel, F., Coldwell, H., and Cassidy, T. (2025) Genuine and spurious bistability in a simple epidemic model with waning immunity. Available on arXiv.
Liessi, D., Santi, E., Vermiglio, R., Thakur, M., Meijer, H.G.E., and Scarabel, F., New functionalities in MatCont: delay equations and Lyapunov exponents, submitted. PREPRINT
Han, Q., Xiao, Y., Shafadeh, M., Scarabel, F., McCarthy, Z., Su, Q., Bragazzi, N.L., Song, P., Lee, J., Shin, T., Thommes, E., Tomovici, A., Chit, A., and Wu, J. Pertussis transmission dynamics and demographic shifts under evolving vaccination programs and the benefits of adult boosting, submitted.
Funk, S., et al. Short-term forecasts to inform the response to the Covid-19 epidemic in the UK, submitted. PREPRINT
Challen, R., Dyson, L., Overton, C.E., Guzman-Rincon, L.M., Hill, E.M., Stage, H.B., Brooks-Pollock, E., Pellis, L., Scarabel, F., Pascall, D.J., Blomquist, P., Tildesley, M., Williamson, D., Siegert, S., Xiong, X., Youngman, B., Read, J.M., Gog, J.R., Keeling, M.J., Danon, L. Early epidemiological signatures of novel SARS-CoV-2 variants: establishment of B.1.617.2 in England, submitted. PREPRINT
Wu, J., Scarabel, F., Majeed, B., Bragazzi, N.L., Orbinski, J. The impact of public health interventions on delaying and mitigating against replacement by SARS-CoV-2 variants of concern, submitted. PREPRINT

2026

Andò, A., De Reggi, S., Scarabel, F., Vermiglio, R., and Wu J. (2026) Behavior-induced oscillations in epidemic outbreaks with distributed memory: beyond the linear chain trick using numerical methods, Mathematical Biosciences and Engineering, 23(1), 76-96. https://doi.org/10.3934/mbe.2026004

2025

Scarabel, F., Polner, M., Wylde, D., Barbarossa, M.V., and Röst, G. (2025) Bistability and complex bifurcation diagrams generated by waning and boosting of immunity, Journal of Mathematical Biology, 91:30. https://doi.org/10.1007/s00285-025-02264-3
Scarabel, F., and Vermiglio, R. (2025) Equations with infinite delay: numerical stability via truncated Laguerre formulas, IFAC-PapersOnLine, 59(13): 105-110. https://doi.org/10.1016/j.ifacol.2025.10.019

2024

Scarabel, F., and Vermiglio, R. (2024) Equations with infinite delay: pseudospectral discretization for numerical stability and bifurcation in an abstract framework, SIAM Journal on Numerical Analysis, 62(4), 1736-1758. https://doi.org/10.1137/23M1581133. Also available on arXiv.
De Reggi, S., Scarabel, F., and Vermiglio, R. (2024) Approximating reproduction numbers: a general numerical method for age-structured models, Mathematical Biosciences and Engineering, 21(4), 5360-5393. https://doi.org/10.3934/mbe.2024236. Part of the Special Issue: Modelling and computational strategies for infectious disease dynamics and ecology of structured populations

2023

Zhang, X., Scarabel, F., Murty, K., Wu, J. (2023) Renewal equations for delayed population behaviour adaptation coupled with disease transmission dynamics: a mechanism for multiple waves of emerging infections, Mathematical Biosciences, 365:109068. https://doi.org/10.1016/j.mbs.2023.109068
Brooks-Pollock, E., Northstone, K., Pellis, L., Scarabel, F., Thomas, A., Nixon, E., Matthews, D.A., Bowyer, V., Garcia, M.P., Stevens, C.J., Timpson, N.J., Danon, L. (2023) Voluntary risk mitigation behaviour can reduce impact of SARS-CoV-2: a real-time modelling study of the January 2022 Omicron wave in England, BMC Medicine, 21:25. https://doi.org/10.1186/s12916-022-02714-5
Andò, A., De Reggi, S., Liessi, D., Scarabel, F. (2023) A pseudospectral method for investigating the stability of linear population models with two physiological structures, Mathematical Biosciences and Engineering, 20(3):4493-4515. https://doi.org/10.3934/mbe.2023208. Part of the Special Issue: Modelling and computational strategies for infectious disease dynamics and ecology of structured populations

2022

Pellis, L., Birrell, P.J., Blake, J., Hall, I., House, T.A., Overton, C.E., Scarabel, F., Stage, H.B., De Angelis, D. (2022) Authors' reply to the discussion of 'Estimation of reproduction numbers in real time: conceptual and statistical challenges' by Pellis et al. in Session 3 of the Royal Statistical Society's Special Topic Meeting on COVID-19 transmission: 11 June 2021, Journal of the Royal Statistical Society A, 185 (Suppl. 1), S153-S157. https://doi.org/10.1111/rssa.12984
Pellis, L., Birrell, P.J., Blake, J., Overton, C.E., Scarabel, F., Stage, H.B., Brooks-Pollock, E., Danon, L., Keeling, M.J., Read, J.M., JUNIPER consortium, De Angelis, D. (2022) Estimation of reproduction numbers in real time: conceptual and statistical challenges, Journal of the Royal Statistical Society A, 185 (Suppl. 1), S112-S130. https://doi.org/10.1111/rssa.12955
Overton, C.E., Pellis, L., Stage, H.B., Scarabel, F., Burton, J., Fraser, C., Hall, I., House, T.A., Jewell, C., Nurtay, A., Pagani, F., Lythgoe, K.A. (2022) EpiBeds: Data informed modelling of the COVID-19 hospital burden in England, PLOS Computational Biology, 18(9):e1010406. https://doi.org/10.1371/journal.pcbi.1010406
Marion, G., Hadley, L., Isham, V., Mollison, D., Panovska-Griffiths, J., Pellis, L., Scalia Tomba, G., Scarabel, F., Swallow, B., Trapman, P., Villela, D. (2022) Modelling: understanding pandemics and how to control them, Epidemics, 39:100588. https://doi.org/10.1016/j.epidem.2022.100588
Kretzschmar, M.E., Ashby, B., Fearon, E., Overton, C.E., Panovska-Griffiths, J., Pellis, L., Quaife, M., Roznhova, G., Scarabel, F., Stage, H.B., Swallow, B., Thompson, R.N., Tildesley, M.J., Villela, F. (2022) Challenges for modelling interventions for future pandemics, Epidemics, 38:100546. https://doi.org/10.1016/j.epidem.2022.100546
David, J., Bragazzi, N.L., Scarabel, F., McCarthy, Z.M., Wu, J. (2022) Non-pharmaceutical intervention levels to reduce the COVID-19 attack ratio among children, Royal Society Open Science, 9:211863. https://doi.org/10.1098/rsos.211863
Zhang, X., Scarabel, F., Wang, X., Wu, J. (2022) Global Continuation of Periodic Oscillations to a Diapause Rhythm. Journal of Dynamics and Differential Equations, 34, 2819-2839. https://doi.org/10.1007/s10884-020-09856-1
Breda, D., De Reggi, S., Scarabel, F., Vermiglio, R., Wu, J. (2022) Bivariate collocation for computing R0 in epidemic models with two structures, Computers & Mathematics with Applications, 116, 15-24. https://doi.org/10.1016/j.camwa.2021.10.026 - arXiv PREPRINT

2021

Wu, J., Scarabel, F., McCarthy, Z., Xiao, Y., Ogden, N.H. (2021) A window of opportunity for intensifying testing and tracing efforts to prevent new COVID-19 outbreaks due to more transmissible variants. Canada Communicable Disease Report, 47(7/8), 329–338. https://doi.org/10.14745/ccdr.v47i78a06
Pellis, L., Scarabel, F., Stage, H.B., Overton, C.E., Chappell, L.H.K., Fearon, E., Bennett, E., University of Manchester COVID-19 Modelling Group, Lythgoe, K.A., House, T.A., Hall, I. (2021) Challenges in control of Covid-19: short doubling time and long delay to effect of interventions, Philosophical Transactions of the Royal Society B, 376:20200264. https://doi.org/10.1098/rstb.2020.0264
Stage, H.B., Shingleton, J., Ghosh, S., Scarabel, F., Pellis, L., Finnie, T. (2021) Shut and re-open: the role of schools in the spread of COVID-19 in Europe, Philosophical Transactions of the Royal Society B, 376:20200277. https://doi.org/10.1098/rstb.2020.0277
Scarabel, F., Pellis, L., Ogden, N.H., Wu, J. (2021) A renewal equation model to assess roles and limitations of contact tracing for disease outbreak control, Royal Society Open Science, 8:202091. http://doi.org/10.1098/rsos.202091
Scarabel, F., Diekmann, O., Vermiglio, R. (2021) Numerical bifurcation analysis of renewal equations via pseudospectral approximation, Journal of Computational and Applied Mathematics, 397:113611. https://doi.org/10.1016/j.cam.2021.113611
De Wolff, B., Scarabel, F., Verduyn Lunel, S., Diekmann, O. (2021) Pseudospectral approximation of Hopf bifurcation for delay differential equations, SIAM Journal on Applied Dynamical Systems, 20(1), 333–370. https://doi.org/10.1137/20M1347577 - arXiv PREPRINT
Scarabel, F., Breda, D., Diekmann, O., Gyllenberg, M., Vermiglio, R. (2021) Numerical bifurcation analysis of physiologically structured population models via pseudospectral approximation, Vietnam Journal of Mathematics, 49, 37–67. https://doi.org/10.1007/s10013-020-00421-3 and CODES

2020

McCarthy, Z., Xiao, Y., Scarabel, F., Tang, B., Bragazzi, N.L., Nah, K., Heffernan, J., Asgary, A., Murty, K., Ogden, N.H., Wu, J. (2020) Quantifying the shift in social contact patterns in response to non-pharmaceutical interventions, Journal of Mathematics in Industry, 10(28). https://doi.org/10.1186/s13362-020-00096-y
Tang, B., Scarabel, F., Bragazzi, N.L., McCarthy, Z., Glazer, M., Xiao, Y., Heffernan, J.M., Asgary, A., Ogden, N.H., Wu, J. (2020) De-escalation by Reversing the Escalation with a Stronger Synergistic Package of Contact Tracing, Quarantine, Isolation and Personal Protection: Feasibility of Preventing a COVID-19 Rebound in Ontario, Canada, as a Case Study. Biology, 9(5), 100. https://doi.org/10.3390/biology9050100
Scarabel, F., Pellis, L., Bragazzi, N.L., Wu, J. (2020) Canada Needs to Rapidly Escalate Public Health Interventions for Its COVID-19 Mitigation Strategies. Infectious Disease Modelling, 5, 316-322. https://doi.org/10.1016/j.idm.2020.03.004
Diekmann, O., Scarabel, F., Vermiglio, R. (2020) Pseudospectral discretization of delay differential equations in sun-star formulation: results and conjectures, Discrete and Continuous Dynamical Systems Series - S, 13(9): 2575-2602. https://doi.org/10.3934/dcdss.2020196
Andò, A., Breda, D., Scarabel, F. (2020) Numerical continuation and delay equations: A novel approach for complex models of structured populations, Discrete and Continuous Dynamical Systems Series - S, 13(9): 2619-2640. https://doi.org/10.3934/dcdss.2020165

2019

Getto, Ph., Gyllenberg, M., Nakata, Y., Scarabel, F. (2019) Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods, Journal of Mathematical Biology, 79(1), 281-328. https://doi.org/10.1007/s00285-019-01357-0

2018

Gyllenberg, M., Scarabel, F., Vermiglio, R. (2018) Equations with infinite delay: numerical bifurcation analysis via pseudospectral discretization, Applied Mathematics and Computation, 333, 490–505. https://doi.org/10.1016/j.amc.2018.03.104

2016
MATLAB CODES

Breda, D., Diekmann, O., Liessi, D., Scarabel, F. (2016) Numerical bifurcation analysis of a class of nonlinear renewal equations, Electronic Journal of Qualitative Theory of Differential Equations, 65, 1–24. https://doi.org/10.14232/ejqtde.2016.1.65
Breda, D., Diekmann, O., Gyllenberg, M., Scarabel, F., Vermiglio, R. (2016) Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis, SIAM Journal on Applied Dynamical Systems, 15(1), 1–23. https://doi.org/10.1137/15M1040931

Book chapters

Nah, K., Chen, M., Asgary, A., McCarthy, Z., Scarabel, F., Xiao, Y., Bragazzi, N.L., Heffernan, J.M., Ogden, N.H., Wu, J. (2022) Optimal Staged Reopening Schedule Based on ICU Capacity: A Model-Informed Strategy. In: Murty V.K., Wu J. (eds) Mathematics of Public Health. Fields Institute Communications, vol 85. Springer, Cham. https://doi.org/10.1007/978-3-030-85053-1_15
Andò, A., Breda, D., Liessi, D., Maset, S., Scarabel, F., Vermiglio, R. (2022) 15 Years or So of Pseudospectral Collocation Methods for Stability and Bifurcation of Delay Equations. In: Valmorbida, G., Michiels, W., Pepe, P. (eds) Accounting for Constraints in Delay Systems. Advances in Delays and Dynamics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-89014-8_7

PhD Thesis

Scarabel, F. (2018) Capture the past to portray the future: Numerical bifurcation analysis of delay equations, with a focus on population dynamics. PhD thesis, University of Helsinki. Available online.

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