Publications

  • [77] D. Breda, D. Liessi and R. Vermiglio, A practical guide to piecewise pseudospectral collocation for Floquet multipliers of delay equations in MATLAB, submitted, arXiv: 2203.12734 [math.NA].
  • [76] S. De Reggi, F. Scarabel and R. Vermiglio, On the convergence of the pseudospectral approximation of reproduction numbers for age-structured models, submitted, arXiv: 2409.01520 [math.NA, math.DS].
  • [75] R. Challen, L. Dyson, C. E. Overton, L. M. Guzman-Rincon, E. M. Hill, H. B. Stage, E. Brooks-Pollock, L. Pellis, F. Scarabel, D. J. Pascall, P. Blomquist, M. Tildesley, D. Williamson, S. Siegert, X. Xiong, B. Youngman, J. M. Read, J. R. Gog, M. J. Keeling and L. Danon, Early epidemiological signatures of novel SARS-CoV-2 variants: establishment of B.1.617.2 in England, submitted.
  • [74] S. Funk et al., Short-term forecasts to inform the response to the Covid-19 epidemic in the UK, submitted.
  • [73] J. Wu, F. Scarabel, B. Majeed, N. L. Bragazzi and J. Orbinski, The impact of public health interventions on delaying and mitigating against replacement by SARS-CoV-2 variants of concern, submitted.
  • [72] A. Andò and R. Vermiglio, Exponential time integration for delay differential equations via pseudospectral discretization, IFAC-PapersOnLine, to appear.
  • [71] E. Bozzo, D. Breda and M. Tanveer, Sparse identification of time delay systems via pseudospectral collocation, IFAC-PapersOnLine, to appear, arXiv: 2408.01971 [math.DS, math.NA].
  • [70] M. Sabbatino, S. De Reggi and A. Pugliese, A theoretical analysis of mass testing strategies to control epidemics, Bull. Math. Biol., to appear.
  • [69] A. Pecile, N. Demo, M. Tezzele, G. Rozza and D. Breda, Data-driven discovery of delay differential equations with discrete delays, J. Comput. Appl. Math., 461, 116439 (2025), DOI: 10.1016/j.cam.2024.116439.
  • [68] A. Andò, R. Edwards and N. Guglielmi, Nonuniqueness phenomena in discontinuous dynamical systems and their regularizations, SIAM J. Appl. Dyn. Sys., 23 (2024), pp. 1345–1371, DOI: 10.1137/23M1587488.
  • [67] A. Andò and R. Vermiglio, Exponential Runge–Kutta methods for delay equations in the sun–star abstract framework, Discrete Contin. Dyn. Syst. Ser. B (2024), DOI: 10.3934/dcdsb.2024139.
  • [66] D. Breda, S. De Reggi and R. Vermiglio, A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion, SIAM J. Sci. Comp., 46 (2024), A953–A973, DOI: 10.1137/23M1568971.
  • [65] D. Breda and D. Liessi, A practical approach to computing Lyapunov exponents of renewal and delay equations, Math. Biosci. Eng., 21 (2024), pp. 1249–1269, DOI: 10.3934/mbe.2024053.
  • [64] D. Breda and D. Liessi, Lyapunov exponents of renewal equations: Numerical approximation and convergence analysis, Discrete Contin. Dyn. Syst. Ser. B (2024), DOI: 10.3934/dcdsb.2024152.
  • [63] S. De Reggi, F. Scarabel and R. Vermiglio, Approximating reproduction numbers: a general numerical approach for age-structured models, Math. Biosci. Eng., 21 (2024), pp. 5360–5393, DOI: 10.3934/mbe.2024236.
  • [62] F. Scarabel and R. Vermiglio, Equations with infinite delay: pseudospectral discretization for numerical stability and bifurcation in an abstract framework, SIAM J. Numer. Anal., 62 (2024), pp. 1736–1758, DOI: 10.1137/23M1581133.
  • [61] A. Andò and D. Breda, Piecewise orthogonal collocation for computing periodic solutions of renewal equations, Adv. Comput. Math., 49, 93 (2023), DOI: 10.1007/s10444-023-10094-4.
  • [60] A. Andò and D. Breda, Piecewise orthogonal collocation for computing periodic solutions of coupled delay equations, Appl. Numer. Math., 200 (2023), pp. 58–79, DOI: 10.1016/j.apnum.2023.05.010.
  • [59] A. Andò, S. De Reggi, D. Liessi and F. Scarabel, A pseudospectral method for investigating the stability of linear population models with two physiological structures, Math. Biosci. Eng., 20 (2023), pp. 4493–4515, DOI: 10.3934/mbe.2023208.
  • [58] F. Blanchini, D. Breda, G. Giordano and D. Liessi, Michaelis–Menten networks are structurally stable, Automatica, 147, 110683 (2023), DOI: 10.1016/j.automatica.2022.110683.
  • [57] E. Bozzo, P. Deidda and C. Di Fiore, The Jordan and Frobenius pairs of the inverse, Linear Multilinear Algebra, 71 (2023), pp. 1730–1735, DOI: 10.1080/03081087.2022.2073431.
  • [56] D. Breda, ed., Controlling Delayed Dynamics: Advances in Theory, Methods and Applications, CISM 604, Springer, Cham, 2023, DOI: 10.1007/978-3-031-01129-0.
  • [55] D. Breda, Pseudospectral methods for the stability analysis of delay equations. Part I: The infinitesimal generator approach, in D. Breda, ed., Controlling Delayed Dynamics: Advances in Theory, Methods and Applications, CISM 604, Springer, Cham, 2023, pp. 65–94, DOI: 10.1007/978-3-031-01129-0_3.
  • [54] D. Breda, Pseudospectral methods for the stability analysis of delay equations. Part II: The solution operator approach, in D. Breda, ed., Controlling Delayed Dynamics: Advances in Theory, Methods and Applications, CISM 604, Springer, Cham, 2023, pp. 95–116, DOI: 10.1007/978-3-031-01129-0_4.
  • [53] D. Breda, J. K. Canci and R. D’Ambrosio, An invitation to stochastic differential equations in healthcare, in J. K. Canci, P. Mekler and G. Mu, eds., Quantitative Models in Life Science Business: From Value Creation to Business Processes, SpringerBriefs Econ., Springer, Cham, 2023, pp. 97–110, DOI: 10.1007/978-3-031-11814-2_6.
  • [52] D. Breda, D. Liessi and S. M. Verduyn Lunel, Spectra of evolution operators of a class of neutral renewal equations: Theoretical and numerical aspects, Appl. Numer. Math., 200 (2023), pp. 124–137, DOI: 10.1016/j.apnum.2023.06.018.
  • [51] E. Brooks-Pollock, K. Northstone, L. Pellis, F. Scarabel, A. Thomas, E. Nixon, D. A. Matthews, V. Bowyer, M. P. Garcia, C. J. Steves, N. J. Timpson and L. Danon, 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 (2023), DOI: 10.1186/s12916-022-02714-5.
  • [50] G. Fedele, E. Bozzo and L. D’Alfonso, On the impact of agents with influenced opinions in the swarm social behavior, IEEE Signal Syst. Lett., 7 (2023), pp. 2317–2322, DOI: 10.1109/LCSYS.2023.3285884.
  • [49] F. Fontana, E. Bozzo and A. Bernardini, Extended fixed-point methods for the computation of virtual analog models, IEEE Signal Process. Lett., 30 (2023), pp. 848–852, DOI: 10.1109/LSP.2023.3294132.
  • [48] X. Zhang, F. Scarabel, K. Murty and J. Wu, Renewal equations for delayed population behaviour adaptation coupled with disease transmission dynamics: A mechanism for multiple waves of emerging infections, Math. Biosci., 365, 109068 (2023), DOI: 10.1016/j.mbs.2023.109068.
  • [47] A. Andò, D. Breda, D. Liessi, S. Maset, F. Scarabel and R. Vermiglio, 15 years or so of pseudospectral collocation methods for stability and bifurcation of delay equations, in G. Valmorbida, W. Michiels and P. Pepe, eds., Accounting for Constraints in Delay Systems, Adv. Delays Dyn. 12, Springer, Cham, 2022, pp. 127–149, DOI: 10.1007/978-3-030-89014-8_7.
  • [46] D. Breda, S. De Reggi, F. Scarabel, R. Vermiglio and J. Wu, Bivariate collocation for computing \(R_0\) in epidemic models with two structures, Comput. Math. Appl., 116 (2022), DOI: 10.1016/j.camwa.2021.10.026.
  • [45] D. Breda, D. Frizzera, G. Giordano, E. Seffin, V. Zanni, D. Annoscia, C. J. Topping, F. Blanchini and F. Nazzi, A deeper understanding of system interactions can explain contradictory field results on pesticide impact on honey bees, Nature Commun., 13, 5720 (2022), DOI: 10.1038/s41467-022-33405-7.
  • [44] D. Breda, D. Liessi and R. Vermiglio, Piecewise discretization of monodromy operators of delay equations on adapted meshes, J. Comput. Dyn., 9 (2022), pp. 103–121, DOI: 10.3934/jcd.2022004.
  • [43] J. David, N. L. Bragazzi, F. Scarabel, Z. McCarthy and J. Wu, Non-pharmaceutical intervention levels to reduce the COVID-19 attack ratio among children, Roy. Soc. Open Sci., 9, 211863 (2022), DOI: 10.1098/rsos.211863.
  • [42] M. Kretzschmar, B. Ashby, E. Fearon, C. E. Overton, J. Panovska-Griffiths, L. Pellis, M. Quaife, G. Rozhnova, F. Scarabel, H. B. Stage, B. Swallow, R. N. Thompson, M. J. Tildesley and D. Villela, Challenges for modelling interventions for future pandemics, Epidemics, 38, 100546 (2022), DOI: 10.1016/j.epidem.2022.100546.
  • [41] G. Marion, L. Hadley, V. Isham, D. Mollison, J. Panovska-Griffiths, L. Pellis, G. Scalia Tomba, F. Scarabel, B. Swallow, P. Trapman and D. Villela, Modelling: Understanding pandemics and how to control them, Epidemics, 39, 100588 (2022), DOI: 10.1016/j.epidem.2022.1005886.
  • [40] K. Nah, M. Chen, A. Asgary, Z. McCarthy, F. Scarabel, Y. Xiao, N. L. Bragazzi, J. M. Heffernan, N. H. Ogden and J. Wu, Optimal staged reopening schedule based on ICU capacity: A model-informed strategy, in V. K. Murty and J. Wu, eds., Mathematics of Public Health: Proceedings of the Seminar on the Mathematical Modelling of COVID-19, Fields Inst. Commun. 85, Springer, Cham, 2022, pp. 303–321, DOI: 10.1007/978-3-030-85053-1_15.
  • [39] C. E. Overton, L. Pellis, H. B. Stage, F. Scarabel, J. Burton, C. Fraser, I. Hall, T. A. House, C. Jewell, A. Nurtay, F. Pagani and K. A. Lythgoe, EpiBeds: Data informed modelling of the COVID-19 hospital burden in England, PLOS Comput. Biol., 18, e1010406 (2022), DOI: 10.1371/journal.pcbi.1010406.
  • [38] L. Pellis, P. J. Birrell, J. Blake, C. E. Overton, F. Scarabel, H. B. Stage, E. Brooks-Pollock, L. Danon, I. Hall, T. A. House, M. J. Keeling, J. M. Read, JUNIPER consortium and D. De Angelis, Estimation of reproduction numbers in real time: conceptual and statistical challenges, J. Roy. Statist. Soc. Ser. A, 185 (2022), S112–S130, DOI: 10.1111/rssa.12955.
  • [37] L. Pellis, P. J. Birrell, J. Blake, I. Hall, T. A. House, C. E. Overton, F. Scarabel, H. B. Stage and D. De Angelis, 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, J. Roy. Statist. Soc. Ser. A, 185 (2022), S153–S157, DOI: 10.1111/rssa.12984.
  • [36] R. Vermiglio and A. Zamolo, Sensitivity analysis for stability of uncertain delay differential equations using polynomial chaos expansions, in G. Valmorbida, W. Michiels and P. Pepe, eds., Accounting for Constraints in Delay Systems, Adv. Delays Dyn. 12, Springer, Cham, 2022, pp. 151–173, DOI: 10.1007/978-3-030-89014-8_8.
  • [35] X. Zhang, F. Scarabel, X.-S. Wang and J. Wu, Global continuation of periodic oscillations to a diapause rhythm, J. Dynam. Differential Equations, 34 (2022), pp. 2819–2839, DOI: 10.1007/s10884-020-09856-1.
  • [34] A. Andò, Convergence of collocation methods for solving periodic boundary value problems for renewal equations defined through finite-dimensional boundary conditions, Comput. Math. Methods, 3, e1190 (2021), DOI: 10.1002/cmm4.1190.
  • [33] D. Breda, F. Florian, J. Ripoll and R. Vermiglio, Efficient numerical computation of the basic reproduction number for structured populations, J. Comput. Appl. Math., 384, 113165 (2021), DOI: 10.1016/j.cam.2020.113165.
  • [32] D. Breda and D. Liessi, Floquet theory and stability of periodic solutions of renewal equations, J. Dynam. Differential Equations, 33 (2021), pp. 677–714, DOI: 10.1007/s10884-020-09826-7.
  • [31] L. Pellis, F. Scarabel, H. B. Stage, C. E. Overton, L. H. K. Chappell, E. Fearon, E. Bennett, K. A. Lythgoe, T. House, I. Hall and University of Manchester COVID-19 Modelling Group, Challenges in control of COVID-19: short doubling time and long delay to effect of interventions, Philos. Trans. Roy. Soc. B, 376, 20200264 (2021), DOI: 10.1098/rstb.2020.0264.
  • [30] A. Ramírez, D. Breda and R. Sipahi, A scalable approach to compute delay margin of a class of neutral-type time delay systems, SIAM J. Control Optim., 59 (2021), pp. 805–824, DOI: 10.1137/19M1307408.
  • [29] F. Scarabel, D. Breda, O. Diekmann, M. Gyllenberg and R. Vermiglio, Numerical bifurcation analysis of physiologically structured population models via pseudospectral approximation, Vietnam J. Math., 49 (2021), pp. 37–67, DOI: 10.1007/s10013-020-00421-3.
  • [28] F. Scarabel, O. Diekmann and R. Vermiglio, Numerical bifurcation analysis of renewal equations via pseudospectral approximation, J. Comput. Appl. Math., 397, 113611 (2021), DOI: 10.1016/j.cam.2021.113611.
  • [27] F. Scarabel, L. Pellis, N. H. Ogden and J. Wu, A renewal equation model to assess roles and limitations of contact tracing for disease outbreak control, Roy. Soc. Open Sci., 8, 202091 (2021), DOI: 10.1098/rsos.202091.
  • [26] H. B. Stage, J. Shingleton, S. Ghosh, F. Scarabel, L. Pellis and T. Finnie, Shut and re-open: the role of schools in the spread of COVID-19 in Europe, Philos. Trans. Roy. Soc. B, 376, 20200277 (2021), DOI: 10.1098/rstb.2020.0277.
  • [25] B. de Wolff, F. Scarabel, S. Verduyn Lunel and O. Diekmann, Pseudospectral approximation of Hopf bifurcation for delay differential equations, SIAM J. Appl. Dyn. Syst., 20 (2021), pp. 333–370, DOI: 10.1137/20M1347577.
  • [24] J. Wu, F. Scarabel, Z. McCarthy, Y. Xiao and N. H. Ogden, A window of opportunity for intensifying testing and tracing efforts to prevent new COVID-19 outbreaks due to more transmissible variants, Can. Commun. Dis. Rep., 47 (2021), pp. 329–338, DOI: 10.14745/ccdr.v47i78a06.
  • [23] A. Andò and D. Breda, Collocation techniques for structured populations modeled by delay equations, in M. Aguiar, C. Braumann, B. W. Kooi, A. Pugliese, N. Stollenwerk and E. Venturino, eds., Current Trends in Dynamical Systems in Biology and Natural Sciences, SEMA SIMAI Springer Ser. 21, Springer, Cham, 2020, pp. 43–62, DOI: 10.1007/978-3-030-41120-6_3.
  • [22] A. Andò and D. Breda, Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations, SIAM J. Numer. Anal., 58 (2020), pp. 3010–3039, DOI: 10.1137/19M1295015.
  • [21] A. Andò and D. Breda, Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations, arXiv: 2008.07604 [math.NA], 2020. (full version of [22])
  • [20] A. Andò, D. Breda and G. Gava, How fast is the linear chain trick? A rigorous analysis in the context of behavioral epidemiology, Math. Biosci. Eng., 17 (2020), pp. 5059–5084, DOI: 10.3934/mbe.2020273.
  • [19] A. Andò, D. Breda and F. Scarabel, Numerical continuation and delay equations: A novel approach for complex models of structured populations, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), pp. 2619–2640, DOI: 10.3934/dcdss.2020165.
  • [18] D. Breda, T. Kuniya, J. Ripoll and R. Vermiglio, Collocation of next-generation operators for computing the basic reproduction number of structured populations, J. Sci. Comput., 85, 40 (2020), DOI: 10.1007/s10915-020-01339-1.
  • [17] D. Breda and D. Liessi, Approximation of eigenvalues of evolution operators for linear coupled renewal and retarded functional differential equations, Ric. Mat., 69 (2020), pp. 457–481, DOI: 10.1007/s11587-020-00513-9.
  • [16] O. Diekmann, F. Scarabel and R. Vermiglio, Pseudospectral discretization of delay differential equations in sun-star formulation: Results and conjectures, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), pp. 2575–2602, DOI: 10.3934/dcdss.2020196.
  • [15] F. Florian and R. Vermiglio, PC-based sensitivity analysis of the basic reproduction number of population and epidemic models, in M. Aguiar, C. Braumann, B. W. Kooi, A. Pugliese, N. Stollenwerk and E. Venturino, eds., Current Trends in Dynamical Systems in Biology and Natural Sciences, SEMA SIMAI Springer Ser. 21, Springer, Cham, 2020, pp. 205–222, DOI: 10.1007/978-3-030-41120-6_11.
  • [14] Z. McCarthy, Y. Xiao, F. Scarabel, B. Tang, N. L. Bragazzi, K. Nah, J. M. Heffernan, A. Asgary, V. K. Murty, N. H. Ogden and J. Wu, Quantifying the shift in social contact patterns in response to non-pharmaceutical interventions, J. Math. Ind., 10, 28 (2020), DOI: 10.1186/s13362-020-00096-y.
  • [13] F. Scarabel, L. Pellis, N. L. Bragazzi and J. Wu, Canada needs to rapidly escalate public health interventions for its COVID-19 mitigation strategies, Infectious Disease Modelling, 5 (2020), pp. 316–322, DOI: 10.1016/j.idm.2020.03.004.
  • [12] B. Tang, F. Scarabel, N. L. Bragazzi, Z. McCarthy, M. Glazer, Y. Xiao, J. M. Heffernan, A. Asgary, N. H. Ogden and J. Wu, 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, 100 (2020), DOI: 10.3390/biology9050100.
  • [11] P. Getto, M. Gyllenberg, Y. Nakata and F. Scarabel, Stability analysis of a state-dependent delay differential equation for cell maturation: Analytical and numerical methods, J. Math. Biol., 79 (2019), pp. 281–328, DOI: 10.1007/s00285-019-01357-0.
  • [10] M. Sadeghpour, D. Breda and G. Orosz, Stability of linear continuous-time systems with stochastically changing delay, IEEE Trans. Automat. Control, 64 (2019), pp. 4741–4747, DOI: 10.1109/TAC.2019.2904491.
  • [9] D. Breda and S. Della Schiava, Pseudospectral reduction to compute Lyapunov exponents of delay differential equations, Discrete Contin. Dyn. Syst. Ser. B, 23 (2018), pp. 2727–2741, DOI: 10.3934/dcdsb.2018092.
  • [8] D. Breda and D. Liessi, Approximation of eigenvalues of evolution operators for linear renewal equations, SIAM J. Numer. Anal., 56 (2018), pp. 1456–1481, DOI: 10.1137/17M1140534.
  • [7] D. Breda, G. Menegon and M. Nonino, Delay equations and characteristic roots: Stability and more from a single curve, Electron. J. Qual. Theory Differ. Equ., 2018, 89 (2018), pp. 1–22, DOI: 10.14232/ejqtde.2018.1.89.
  • [6] M. Gyllenberg, F. Scarabel and R. Vermiglio, Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization, Appl. Math. Comput., 333 (2018), pp. 490–505, DOI: 10.1016/j.amc.2018.03.104.
  • [5] V. Clamer, A. Pugliese, D. Liessi and D. Breda, Host coexistence in a model for two host–one parasitoid interactions, J. Math. Biol., 75 (2017), pp. 419–441, DOI: 10.1007/s00285-016-1088-z.
  • [4] R. Vermiglio, Polynomial chaos expansions for the stability analysis of uncertain delay differential equations, SIAM/ASA J. Uncert. Quant., 5 (2017), pp. 278–303, DOI: 10.1137/15M1029618.
  • [3] D. Breda, O. Diekmann, M. Gyllenberg, F. Scarabel and R. Vermiglio, Pseudospectral discretization of nonlinear delay equations: New prospects for numerical bifurcation analysis, SIAM J. Appl. Dyn. Syst., 15 (2016), pp. 1–23, DOI: 10.1137/15M1040931.
  • [2] D. Breda, O. Diekmann, D. Liessi and F. Scarabel, Numerical bifurcation analysis of a class of nonlinear renewal equations, Electron. J. Qual. Theory Differ. Equ., 2016, 65 (2016), pp. 1–24, DOI: 10.14232/ejqtde.2016.1.65.
  • [1] R. Vermiglio, Numerical approximation of the non-essential spectrum of abstract delay differential equations, Math. Comput. Simulat., 125 (2016), pp. 56–69, DOI: 10.1016/j.matcom.2015.10.009.