Submitted
  1. M. Fraia, N. Loy, A. Tosin
    Linear inelastic kinetic equations modelling the spread of fake news and its interplay with personal awareness
    2024. doi:10.13140/RG.2.2.35791.80805 › [preprint]
  2. S. Göttlich, T. Schillinger, A. Tosin
    Probabilistic modelling of car traffic accidents
    2024. doi:10.13140/RG.2.2.30080.85769 › [preprint]
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Papers
  1. E. Cristiani, N. Loy, M. Menci, A. Tosin
    Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions
    Math. Comput. Simulation, 228:362-385, 2025 › paper [preprint]
  2. F. A. Chiarello, S. Göttlich, T. Schillinger, A. Tosin
    Hydrodynamic traffic flow models including random accidents: A kinetic derivation
    Commun. Math. Sci., 22(3):845-870, 2024 › paper [preprint]
  3. T. Lorenzi, E. Paparelli, A. Tosin
    Modelling coevolutionary dynamics in heterogeneous SI epidemiological systems across scales
    Commun. Math. Sci., 22(8):2131-2165, 2024 › paper [preprint]
  4. M. Nurisso, M. Raviola, A. Tosin
    Network-based kinetic models: Emergence of a statistical description of the graph topology
    European J. Appl. Math., 2024. doi:10.1017/S0956792524000020 › paper [preprint]
  5. F. A. Chiarello, A. Tosin
    Macroscopic limits of non-local kinetic descriptions of vehicular traffic
    Kinet. Relat. Models, 16(4):540-564, 2023 › paper [preprint]
  6. R. Della Marca, N. Loy, A. Tosin
    An SIR model with viral load-dependent transmission
    J. Math. Biol., 86(4):61/1-28, 2023 › paper [preprint]
  7. R. Della Marca, N. Loy, A. Tosin
    An SIR-like kinetic model tracking indviduals' viral load
    Netw. Heterog. Media, 17(3):467-494, 2022 › paper [preprint]
  8. G. Dimarco, A. Tosin, M. Zanella
    Kinetic derivation of Aw–Rascle–Zhang-type traffic models with driver-assist vehicles
    J. Stat. Phys., 186(1):17/1-26, 2022 › paper [preprint]
  9. N. Loy, M. Raviola, A. Tosin
    Opinion polarization in social networks
    Philos. Trans. Roy. Soc. A, 380(2224):20210158/1-15, 2022 › paper [preprint]
  10. A. Medaglia, A. Tosin, M. Zanella
    Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties
    Partial Differ. Equ. Appl., 3(4):51, 2022 › paper [preprint]
  11. M. Bertsch, B. Franchi, V. Meschini, M. C. Tesi, A. Tosin
    A sensitivity analysis of a mathematical model for the synergistic interplay of amyloid beta and tau on the dynamics of Alzheimer's disease
    Brain Multiphysics, 2:100020/1-13, 2021 › paper [preprint]
  12. F. A. Chiarello, B. Piccoli, A. Tosin
    Multiscale control of generic second order traffic models by driver-assist vehicles
    Multiscale Model. Simul., 19(2):589-611, 2021 › paper [preprint]
  13. F. A. Chiarello, B. Piccoli, A. Tosin
    A statistical mechanics approach to macroscopic limits of car-following traffic dynamics
    Internat. J. Non-Linear Mech., 137:103806/1-11, 2021 › paper [preprint]
  14. N. Loy, A. Tosin
    Boltzmann-type equations for multi-agent systems with label switching
    Kinet. Relat. Models, 14(5):867-894, 2021 › paper [preprint]
  15. N. Loy, A. Tosin
    A viral load-based model for epidemic spread on spatial networks
    Math. Biosci. Eng., 18(5):5635-5663, 2021 › paper [preprint]
  16. A. Tosin, M. Zanella
    Uncertainty damping in kinetic traffic models by driver-assist controls
    Math. Control Relat. Fields, 11(3):681-713, 2021 › paper [preprint]
  17. G. Dimarco, A. Tosin
    The Aw-Rascle traffic model: Enskog-type kinetic derivation and generalisations
    J. Stat. Phys., 178(1):178-210, 2020 › paper [preprint]
  18. M. Fraia, A. Tosin
    The Boltzmann legacy revisited: kinetic models of social interactions
    Mat. Cult. Soc. Riv. Unione Mat. Ital. (I), 5(2):93-109, 2020 › paper [preprint]
  19. N. Loy, A. Tosin
    Markov jump processes and collision-like models in the kinetic description of multi-agent systems
    Commun. Math. Sci., 18(6):1539-1568, 2020 › paper [preprint]
  20. B. Piccoli, A. Tosin, M. Zanella
    Model-based assessment of the impact of driver-assist vehicles using kinetic theory
    Z. Angew. Math. Phys., 71(5):152/1-25, 2020 › paper [preprint]
  21. G. Toscani, A. Tosin, M. Zanella
    Kinetic modelling of multiple interactions in socio-economic systems
    Netw. Heterog. Media, 15(3):519-542, 2020 › paper [preprint]
  22. S. Cacace, F. Camilli, R. De Maio, A. Tosin
    A measure theoretic approach to traffic flow optimisation on networks
    European J. Appl. Math., 30(6):1187-1209, 2019 › paper [preprint]
  23. L. Pareschi, G. Toscani, A. Tosin, M. Zanella
    Hydrodynamic models of preference formation in multi-agent societies
    J. Nonlinear Sci., 29(6):2761-2796, 2019 › paper [preprint]
  24. G. Toscani, A. Tosin, M. Zanella
    Multiple-interaction kinetic modeling of a virtual-item gambling economy
    Phys. Rev. E, 100(1):012308/1-16, 2019 › paper [preprint]
  25. A. Tosin, M. Zanella
    Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
    Multiscale Model. Simul., 17(2):716-749, 2019 › paper [preprint]
  26. M. Bertsch, B. Franchi, M. C. Tesi, A. Tosin
    Well-posedness of a mathematical model for Alzheimer's disease
    SIAM J. Math. Anal., 50(3):2362-2388, 2018 › paper [preprint]
  27. F. Camilli, R. De Maio, A. Tosin
    Measure-valued solutions to nonlocal transport equations on networks
    J. Differential Equations, 264(12):7213-7241, 2018 › paper [preprint]
  28. E. Cristiani, A. Tosin
    Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls
    Multiscale Model. Simul., 16(1):528-549, 2018 › paper [preprint]
  29. A. Festa, A. Tosin, M.-T. Wolfram
    Kinetic description of collision avoidance in pedestrian crowds by sidestepping
    Kinet. Relat. Models, 11(3):491-520, 2018 › paper [preprint]
  30. M. Herty, A. Tosin, G. Visconti, M. Zanella
    Hybrid stochastic kinetic description of two-dimensional traffic dynamics
    SIAM J. Appl. Math., 78(5):2737-2762, 2018 › paper [preprint]
  31. G. Toscani, A. Tosin, M. Zanella
    Opinion modeling on social media and marketing aspects
    Phys. Rev. E, 98(2):022315/1-15, 2018 › paper [preprint]
  32. A. Tosin, M. Zanella
    Boltzmann-type models with uncertain binary interactions
    Commun. Math. Sci., 16(4):963-985, 2018 › paper [preprint]
  33. M. Bertsch, B. Franchi, N. Marcello, M. C. Tesi, A. Tosin
    Alzheimer's disease: a mathematical model for onset and progression
    Math. Med. Biol., 34(2):193-214, 2017 › paper [preprint]
  34. M. Bertsch, B. Franchi, M. C. Tesi, A. Tosin
    Microscopic and macroscopic models for the onset and progression of Alzheimer's disease
    J. Phys. A: Math. Theor., 50(41):414003/1-22, 2017 › paper [preprint]
  35. F. Camilli, R. De Maio, A. Tosin
    Transport of measures on networks
    Netw. Heterog. Media, 12(2):191-215, 2017 › paper [preprint]
  36. P. Freguglia, A. Tosin
    Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach
    Commun. Math. Sci., 15(1):213-236, 2017 › paper [preprint]
  37. G. Puppo, M. Semplice, A. Tosin, G. Visconti
    Analysis of a multi-population kinetic model for traffic flow
    Commun. Math. Sci., 15(2):379-412, 2017 › paper [preprint]
  38. G. Puppo, M. Semplice, A. Tosin, G. Visconti
    Kinetic models for traffic flow resulting in a reduced space of microscopic velocities
    Kinet. Relat. Models, 10(3):823-854, 2017 › paper [preprint]
  39. G. Visconti, M. Herty, G. Puppo, A. Tosin
    Multivalued fundamental diagrams of traffic flow in the kinetic Fokker-Planck limit
    Multiscale Model. Simul., 15(3):1267-1293, 2017 › paper [preprint]
  40. L. Bruno, A. Corbetta, A. Tosin
    From individual behaviour to an evaluation of the collective evolution of crowds along footbridges
    J. Engrg. Math., 101(1):153-173, 2016 › paper [preprint]
  41. A. Colombi, M. Scianna, A. Tosin
    Moving in a crowd: Human perception as a multiscale process
    J. Coupled Syst. Multiscale Dyn., 4(1):25-29, 2016 › paper [preprint]
  42. A. Corbetta, A. Tosin
    Comparing first order microscopic and macroscopic crowd models for an increasing number of massive agents
    Adv. Math. Phys., 2016:6902086/1-17, 2016 › paper [preprint]
  43. G. Puppo, M. Semplice, A. Tosin, G. Visconti
    Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models
    Commun. Math. Sci., 14(3):643-669, 2016 › paper [preprint]
  44. A. Colombi, M. Scianna, A. Tosin
    Differentiated cell behavior: a multiscale approach using measure theory
    J. Math. Biol., 71(5):1049-1079, 2015 › paper [preprint]
  45. E. Cristiani, F. S. Priuli, A. Tosin
    Modeling rationality to control self-organization of crowds: an environmental approach
    SIAM J. Appl. Math., 75(2):605-629, 2015 › paper [preprint]
  46. L. Fermo, A. Tosin
    A fully-discrete-state kinetic theory approach to traffic flow on road networks
    Math. Models Methods Appl. Sci., 25(3):423-461, 2015 › paper [preprint]
  47. L. Fermo, A. Tosin
    Fundamental diagrams for kinetic equations of traffic flow
    Discrete Contin. Dyn. Syst. Ser. S, 7(3):449-462, 2014 › paper [preprint]
  48. N. Bellomo, M. A. Herrero, A. Tosin
    On the dynamics of social conflicts: Looking for the Black Swan
    Kinet. Relat. Models, 6(3):459-479, 2013 › paper [preprint]
  49. L. Fermo, A. Tosin
    A fully-discrete-state kinetic theory approach to modeling vehicular traffic
    SIAM J. Appl. Math., 73(4):1533-1556, 2013 › paper [preprint]
  50. A. Tosin
    Initial/boundary-value problems of tumor growth within a host tissue
    J. Math. Biol., 66(1):163-202, 2013 › paper [preprint]
  51. A. Tosin
    Un approccio multiscala alla dinamica delle folle mediante misure che evolvono nel tempo
    Boll. Unione Mat. Ital., 9(6):531-548, 2013 › [preprint]
  52. N. Bellomo, B. Piccoli, A. Tosin
    Modeling crowd dynamics from a complex system viewpoint
    Math. Models Methods Appl. Sci., 22(supp02):1230004 (29 pages), 2012 › paper
  53. L. Bruno, A. Tosin, P. Tricerri, F. Venuti
    Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications
    Appl. Math. Model., 35(1):426-445, 2011 › paper [preprint]
  54. E. Cristiani, B. Piccoli, A. Tosin
    Multiscale modeling of granular flows with application to crowd dynamics
    Multiscale Model. Simul., 9(1):155-182, 2011 › paper [preprint]
  55. B. Piccoli, A. Tosin
    Time-evolving measures and macroscopic modeling of pedestrian flow
    Arch. Ration. Mech. Anal., 199(3):707-738, 2011 › paper [preprint]
  56. A. Tosin, P. Frasca
    Existence and approximation of probability measure solutions to models of collective behaviors
    Netw. Heterog. Media, 6(3):561-596, 2011 › paper [preprint]
  57. A. Tosin, L. Preziosi
    Multiphase modeling of tumor growth with matrix remodeling and fibrosis
    Math. Comput. Modelling, 52(7-8):969-976, 2010 › paper [preprint]
  58. J. Galle, L. Preziosi, A. Tosin
    Contact inhibition of growth described using a multiphase model and an individual cell-based model
    Appl. Math. Lett., 22(10):1483-1490, 2009 › paper [preprint]
  59. B. Piccoli, A. Tosin
    Pedestrian flows in bounded domains with obstacles
    Contin. Mech. Thermodyn., 21(2):85-107, 2009 › paper [preprint]
  60. L. Preziosi, A. Tosin
    Multiphase and multiscale trends in cancer modelling
    Math. Model. Nat. Phenom., 4(3):1-11, 2009 › paper [preprint]
  61. L. Preziosi, A. Tosin
    Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications
    J. Math. Biol., 58(4-5):625-656, 2009 › paper [preprint]
  62. A. Tosin
    From generalized kinetic theory to discrete velocity modeling of vehicular traffic. A stochastic game approach
    Appl. Math. Lett., 22(7):1122-1125, 2009 › paper [preprint]
  63. A. Tosin
    Teoria cinetica discreta e teoria dei giochi stocastica per il traffico veicolare: modellistica e problemi matematici
    Boll. Unione Mat. Ital. Sez. A Mat. Soc. Cult. (8), 2(2):299-302, 2009 › [preprint]
  64. A. Tosin
    Multiphase modeling and qualitative analysis of the growth of tumor cords
    Netw. Heterog. Media, 3(1):43-83, 2008 › paper [preprint]
  65. S. Astanin, A. Tosin
    Mathematical model of tumour cord growth along the source of nutrient
    Math. Model. Nat. Phenom., 2(3):153-177, 2007 › paper
  66. M. Delitala, A. Tosin
    Mathematical modeling of vehicular traffic: A discrete kinetic theory approach
    Math. Models Methods Appl. Sci., 17(6):901-932, 2007 › paper
  67. A. Tosin, D. Ambrosi, L. Preziosi
    Mechanics and chemotaxis in the morphogenesis of vascular networks
    Bull. Math. Biol., 68(7):1819-1836, 2006 › paper [preprint]
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Books
  1. G. Puppo, A. Tosin, Eds.
    Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models
    ICIAM 2019 SEMA SIMAI Springer Series, volume 12, Springer, 2021 › book
  2. E. Cristiani, B. Piccoli, A. Tosin
    Multiscale Modeling of Pedestrian Dynamics
    MS&A: Modeling, Simulation and Applications, volume 12, Springer, 2014 › book
  3. G. Ajmone Marsan, N. Bellomo, A. Tosin
    Complex Systems and Society - Modeling and Simulation
    SpringerBriefs in Mathematics, Springer, 2013 › book
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Book Chapters
  1. M. Conte, M. Groppi, A. Tosin
    Kinetic and macroscopic equations for action potential in neural networks
    In A. d'Onofrio, A. Fasano, F. Papa, C. Sinisgalli, Eds., Problems in Mathematical Biophysics
    SEMA SIMAI Springer Series, volume 38. Springer, Cham, 2024 › chapter [preprint]
  2. M. Herty, A. Tosin, G. Visconti, M. Zanella
    Reconstruction of traffic speed distributions from kinetic models with uncertainties
    In G. Puppo, A. Tosin, Eds., Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models
    ICIAM 2019 SEMA SIMAI Springer Series, volume 12, pages 1-16. Springer, 2021 › chapter [preprint]
  3. A. Tosin, M. Zanella
    Boltzmann-type description with cutoff of Follow-the-Leader traffic models
    In G. Albi, S. Merino-Aceituno, A. Nota, M. Zanella, Eds., Trails in Kinetic Theory: Foundational Aspects and Numerical Methods
    SEMA SIMAI Springer Series, volume 25, pages 227-251. Springer, 2021 › chapter [preprint]
  4. G. Ajmone Marsan, N. Bellomo, M. A. Herrero, A. Tosin
    From five key questions to a System Sociology theory
    In J. Bissell, C. C. S. Caiado, S. Curtis, M. Goldstein, B. Straughan, Eds., Tipping Points: Modelling Social Problems and Health
    chapter 7, pages 113-129. Wiley-Interscience, 2015 › chapter [preprint]
  5. A. Tosin
    Kinetic equations and stochastic game theory for social systems
    In A. Celletti, U. Locatelli, T. Ruggeri, E. Strickland, Eds., Mathematical Models and Methods for Planet Earth
    Springer INdAM Series, volume 6, pages 37-57. Springer, 2014 › chapter [preprint]
  6. A. Tosin
    Multiscale crowd dynamics: Modeling and theory
    In A. Muntean, F. Toschi, Eds., Collective Dynamics from Bacteria to Crowds
    CISM International Centre for Mechanical Sciences, volume 553, pages 157-177. Springer, 2014 › chapter [preprint]
  7. E. Cristiani, B. Piccoli, A. Tosin
    Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints
    In G. Naldi, L. Pareschi, G. Toscani, Eds., Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences
    Modeling and Simulation in Science, Engineering and Technology, pages 337-364. Birkhäuser, 2010 › chapter [preprint]
  8. B. Piccoli, A. Tosin
    Vehicular traffic: A review of continuum mathematical models
    In R. A. Meyers, Ed., Encyclopedia of Complexity and Systems Science
    volume 22, pages 9727-9749. Springer, 2009 › chapter [preprint]
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Conference Papers
  1. A. Tosin, M. Zanella
    Control strategies for road risk mitigation in kinetic traffic modelling
    IFAC-PapersOnLine, 51(9):67-72, 2018 › paper [preprint]
  2. E. Cristiani, B. Piccoli, A. Tosin
    How can macroscopic models reveal self-organization in traffic flow?
    Proceedings of the 51st IEEE Conference on Decision and Control, pp. 6989-6994, 2012 › paper [preprint]
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Theses
  1. Discrete kinetic and stochastic game theory for vehicular traffic: Modeling and mathematical problems
    Ph.D. Thesis, 2008 › pdf
    (Awarded one of the four INdAM-SIMAI 2010 prizes for the best Ph.D. Italian theses in Applied Mathematics)
  2. Modellizzazione delle interazioni meccaniche e chimiche nel processo di formazione delle reti di capillari
    Master's Degree Thesis, 2004 › pdf
  3. Stabilità ingresso-uscita per i sistemi lineari
    Bachelor's Degree Thesis, 2002 › pdf
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Media Coverage
  1. La popolarità delle opinioni (with Mattia Zanella)
    MaddMaths!, June 2018 › article (in Italian)
  2. "Il momento peggiore è l'inizio della fuga, perciò sabato erano inevitabili molti feriti"
    (Interview about the crowd events in Torino, Italy, on 3rd June 2017)
    La Repubblica, June 2017 › article (in Italian)
  3. Quando un modello matematico può salvare molte vite
    IMQ Notizie, December 2014 › article (in Italian)
  4. Predicting the Unpredictable - Human Behaviors and Beyond
    Mathematics of Planet Earth 2013 Blog, June 2013 › article
  5. Conclave 2013, CNR: "Un modello matematico per gestire la folla"
    Il Fatto Quotidiano, March 2013 › article (in Italian)
  6. Così la matematica considera la 'grandezza'
    ANSA, June 2011 › article (in Italian)
  7. Folla: un'equazione per gestirla
    Almanacco della Scienza - CNR, June 2011 › article (in Italian)
  8. Alla radio i modelli di folla
    Controradio, May 2011 › audio (in Italian)
  9. Modello matematico simula comportamento folla
    ANSA, May 2011 › article (in Italian)
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