Research Areas

Kinetic Theory and Multiscale Modelling of Living Systems:
Development of kinetic and multiscale mathematical frameworks for complex living systems, with particular attention to interactions across microscopic, mesoscopic, and macroscopic scales and to the emergence of collective dynamics.

D. Burini and D.A. Knopoff, Multiscale kinetic structures for the collective dynamics of living systems, Mathematical Models and Methods in Applied Sciences, 2026.

N. Bellomo, D. Burini and J. Liao, New Trends in Kinetic Theory Towards the Complexity of Living Systems, Mathematical Models and Methods in Applied Sciences, 36(2), 341-397, 2026.

D. Burini, N. Chouhad and N. Bellomo, Waiting for a Mathematical Theory of Living Systems from a Critical Review to Research Perspectives, Symmetry, 15(2), 351, 2023.

Mathematical Biology and Immune Dynamics:
Mathematical modelling of immune and disease dynamics through kinetic and multiscale approaches, with particular emphasis on the interplay between biological processes, immune responses, and individual-level heterogeneity.

D. Burini and D.A. Knopoff, A multiscale kinetic theory approach to viral-immune competition, Mathematical Models and Methods in Applied Sciences, 36(6), 1307–1324, 2026.

D. Burini, D.A. Knopoff and L. Serrano, Multiscale Kinetic Model for Immune Reaction in Coeliac Disease, Mathematics, 14(8), 1333, 2026.

Epidemics and Social Dynamics:
Multiscale modelling of epidemic dynamics accounting for interactions between disease transmission, individual behaviour, social responses, and population heterogeneity.

G. Bertaglia, A. Bondesan, D. Burini, R. Eftimie, L. Pareschi and G. Toscani, New Trends on the Systems Approach to Modeling SARS-CoV-2 Pandemics in a Globally Connected Planet, Mathematical Models and Methods in Applied Sciences, 34(11), 1995–2054, 2024.

D. Burini and D.A. Knopoff, Epidemics and society—A multiscale vision from the small world to the globally interconnected world, Mathematical Models and Methods in Applied Sciences, 34(8), 1567–1596, 2024.

N. Bellomo, D. Burini and N. Outada, Multiscale Models of Covid-19 with Mutations and Variants, Networks Heterogeneous Media, 17(3), 293–310, 2022.

Micro-to-Macro Methods:
Derivation of macroscopic models from kinetic descriptions, with particular emphasis on multiscale methods, nonlinear diffusion, and the transition from individual interactions to collective dynamics.

D. Burini and N. Chouhad, Cross diffusion models in complex frameworks from microscopic to macroscopic, Mathematical Models and Methods in Applied Sciences, 33(9), 1909–1928, 2023.

D. Burini and N. Chouhad, A multiscale view of nonlinear diffusion in biology: From cells to tissues, Mathematical Models and Methods in Applied Sciences, 29(4), 791–823, 2019.

Mathematics and Economics:
Application of kinetic and active-particle methods to economic and socioeconomic systems, with particular attention to interactions among heterogeneous agents and the emergence of collective behaviours.

N. Bellomo, D. Burini, V. Secchini and P. Terna, Active Particles Methods: New perspectives in the interaction between mathematics and economics, Cambridge University Press. Series: Cambridge Elements in Complexity and Agent-based Economics, Cambridge University Press, 2024.

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Bibliometrics

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