bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Pareschi, Lorenzo and Toscani, Giuseppe:
Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana Serie 1 6 (2021), fasc. n.3, p. 215-230, (Italian)
pdf (5.18 MB), djvu (457 Kb).

Sunto

In questo breve sunto divulgativo discuteremo l'importanza delle dinamiche sociali in ambito epidemico e la loro modellizzazione matematica tramite equazioni alle derivate parziali. Presenteremo inizialmente modelli di interazione tra individui in cui le caratteristiche sociali, come l'età degli individui, il numero dicontatti sociali e la loro ricchezza economica, giocano un ruolo chiave nella diffusione di un'epidemia. Successivamente, accenneremo a modelli che tengono conto anche di caratteristiche aggiuntive quali la carica virale e le difese immunitarie dell'individuo. Infine, analizzeremo alcuni modelli alle derivate parziali per ladescrizione degli spostamenti degli individui, sia su scala urbana che extra urbana, ed evidenzieremo come le dinamiche di movimento giochino un ruolo chiave sull'avanzamento dell'epidemia.
Referenze Bibliografiche
[1] G. ALBI, G. BERTAGLIA, W. BOSCHERI, G. DIMARCO, L. PARESCHI, G. TOSCANI, M. ZANELLA. Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics. In corso di stampa su: Predicting Pandemics in a Globally Connected World, Vol. 1, N. Bellomo and M. Chaplain Editors, Springer Nature (2021). | Zbl 07615909
[2] G. ALBI, L. PARESCHI, M. ZANELLA. Control with uncertain data of socially structured compartmental epidemic models. J. Math. Biol., 82:63 (2021). | fulltext (doi) | MR 4263205 | Zbl 1467.92167
[3] G. ALBI, L. PARESCHI, M. ZANELLA. Modelling lockdown measures in epidemic outbreaks using selective socioeconomic containment with uncertainty. Math. Biosci. Eng., 18(6):7161-7190 (2021). | fulltext (doi) | MR 4313914 | Zbl 07610974
[4] N. BELLOMO, R. BINGHAM, M.A.J. CHAPLAIN, G. DOSI, G. FORNI, D.A. KNOPOFF, J. LOWENGRUB, R. TWAROCK, M.E. VIRGILLITO. A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world. Math. Mod. Meth. Appl. Scie. 30 (8): 1591-1651, (2020). | fulltext (doi) | MR 4144366 | Zbl 1451.92276
[5] G. BÉRAUD, S. KAZMERCZIAK, P. BEUTELS, D. LEVY-BRUHL, X. LENNE, N. MIELCAREK, Y. YAZDANPANA, P-Y. BOÈLLE, N. HENS, B. DERVAUX. The French Connection: The First Large Population-Based Contact Survey in France Relevant for the Spread of Infectious Diseases. PLOS ONE 10 (7): e0133203, (2015).
[6] G. BERTAGLIA, W. BOSCHERI, G. DIMARCO, L. PARESCHI. Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty. Math. Biosci. Eng., 18(5):7028-7059 (2021). | fulltext (doi) | MR 4313909 | Zbl 07610969
[7] G. BERTAGLIA, L. PARESCHI. Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods, ESAIM Math. Model. Numer. Anal. 55(2):381-407 (2021). | fulltext (doi) | MR 4229196 | Zbl 1472.65105
[8] G. BERTAGLIA, L. PARESCHI. Hyperbolic compartmental models for epidemic spread on networks with uncertain data: application to the emergence of COVID-19 in Italy. Math. Mod. Meth. App. Scie., in corso di stampa (2021). | fulltext (doi) | MR 4363010 | Zbl 1478.92178
[9] W. BOSCHERI, G. DIMARCO, L. PARESCHI. Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations. Math. Mod. Meth. App. Scie., 31(6):1059-1097 (2021). | fulltext (doi) | MR 4287586 | Zbl 1473.92006
[10] L. BOLZONI, E. BONACINI, C. SORESINA, M. GROPPI, Time optimal control strategies in SIR epidemic models. Math. Biosci., 292:86-96, (2017). | fulltext (doi) | MR 3688684 | Zbl 1378.92065
[11] T. BRITTON, F. BALL, P. TRAPMAN. A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2. Science, 369:6505, (2020). | fulltext (doi) | MR 4269269 | Zbl 1478.92180
[12] B. BUONOMO, R. DELLA MARCA. Effects of information induced behavioural changes during the COVID-19 lockdowns: The case of Italy: COVID-19 lockdowns and behavioral change. R. Soc. Open Sci., 7:201635 (2020).
[13] V. CAPASSO, G. SERIO. A generalization of the Kermack McKendrick deterministic epidemic model. Math. Biosci., 42(1): 43-61, (1978). | fulltext (doi) | MR 529097 | Zbl 0398.92026
[14] C. CERCIGNANI. The Boltzmann Equation and its Applications. Springer Series in Applied Mathematical Sciences, vol. 67 Springer-Verlag, New York, NY, (1988). | fulltext (doi) | MR 1313028 | Zbl 0646.76001
[15] R.M. COLOMBO, M. GARAVELLO, F. MARCELLINI, E. ROSSI. An age and space structured SIR model describing the COVID-19 pandemic. J. Math. Ind., 10(1):22 (2020). | fulltext (doi) | MR 4139038 | Zbl 1469.92107
[16] E. CRISTIANI, B. PICCOLI, A. TOSIN. Multiscale Modeling of Pedestrian Dynamics. Springer series in Modelling Simulation & Applications, vol. 12, (2014). | fulltext (doi) | MR 3308728 | Zbl 1314.00081
[17] R. DELLA MARCA, N. LOY, A. TOSIN. A SIR-like kinetic model tracking individuals' viral load. Preprint arXiv:2106.14480, (2021). | fulltext (doi) | MR 4421535 | Zbl 1497.92279
[18] G. DIMARCO, L. PARESCHI, G. TOSCANI, M. ZANELLA. Wealth distribution under the spread of infectious diseases. Phys. Rev. E, 102:022303, (2020). | fulltext (doi) | MR 4147945
[19] G. DIMARCO, B. PERTHAME, G. TOSCANI, M. ZANELLA. Kinetic models for epidemic dynamics with social heterogeneity. J. Math. Bio., 83:4, (2021). | fulltext (doi) | MR 4278446 | Zbl 1467.92189
[20] M. GATTO, E. BERTUZZO, L. MARI, S. MICCOLI, L. CARRARO, R. CASAGRANDI, A. RINALDO. Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures. PNAS, 117(19): 10484-10491, (2020).
[21] G. GIORDANO, F. BLANCHINI, R. BRUNO, P. COLANERI, A. DI FILIPPO, A. DI MATTEO, M. COLANERI. Modelling the COVID-19 epidemic and implementation of populationwide interventions in Italy. Nat. Med., 26:855-860, (2020).
[22] N. GUGLIELMI, E. IACOMINI, A. VIGUERIE. Delay differential equations for the spatially-resolved simulation of epidemics with specific application to COVID-19. Math. Meth. in Appl. Sci., in corso di stampa, (2021) | fulltext (doi) | MR 4420143
[23] H.W. HETHCOTE. The mathematics of infectious diseases. SIAM Review, 42(4): 599-653, (2000). | fulltext (doi) | MR 1814049 | Zbl 0993.92033
[24] N.P. JEWELL, J.A. LEWNARD, B.L. JEWELL. Predictive Mathematical Models of the COVID-19 Pandemic. Underlying Principles and Value of Projections. JAMA 323(19):1893-1894, (2020).
[25] W.O. KERMACK, A.G. MCKENDRICK. A Contribution to the Mathematical Theory of Epidemics. Proc. Roy. Soc. Lond. A, 115:700-721, (1927). | Zbl 53.0517.01
[26] N. LOY, A. TOSIN. A viral load-based model for epidemic spread on spatial networks. Math. Biosci. Eng., 18(5):5635-5663, (2021). | fulltext (doi) | MR 4276084 | Zbl 07610904
[27] G. NALDI, L. PARESCHI, G. TOSCANI eds.. Mathematical modeling of collective behavior in socio-economic and life sciences, Birkhauser, Boston (2010). | fulltext (doi) | MR 2761862 | Zbl 1200.91010
[28] L. PARESCHI, G. TOSCANI. Interacting Multiagent Systems. Kinetic Equations & Monte Carlo Methods, Oxford University Press, Oxford (2013). | Zbl 1330.93004
[29] B. PICCOLI, M. GARAVELLO. Traffic Flow on Networks. American Institute of Mathematical Sciences (2006). | MR 2328174 | Zbl 1136.90012
[30] K. PREM, A.R. COOK, M. JIT. Projecting social contact matrices in 152 countries using contact surveys and demographic data. PLoS ONE, 13(9):e1005697, (2017).
[31] A. PUGLIESE. Cenni su teoria e utilizzo di modelli matematici per le epidemie. Matematica, Cultura e Società - Rivista dell'Unione Matematica Italiana, Serie I, 5(1): 5-15, (2020). | fulltext bdim
[32] M. PULVIRENTI, S. SIMONELLA. A kinetic model for epidemic spread. MEMOCS, 8:3, (2020). | fulltext (doi) | MR 4149075 | Zbl 1452.92040
[33] X. SALA-I-MARTIN, S. MOHAPATRA. Poverty, inequality and the distribution of income in the Group of 20, Discussion Paper #:0203-10, Department of Economics Columbia University, New York, (2002).
[34] A. VIGUERIE, A. VENEZIANI, G. LORENZO, D. BAROLI, N. ARETZ-NELLESEN, A. PATTON, T.E. YANKEELOV, A. REALI, T.J.R. HUGHES, F. AURICCHIO. Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study. Comput. Mech., 66:1131-1152, (2020). | fulltext (doi) | MR 4163347 | Zbl 1469.92127
[35] M. ZANELLA, C. BARDELLI, M. AZZI, S. DEANDREA, P. PEROTTI, S. SILVA, E. CADUM, S. FIGINI, G. TOSCANI. Social contacts, epidemic spreading and health system. Mathematical modeling and applications to COVID-19 infection. Math. Biosci. Eng., 18 (4):3384-3403, (2021). | fulltext (doi) | MR 4256519 | Zbl 1471.92367
[36] M. ZANELLA, C. BARDELLI, G. DIMARCO, S. DEANDREA, P. PEROTTI, M. AZZI, S. FIGINI, G. TOSCANI. A data-driven epidemic model with social structure for understanding the COVID-19 infection on a heavily affected Italian Province. Math. Mod. Meth. Appl. Sci., in corso di stampa, (2021). | fulltext (doi) | MR 4363011 | Zbl 1481.92174

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali