Geodesic
Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico
Matematica, cultura e società, Série 1, Tome 6 (2021) no. 3, pp. 215-230.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
In this short survey, we will discuss the importance of social dynamics in epidemiology and their mathematical modeling using partial differential equations. We will initially present models of interactions between individuals in which social characteristics, such as the age of individuals, the number of social contacts, and their economic wealth, play a key role in the spread of an epidemic. Next, we will outline models that also account for additional characteristics such as viral load and the individual's immune defenses. Finally, we will analyze some partial differential models for describing the mobility of individuals, both at urban and extra-urban scales, and highlight how movement dynamics play a key role inthe progress of the epidemic 
@article{RUMI_2021_1_6_3_a1,
     author = {Pareschi, Lorenzo and Toscani, Giuseppe},
     title = {Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico},
     journal = {Matematica, cultura e societ\`a},
     pages = {215--230},
     publisher = {mathdoc},
     volume = {Ser. 1, 6},
     number = {3},
     year = {2021},
     zbl = {07615909},
     mrnumber = {4263205},
     language = {it},
     url = {http://geodesic.mathdoc.fr/item/RUMI_2021_1_6_3_a1/}
}
TY  - JOUR
AU  - Pareschi, Lorenzo
AU  - Toscani, Giuseppe
TI  - Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico
JO  - Matematica, cultura e società
PY  - 2021
SP  - 215
EP  - 230
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RUMI_2021_1_6_3_a1/
LA  - it
ID  - RUMI_2021_1_6_3_a1
ER  - 
%0 Journal Article
%A Pareschi, Lorenzo
%A Toscani, Giuseppe
%T Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico
%J Matematica, cultura e società
%D 2021
%P 215-230
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RUMI_2021_1_6_3_a1/
%G it
%F RUMI_2021_1_6_3_a1
Pareschi, Lorenzo; Toscani, Giuseppe. Dinamiche sociali ed equazioni alle derivate parziali in ambito epidemiologico. Matematica, cultura e società, Série 1, Tome 6 (2021) no. 3, pp. 215-230. http://geodesic.mathdoc.fr/item/RUMI_2021_1_6_3_a1/

[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

[2] G. Albi, L. Pareschi, M. Zanella. Control with uncertain data of socially structured compartmental epidemic models. J. Math. Biol., 82:63 (2021). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[10] L. Bolzoni, E. Bonacini, C. Soresina, M. Groppi, Time optimal control strategies in SIR epidemic models. Math. Biosci., 292:86-96, (2017). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[14] C. Cercignani. The Boltzmann Equation and its Applications. Springer Series in Applied Mathematical Sciences, vol. 67 Springer-Verlag, New York, NY, (1988). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[16] E. Cristiani, B. Piccoli, A. Tosin. Multiscale Modeling of Pedestrian Dynamics. Springer series in Modelling Simulation & Applications, vol. 12, (2014). | DOI | MR | Zbl

[17] R. Della Marca, N. Loy, A. Tosin. A SIR-like kinetic model tracking individuals' viral load. Preprint arXiv:2106.14480, (2021). | DOI | MR | Zbl

[18] G. Dimarco, L. Pareschi, G. Toscani, M. Zanella. Wealth distribution under the spread of infectious diseases. Phys. Rev. E, 102:022303, (2020). | DOI | MR

[19] G. Dimarco, B. Perthame, G. Toscani, M. Zanella. Kinetic models for epidemic dynamics with social heterogeneity. J. Math. Bio., 83:4, (2021). | DOI | MR | Zbl

[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) | DOI | MR

[23] H.W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42(4): 599-653, (2000). | DOI | MR | Zbl

[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

[26] N. Loy, A. Tosin. A viral load-based model for epidemic spread on spatial networks. Math. Biosci. Eng., 18(5):5635-5663, (2021). | DOI | MR | Zbl

[27] G. NALDI, L. PARESCHI, G. TOSCANI eds.. Mathematical modeling of collective behavior in socio-economic and life sciences, Birkhauser, Boston (2010). | DOI | MR | Zbl

[28] L. Pareschi, G. Toscani. Interacting Multiagent Systems. Kinetic Equations & Monte Carlo Methods, Oxford University Press, Oxford (2013). | Zbl

[29] B. Piccoli, M. Garavello. Traffic Flow on Networks. American Institute of Mathematical Sciences (2006). | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl

[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). | DOI | MR | Zbl