I modelli compartimentali sono tra gli strumenti matematici più utilizzati per comprendere le dinamiche delle malattie infettive. In questa rassegna, dopo aver richiamato degli argomenti di base su tali modelli, forniamo una breve panoramica di alcuni studi sul COVID-19 in Italia effettuati mediante l'uso dei modelli compartimentali, evidenziando gli aspetti salienti e i risultati principali nelle diverse fasi delle prime ondate della pandemia.
Referenze Bibliografiche
[1] ISS, Istituto Superiore di Sanita± Latest available data; 2020. (Visitato a ottobre 2021). https://www.epicentro.iss.it/en/coronavirus/.
[2] WHO, World Health Organization. WHO Coronavirus (COVID-19) Dashboard; 2021. (Visitato a ottobre 2021). https://covid19.who.int/.
[3] Governo Italiano Presidenza del Consiglio dei Ministri. Report Vaccini Anti COVID-19; 2021. (Visitato a ottobre 2021). https://www.governo.it/it/cscovid19/report-vaccini/.
[4] BUONOMO B, DELLA MARCA R. Effects of information induced behavioural changes during the COVID-19 lockdowns: the case of Italy. Royal Society open science. 2020; 7(10):201635.
[5] ANDERSON RM, MAY RM. Infectious diseases of humans:dynamics and control. Oxford University Press; 1992.
[7]
KEELING MJ,
ROHANI P.
Modeling infectious diseases in humans and animals.
Princeton University Press;
2011. |
MR 2354763 |
Zbl 1279.92038[9]
KERMACK WO,
MCKENDRICK AG.
A contribution to the mathematical theory of epidemics.
Proceedings of the Royal Society of London Series A. 1927;
115(772):700-721. |
Zbl 53.0517.01[10] KERMACK WO, MCKENDRICK AG. Contributions to the mathematical theory of epidemics-I. 1927. Bulletin of Mathematical Biology. 1991; 53(1-2):33-55.
[11] KERMACK WO, MCKENDRICK AG. Contributions to the mathematical theory of epidemics-II. The problem ofendemicity. Bulletin of Mathematical Biology. 1991;53(1-2):57-87.
[12] KERMACK W, MCKENDRICK A. Contributions to the mathematical theory of epidemics-III. Further studies of theproblem of endemicity. Bulletin of Mathematical Biology. 1991; 53(1-2):89-118.
[13]
GROPPI M,
DELLA MARCA R.
Modelli epidemiologici e 50 vaccinazioni: da Bernoulli a oggi.
Matematica, Cultura e Società - Rivista dell'Unione Matematica Italiana.
2018;
3(1):45-59. |
fulltext bdim |
fulltext EuDML |
MR 3821682[14]
PUGLIESE A.
Cenni su teoria e utilizzo di modelli matematici per le epidemie.
Matematica, Cultura e Società - Rivista dell'Unione Matematica Italiana.
2020;
5(1):5-15. |
fulltext bdim[16]
IANNELLI M,
PUGLIESE A.
An introduction to mathematical population dynamics: along the trail of Volterra and Lotka. vol.
79.
Springer;
2015. |
fulltext (doi) |
MR 3288300 |
Zbl 1305.92003[17]
DIEKMANN O,
HEESTERBEEK JAP,
METZ JA.
On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations.
Journal of Mathematical Biology.
1990;
28(4):365-382. |
fulltext (doi) |
MR 1057044 |
Zbl 0726.92018[18]
VAN DEN DRIESSCHE P,
WATMOUGH J.
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.
Mathematical Biosciences. 20
02;
180(1-2):29-48. |
fulltext (doi) |
MR 1950747 |
Zbl 1015.92036[19] GOERING R, DOCKRELL H, ZUCKERMAN M, CHIODINI PL. Mims' Medical Microbiology E-Book. Elsevier Health Sciences; 2018.
[20] RHODES CJ, DEMETRIUS L. Evolutionary entropy determines invasion success in emergent epidemics. PLoSONE. 2010; 5(9):e12951.
[21] LOCATELLI I, TRÄCHSEL B, ROUSSON V. Estimating the basic reproduction number for COVID-19 in Western Europe. PLoS ONE. 2021; 16(3):e0248731.
[22]
KE R,
ROMERO-SEVERSON E,
SANCHE S,
HENGARTNER N.
Estimating the reproductive number $R_0$ of SARS-CoV-2 in the United States and eight European countries and implications for vaccination.
Journal of Theoretical Biology.
2021;
517:110621. |
fulltext (doi) |
MR 4226414 |
Zbl 1460.92204[24] GUMEL AB, RUAN S, DAY T, WATMOUGH J, BRAUER F, VAN DEN DRIESSCHE P, et al. Modelling strategies for controlling SARS outbreaks. Proceedings of the Royal Society of London Series B: Biological Sciences. 2004; 271(1554):2223-2232.
[25] MULLER CP. Do asymptomatic carriers of SARS-COV-2 transmit the virus? The Lancet Regional Health-Europe. 2021; 4.
[26] GATTO M, BERTUZZO E, MARI L, MICCOLI S, CARRARO L, CASAGRANDI R, et al. Spread and dynamics of the COVID19 epidemic in Italy: Effects of emergency containment measures. Proceedings of the National Academy of Sciences. 2020; 117(19):10484-10491.
[27] DELLA ROSSA F, SALZANO D, DI MEGLIO A, DE LELLIS F, CORAGGIO M, CALABRESE C, et al. A network model of Italy shows that intermittent regional strategies can alleviate the COVID-19 epidemic. Nature Communications. 2020; 11(1):1-9.
[28]
STOLERMAN LM,
COOMBS D,
BOATTO S.
SIR-network model and its application to dengue fever.
SIAM Journalon Applied Mathematics. 2015;
75(6):2581-2609. |
fulltext (doi) |
MR 3431133 |
Zbl 1357.92075[30] Johns Hopkins University, Center for Systems Scienceand Engineering. COVID-19 dashboard; 2020. (Visitato aottobre 2021). https://coronavirus.jhu.edu.
[31] LOLI PICCOLOMINI E, ZAMA F. Monitoring Italian COVID19 spread by a forced SEIRD model. PLoS ONE. 2020; 15(8):e0237417.
[32]
MANFREDI P,
D'ONOFRIO A, editors.
Modeling the Interplay Between Human Behavior and the Spread of Infectious Diseases. New York:
Springer;
2013. |
fulltext (doi) |
MR 3075953[33]
WANG Z,
BAUCH CT,
BHATTACHARYYA S,
D'ONOFRIO A,
MANFREDI P,
PERC M, et al.
Statistical physics of vaccination.
Physics Reports.
2016;
664:1-113. |
fulltext (doi) |
MR 3577272 |
Zbl 1359.92111[34]
D'ONOFRIO A,
MANFREDI P.
Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious diseases.
Journal of Theoretical Biology. 2009;
256(3):473-478. |
fulltext (doi) |
MR 2973467 |
Zbl 1400.92570[35]
D'ONOFRIO A,
MANFREDI P,
SALINELLI E.
Vaccinating behaviour, information, and the dynamics of SIR vaccine preventable diseases.
Theoretical Population Biology.
2007;
71(3):301-317. |
Zbl 1124.92029[36]
BUONOMO B,
MANFREDI P,
D'ONOFRIO A.
Optimal time profiles of public health intervention to shape voluntary vaccination for childhood diseases.
Journal of Mathematical Biology. 2019;
78(4):1089-1113. |
fulltext (doi) |
MR 3922966 |
Zbl 1409.92145[37]
BUONOMO B,
DELLA MARCA R.
Oscillations and hysteresisin an epidemic model with information-dependent imperfect vaccination.
Mathematics and Computers in Simulation. 2019;
162:97-114. |
fulltext (doi) |
MR 3958585 |
Zbl 07316691[38]
PAROLINI N,
DEDÈ L,
ANTONIETTI PF,
ARDENGHI G,
MANZONI A,
MIGLIO E, et al.
SUIHTER: a new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
2021;
477(2253):20210027. |
MR 4334820[39] GIORDANO G, BLANCHINI F, BRUNO R, COLANERI P, DIFILIPPO A, DI MATTEO A, et al. Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nature Medicine. 2020; 26:855-60.
[40]
ISTAT, Istituto Nazionale di Statistica. Impatto dell'epidemia Covid-19 sulla mortalità totale della popolazione residente;
2021. (Visitato ad agosto 2021). https://www.istat.it/it/archivio/254507. |
fulltext (doi) |
MR 4217634[41]
LACITIGNOLA D,
SACCOMANDI G.
Managing awareness can avoid hysteresis in disease spread: an application to Coronavirus Covid-19.
Chaos Solitons & Fractals.
2021;
144:110739. |
fulltext (doi) |
MR 4214915[42]
LACITIGNOLA D,
DIELE F.
Using awareness to Z-control a SEIR model with overexposure. Insights on Covid-19 pandemic.
Chaos Solitons & Fractals.
2021;
150:111063. |
fulltext (doi) |
MR 4272545[44] GUO D, ZHANG Y. Neural dynamics and Newton-Raphson iteration for non-linear optimization. Journal of Computational and Nonlinear Dynamics. 2014; 9(2):021016.
[46] EFFENBERGER M, KRONBICHLER A, IL SHIN J, MAYER G, TILG H, PERCO P. Association of the COVID-19 pandemic with Internet Search Volumes: A Google Trends TM Analysis. International Journal of Infectious Diseases. 2020; 95:192-197.
[47] ROBERT A. Lessons from New Zealand's COVID-19 outbreak response. Lancet Public Health. 2020; 5(11):e569-570.
[48] AIFA, Agenzia italiana del Farmaco. Vaccini COVID-19; 2021. (Visitato ad agosto 2021). https://www.aifa.gov.it/web/guest/vaccini-covid-19.
[49] Ministero della Salute. Vaccinazione anti-SARS-CoV-2/COVID-19, Piano Strategico, elementi di preparazione e di implementazione della strategia vaccinale.; 2020. (Visitatoad agosto 2021). http://www.salute.gov.it/imgs/C_17_pubblicazioni_2986_allegato.pdf.
[50] GIORDANO G, COLANERI M, DI FILIPPO A, BLANCHINI F, BOLZERN P, DE NICOLAO G, et al. Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy. Nature Medicine. 2021; 27(6):993-998.
[51] ROBERTS M, ANDREASEN V, LLOYD A, PELLIS L. Nine challenges for deterministic epidemic models. Epidemics. 2015; 10:49-53.
[52]
CALLERI F,
NASTASI G,
ROMANO V.
Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and compariso nwith deterministic models.
Journal of Mathematical Biology.
2021;
83(4):34. |
fulltext (doi) |
MR 4316122 |
Zbl 1471.92294[53] GATTO A, ACCARINO G, ALOISI V, IMMORLANO F, DONATO F, ALOISIO G. Limits of compartmental models and new opportunities for machine learning: a case study to forecast the second wave of COVID-19 hospitalizations in Lombardy, Italy. Informatics. 2021; 8(3).
[54] GNANVI JE, SALAKO KV, KOTANMI GB, GLÈLÈ KAKAIÈ R. On the reliability of predictions on Covid-19 dynamics: Asystematic and critical review of modelling techniques. Infectious Disease Modelling. 2021; 6:258-72.
Con il contributo del Ministero per i Beni e le Attività Culturali