{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:01:13Z","timestamp":1760234473788,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper addresses the problem of describing the spread of COVID-19 by a mathematical model introducing all the possible control actions as prevention (informative campaign, use of masks, social distancing, vaccination) and medication. The model adopted is similar to SEIQR, with the infected patients split into groups of asymptomatic subjects and isolated ones. This distinction is particularly important in the current pandemic, due to the fundamental the role of asymptomatic subjects in the virus diffusion. The influence of the control actions is considered in analysing the model, from the calculus of the equilibrium points to the determination of the reproduction number. This choice is motivated by the fact that the available organised data have been collected since from the end of February 2020, and almost simultaneously containment measures, increasing in typology and effectiveness, have been applied. The characteristics of COVID-19, not fully understood yet, suggest an asymmetric diffusion among countries and among categories of subjects. Referring to the Italian situation, the containment measures, as applied by the population, have been identified, showing their relation with the government\u2019s decisions; this allows the study of possible scenarios, comparing the impact of different possible choices.<\/jats:p>","DOI":"10.3390\/sym13050890","type":"journal-article","created":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T00:06:54Z","timestamp":1621296414000},"page":"890","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Control Based Mathematical Model for the Evaluation of Intervention Lines in COVID-19 Epidemic Spread: The Italian Case Study"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9113-8608","authenticated-orcid":false,"given":"Paolo","family":"Di Giamberardino","sequence":"first","affiliation":[{"name":"Department of Computer, Control and Management Engineering Antonio Ruberti, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy"}]},{"given":"Rita","family":"Caldarella","sequence":"additional","affiliation":[{"name":"Department of Computer, Control and Management Engineering Antonio Ruberti, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy"}]},{"given":"Daniela","family":"Iacoviello","sequence":"additional","affiliation":[{"name":"Department of Computer, Control and Management Engineering Antonio Ruberti, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"key":"ref_1","unstructured":"(2021, April 10). World Health Organization. Available online: https:\/\/www.who.int\/."},{"key":"ref_2","unstructured":"(2021, April 10). Protezione Civile. Available online: http:\/\/www.protezionecivile.gov.it\/."},{"key":"ref_3","unstructured":"(2021, April 10). Ministero della Salute, Available online: http:\/\/www.salute.gov.it\/portale\/home.html."},{"key":"ref_4","unstructured":"(2021, April 10). Istituto Superiore di Sanit\u00e0. Available online: https:\/\/www.iss.it\/."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Iype, E., and Gulati, S. (2021). Understanding the asymmetric spread and case fatality rate (CFR) for COVID-19 among countries. medRxiv.","DOI":"10.1101\/2020.04.21.20073791"},{"key":"ref_6","unstructured":"(2021, April 10). Sapienza University of Rome. Available online: https:\/\/www.uniroma1.it\/en\/notizia\/covid-19-free-swabs-students."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1109\/JBHI.2020.3009038","article-title":"Dynamical Evolution of COVID-19 in Italy with an Evaluation of the Size of the Asymptomatic Infective Population","volume":"25","author":"Iacoviello","year":"2021","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3201","DOI":"10.1002\/jmv.26897","article-title":"Estimation of undetected symptomatic ans asymptomatic cases of COVID-19 infection and prediction of its spread in the USA","volume":"93","author":"Mahajan","year":"2021","journal-title":"J. Med. Virol."},{"key":"ref_9","unstructured":"(2021, April 10). Istituto Nazionale di Statistica. Available online: https:\/\/www.istat.it\/en\/."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/S0140-6736(20)30260-9","article-title":"Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: A modelling study","volume":"395","author":"Wu","year":"2020","journal-title":"Lancet"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1038\/s41591-020-0883-7","article-title":"Modeling the COVID-19 epidemic an implementation of population wide interventions in Italy","volume":"26","author":"Giordano","year":"2020","journal-title":"Nat. Med."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"165","DOI":"10.21037\/jtd.2020.02.64","article-title":"Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions","volume":"12","author":"Yang","year":"2020","journal-title":"J. Thorac. Dis."},{"key":"ref_13","first-page":"1","article-title":"Estimating and Simulating a SIRD Model of COVID-19 for Many Countries, States, and Cities","volume":"15","author":"Villaverde","year":"2020","journal-title":"NBER Work. Paper SERIES"},{"key":"ref_14","first-page":"248","article-title":"An updated estimation of the risk of transmission of the novel coronavirus 2019-nCov","volume":"5","author":"Tang","year":"2020","journal-title":"Infect. Dis. Model."},{"key":"ref_15","first-page":"1","article-title":"An age and space structured SIR model describing the Covid-19 pandemic","volume":"10","author":"Colombo","year":"2020","journal-title":"J. Math. Ind."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Di Giamberardino, P., Iacoviello, D., Albano, F., and Frasca, F.T. (2020, January 8\u201310). Age based modelling of SARS-CoV-2 Contagion: The Italian case. Proceedings of the 24th International Conference on System Theory, Control and Computing, ICSTCC 2020\u2014Proceedings, Sinaia, Romania.","DOI":"10.1109\/ICSTCC50638.2020.9259749"},{"key":"ref_17","first-page":"256","article-title":"Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020","volume":"5","author":"Roosa","year":"2021","journal-title":"Infect. Dis. Model."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-021-85875-2","article-title":"Multiwave pandemic dynamics explained: How to tame the next wave of infectious diseases","volume":"11","author":"Cacciapaglia","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_19","first-page":"293","article-title":"To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic","volume":"5","author":"Eikenberry","year":"2020","journal-title":"Infect. Dis. Model."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/em-2020-0044","article-title":"An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting","volume":"10","author":"Gounane","year":"2021","journal-title":"Epidemiol. Methods"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.chaos.2020.110364","article-title":"Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia","volume":"141","author":"Aldila","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1038\/s41562-020-0931-9","article-title":"Modelling the impact of testing, contact tracing and household quarantine on second waves of COVID-19","volume":"4","author":"Aleta","year":"2020","journal-title":"Nat. Hum. Behav."},{"key":"ref_23","first-page":"1","article-title":"Evaluation of the effect of different policies in the containment of epidemic spreads for the COVID-19 case","volume":"102325","author":"Iacoviello","year":"2021","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Martcheva, M. (2015). An Introduction to Mathematical Epidemiology. Text Applied Mathematics, Springer.","DOI":"10.1007\/978-1-4899-7612-3"},{"key":"ref_25","unstructured":"Dorf, R.C., and Bishop, R.H. (2001). Modern Control Systems, Pearson."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Nishiura, H., and Chowell, G. (2009). The Effective Reproduction Number as a Prelude to Statistical Estimation of Time-Dependent Epidemic Trends. Mathematical and Statistical Estimation Approaches in Epidemiology, Springer.","DOI":"10.1007\/978-90-481-2313-1_5"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub\u2013threshold endemic equilibria for compartmental models of disease transmission","volume":"180","author":"Watmough","year":"2002","journal-title":"Math. Biosci."},{"key":"ref_28","unstructured":"(2020). Reproduction Number (R) and Growth Rate (r) of the COVID-19 Epidemic in the UK: Methods of Estimation, Data Sources, Causes of Heterogeneity, and Use as a Guide in Policy Formulation, The Royal Society."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"e8601","DOI":"10.7717\/peerj.8601","article-title":"Modeling the effective reproduction number of vector-borne diseases: The yellow fever outbreak in Luanda, Angola 2015\u20132016 as an example","volume":"8","author":"Zhao","year":"2020","journal-title":"PeerJ"},{"key":"ref_30","first-page":"148","article-title":"A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations","volume":"6","author":"Gumel","year":"2021","journal-title":"Infect. Dis. Model."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/S0140-6736(20)30251-8","article-title":"Genomic characterisation and epidemiology of 2019 novel coronavirus: Implications for virus origins and receptor binding","volume":"395","author":"Lu","year":"2020","journal-title":"Lancet"},{"key":"ref_32","unstructured":"(2021, April 10). Epicentro. Available online: https:\/\/www.epicentro.iss.it."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/890\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:02:56Z","timestamp":1760162576000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/890"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,17]]},"references-count":32,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["sym13050890"],"URL":"https:\/\/doi.org\/10.3390\/sym13050890","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,5,17]]}}}