Optimal control to limit the spread of COVID-19 in Italy





We apply optimal control theory to a generalized SEIR-type model. The proposed system has three controls, representing social distancing, preventive means, and treatment measures to combat the spread of the COVID-19 pandemic. We analyze such optimal control problem with respect to real data transmission in Italy. Our results show the appropriateness of the model, in particular with respect to the number of quarantined/hospitalized (confirmed and infected) and recovered individuals. Considering the Pontryagin controls, we show how in a perfect world one could drastically diminish the number of susceptible, exposed, infected, quarantined/hospitalized, and death individuals, by increasing the population of insusceptible/protected.

Author Biographies

Mohamed Abdelaziz Zaitri, University of Bejaia

PhD student.

Delfim F. M. Torres, University of Aveiro


Professor Dr. Delfim F. M. Torres <delfim@ua.pt> D.Sc. (Habilitation) in Mathematics, Ph.D. in Mathematics Web of Science Highly Cited Researcher 2015, 2016, 2017 and 2019 Full Professor of Mathematics Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal Director of the R&D unit CIDMA Coordinator of the Systems and Control Group Director of the Doctoral/PhD Programme in Mathematics and Applications (PDMA) Lifetime Member of The American Mathematical Society ISI Web of Science: http://www.researcherid.com/rid/A-7682-2008 Scopus: http://scopus.com/authid/detail.url?authorId=7102800859 MathSciNet: http://www.ams.org/mathscinet/search/author.html?mrauthid=657307 zbMATH: http://zbmath.org/authors/?q=ai:torres.delfim-f-m ORCID: http://orcid.org/0000-0001-8641-2505 Google Scholar: http://scholar.google.com/citations?user=PAeWCi8AAAAJ ResearchGate: https://www.researchgate.net/profile/Delfim_F_M_Torres arXiv: http://arxiv.org/a/torres_d_1.html University of Aveiro: https://www.ua.pt/pt/p/10312819