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Silva CJ, Cruz C, Torres DFM, Muñuzuri AP, Carballosa A, Area I, Nieto JJ, Fonseca-Pinto R, Passadouro R, Santos ESD, Abreu W, Mira J. Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal. Sci Rep 2021; 11:3451. [PMID: 33568716 PMCID: PMC7876047 DOI: 10.1038/s41598-021-83075-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 01/27/2021] [Indexed: 02/08/2023] Open
Abstract
The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to "normal life" and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.
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Affiliation(s)
- Cristiana J Silva
- Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal.
| | - Carla Cruz
- Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal
| | - Delfim F M Torres
- Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal
| | - Alberto P Muñuzuri
- Department of Physics, Institute CRETUS, Group of Nonlinear Physics, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Alejandro Carballosa
- Department of Physics, Institute CRETUS, Group of Nonlinear Physics, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Iván Area
- Departamento de Matemática Aplicada II, E. E. Aeronáutica e do Espazo, Campus de Ourense, Universidade de Vigo, 32004, Ourense, Spain
| | - Juan J Nieto
- Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Rui Fonseca-Pinto
- Center for Innovative Care and Health Technology (ciTechCare), Polytechnic of Leiria, Leiria, Portugal
| | - Rui Passadouro
- Center for Innovative Care and Health Technology (ciTechCare), Polytechnic of Leiria, Leiria, Portugal
- ACES Pinhal Litoral-ARS Centro, Leiria, Portugal
| | | | - Wilson Abreu
- School of Nursing and Research Centre "Centre for Health Technology and Services Research/ESEP-CINTESIS", Porto, Portugal
| | - Jorge Mira
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain.
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