{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T06:24:24Z","timestamp":1766298264258,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T00:00:00Z","timestamp":1602028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MCIU\/AEI\/FEDER, UE","award":["RTI2018-094336-B-I00"],"award-info":[{"award-number":["RTI2018-094336-B-I00"]}]},{"name":"COV 20\/01213","award":["Institute of Health Carlos III"],"award-info":[{"award-number":["Institute of Health Carlos III"]}]},{"name":"Basque Goverrment","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability requirements on bed disposal and other necessary treatment means for the seriously infectious subpopulations. The seriously infectious individuals are assumed to be a part of the total infectious being described by a time-varying proportional function. A time-varying upper-bound of those seriously infected individuals has to be satisfied as objective by either a total confinement or partial quarantine intervention of the susceptible subpopulation. Afterwards, a new extended SEIR (susceptible-exposed-infectious-recovered) epidemic model, which is referred to as an SEIAR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-recovered) epidemic model with demography and disease mortality is given and focused on so as to extend the above developed ideas on the SIR model. A proportionally gain in the model parameterization is assumed to distribute the transition from the exposed to the infectious into the two infectious individuals (namely, symptomatic and asymptomatic individuals). Such a model is evaluated under total or partial quarantines of all or of some of the subpopulations which have the effect of decreasing the number of contagions. Simulated numerical examples are also discussed related to model parameterizations of usefulness related to the current COVID-19 pandemic outbreaks.<\/jats:p>","DOI":"10.3390\/sym12101646","type":"journal-article","created":{"date-parts":[[2020,10,8]],"date-time":"2020-10-08T08:52:41Z","timestamp":1602147161000},"page":"1646","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["On Confinement and Quarantine Concerns on an SEIAR Epidemic Model with Simulated Parameterizations for the COVID-19 Pandemic"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"first","affiliation":[{"name":"Campus of Leioa, Institute of Research and Development of Processes IIDP, University of the Basque Country, 48940 Leioa (Bizkaia), Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5094-3152","authenticated-orcid":false,"given":"Asier","family":"Ibeas","sequence":"additional","affiliation":[{"name":"Department of Telecommunications and Systems Engineering, Universitat Aut\u00f2noma de Barcelona, UAB, 08193 Barcelona, Spain"}]},{"given":"Ravi","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas A &amp; M University, 700 Univ Blvd, Kingsville, TX 78363, USA"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rass, L., and Radcliffe, J. (2003). Spatial Deterministic Epidemics, Mathematical Surveys and Monographs, American Mathematical Society.","DOI":"10.1090\/surv\/102"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Keeling, M.J., and Rohani, P. (2008). Modeling Infectious Diseases, Princeton University Press.","DOI":"10.1515\/9781400841035"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1137\/120876642","article-title":"Global stability of infectious disease models using Lyapunov functions","volume":"73","author":"Shuai","year":"2013","journal-title":"SIAM J. Appl. Math."},{"key":"ref_4","first-page":"1","article-title":"Some formal results on positivity, stability and endemic steady-state attainability based on linear algebraic tools for a class of epidemic models with eventual incommensurate delays","volume":"2019","author":"Nistal","year":"2019","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.amc.2014.03.030","article-title":"Exact analytical solutions of the susceptible-infected-recovered (SIR) epidemic model and on SIR model with equal death and birth rates","volume":"236","author":"Harko","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1137\/S0036144500371907","article-title":"The mathematics of infectious diseases","volume":"42","author":"Hethcote","year":"2000","journal-title":"SIAM Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s40745-016-0075-y","article-title":"Computational stochastic modelling to handle the crisis occurred during community epidemic","volume":"3","author":"Verma","year":"2016","journal-title":"Ann. Data. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s00285-018-1273-3","article-title":"State estimators for some epidemiological systems","volume":"78","author":"Iggidr","year":"2018","journal-title":"J. Math. Biol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s12064-019-00300-7","article-title":"A deterministic time-delayed SIR epidemic model: Mathematical modelling and analysis","volume":"139","author":"Kumar","year":"2020","journal-title":"Theory Biosci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1007\/s00285-009-0256-9","article-title":"An SIR epidemic model with partial temporary immunity modelled with delay","volume":"59","author":"Taylor","year":"2009","journal-title":"J. Math. Biol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.3934\/cpaa.2020084","article-title":"On a delayed epidemic model with non-instantaneous impulses","volume":"19","author":"Bai","year":"2020","journal-title":"Commun. Pure Appl. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"837","DOI":"10.3934\/mbe.2010.7.837","article-title":"Global stability of an SIR epidemic model with delay and general nonlinear incidence","volume":"7","author":"McCluskey","year":"2010","journal-title":"Math. Biosci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"De la Sen, M., Ibeas, A., Alonso-Quesada, S., and Nistal, R. (2019). On a SIR model in a patchy environment under constant and feedback decentralized controls with asymmetric parameterizations. Symmetry, 11.","DOI":"10.3390\/sym11030430"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2819","DOI":"10.3934\/dcdsb.2015.20.2819","article-title":"Mathematical analysis of population migration and its effects to spread of epidemics","volume":"20","author":"Cui","year":"2015","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.matcom.2019.02.012","article-title":"On an SEIADR epidemic model with vaccination, treatment and dead-infectious corpses removal controls","volume":"163","author":"Ibeas","year":"2019","journal-title":"Math. Comput. Simul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.amc.2016.05.043","article-title":"A time-delayed epidemic model for Ebola disease transmission","volume":"290","author":"Yuan","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"He, Z.L., and Nie, L.F. (2015). The effect of pulse vaccination and treatment on SIR epidemic model with media impact. Discret. Dyn. Nat. Soc., 2015.","DOI":"10.1155\/2015\/532494"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3038","DOI":"10.1016\/j.matcom.2009.02.001","article-title":"Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates","volume":"79","author":"Hou","year":"2009","journal-title":"Math. Comput. Simul."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0096-3003(03)00331-X","article-title":"Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times","volume":"151","year":"2004","journal-title":"Appl. Math. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ameen, I., Baleanu, D., and Ali, H.M. (2020). An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment. Chaos Solitons Fractals, 137.","DOI":"10.1016\/j.chaos.2020.109892"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Boonyaprapasorn, A., Natsupakpong, N., Ngiamsunthorn, P.S., and Thung-Od, K. (2017, January 14\u201317). An application of finite time synergetic control for vaccination in epidemic systems. Proceedings of the 2017 IEEE Conference on Systems, Process and Control (ICSPC), Melaka, Malaysia.","DOI":"10.1109\/SPC.2017.8313017"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Boonyaprapasorn, A., Natsupakpong, N., Ngiamsunthorn, P.S., and Thung-Od, K. (2017, January 3\u20137). Fractional order sliding mode control for vaccination in epidemic systems. Proceedings of the 2017 2nd International Conference on Control and Robotics Engineering (ICCRE 2017), Bangkok, Thailand.","DOI":"10.1109\/ICCRE.2017.7935059"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sethaput, T., and Boonyaprapasorn, A. (2018, January 1\u20134). Fractional order sliding mode control applying on the HIV infection system. Proceedings of the 2018 International Conference on Artificial Life and Robotics, Beppu, Japan.","DOI":"10.5954\/ICAROB.2018.GS7-1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"104764","DOI":"10.1155\/2014\/104764","article-title":"Robust sliding control of SEIR epidemic models","volume":"2014","author":"Ibeas","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"De la Sen, M., Nistal, R., Ibeas, A., and Garrido, A.J. (2020). On the use of entropy issues to evaluate and control the transients in some epidemic models. Entropy, 22.","DOI":"10.3390\/e22050534"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"De la Sen, M., Ibeas, A., and Nistal, R. (2020). On the entropy of events under eventually inflated or deflated probability constraints. Application to the supervision of epidemic models under vaccination controls. Entropy, 22.","DOI":"10.3390\/e22030284"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2143","DOI":"10.1007\/s11433-013-5321-0","article-title":"Modelling the spreading rate of controlled communicable epidemics through and entropy-based thermodynamic model","volume":"56","author":"Wang","year":"2013","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.mbs.2018.03.012","article-title":"Epidemic as a natural process","volume":"299","author":"Annila","year":"2018","journal-title":"Math. Biosci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2708","DOI":"10.3934\/mbe.2020148","article-title":"A mathematical model for the novel coronavirus epidemic in Wuhan, China","volume":"17","author":"Yang","year":"2020","journal-title":"AIMS Math. Biosci. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.cnsns.2009.04.018","article-title":"Dynamics of a delayed epidemic model with non-monotonic incidence rate","volume":"15","author":"Huo","year":"2010","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, X., Liu, W.Y., Zhao, C.L., Zhang, X., and Yi, D.Y. (2019). Locating multiple sources of contagion in complex networks under the SIR model. Appl. Sci., 9.","DOI":"10.3390\/app9204472"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3195","DOI":"10.3934\/mbe.2019159","article-title":"Biological view of vaccination described by mathematical modellings: From rubella to dengue vaccines","volume":"16","author":"Yang","year":"2019","journal-title":"Math. Biosci. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Thakare, P.R., and Mathurkar, S.S. (2016, January 20\u201326). Modeling of epidemic spread by social interactions. Proceedings of the 2016 IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT), Bangalore, India.","DOI":"10.1109\/RTEICT.2016.7808045"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Darabi Sahneh, F., and Scoglio, C. (2011, January 12\u201315). Epidemic spread in human networks. Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA.","DOI":"10.1109\/CDC.2011.6161529"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhang, Z., and Wang, H. (2015, January 14\u201317). Epidemic source tracing on social contact networks. Proceedings of the 2015 17th International Conference on E-Health Networking, Application & Services (HealthCom), Boston, MA, USA.","DOI":"10.1109\/HealthCom.2015.7454525"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"e56","DOI":"10.1017\/S0950268819002188","article-title":"Research about the optimal strategies for prevention and control of varicella outbreak in a school in a central city of China: Based on an SEIR dynamic model","volume":"148","author":"Zha","year":"2020","journal-title":"Epidemiol. Infect."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"132599","DOI":"10.1016\/j.physd.2020.132599","article-title":"COVID-19: Development of a robust mathematical model and simulation package with consideration for ageing population and time delay for control action and resusceptibility","volume":"411","author":"Ng","year":"2020","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"e19115","DOI":"10.2196\/19115","article-title":"Prediction of the COVID-19 pandemic for the top 15 affected countries: Advanced autoregressive integrated moving average (ARIMA) model","volume":"6","author":"Kumar","year":"2020","journal-title":"JMIR Public Health Surveill."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"490","DOI":"10.3934\/publichealth.2020040","article-title":"Possible effects of mixed prevention strategy for COVID-19 epidemic: Massive testing, quarantine and social distance","volume":"7","author":"Kuniya","year":"2020","journal-title":"AIMS Public Health"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Liu, Y. (2020, September 24). Death Toll Estimation for COVID-19: Is the Curve Flattened Yet?. Available online: https:\/\/ssrn.com\/abstract=3592343.","DOI":"10.2139\/ssrn.3592343"},{"key":"ref_41","unstructured":"(2020, June 09). Mortality Rate of COVID-19 in Spain as of May 22, 2020, by Age Group. Available online: https:\/\/www.statista.com\/statistics\/1105596\/covid-19-mortality-rate-by-age-group-in-spain-march."},{"key":"ref_42","unstructured":"Abdulrahman, I.K. (2020, September 24). SimCOVID: An Open Source Simulation Program for the COVID-19 Outbreak. medRxiv. Paper in Collection COVID-19 SARS-CoV-2 Preprints from medRxiv and bioRxiv 2020. Available online: https:\/\/www.medrxiv.org\/content\/10.1101\/2020.04.13.20063354v2."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"281612","DOI":"10.1186\/1687-1847-2010-281612","article-title":"On a generalized time-varying SEIR epidemic model with mixed point and distributed delays and combined regular and impulsive vaccination controls","volume":"2010","author":"Agarwal","year":"2010","journal-title":"Adv. Differ. Equ."},{"key":"ref_44","unstructured":"(2020, June 29). Demographic data of Madrid. Available online: http:\/\/www.madrid.org\/iestadis\/fijas\/estructu\/demograficas\/mnp\/estructuespevida.htm."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"109953","DOI":"10.1016\/j.chaos.2020.109953","article-title":"A nonlinear epidemiological model considering asymptomatic and quarantine classes for SARS CoV-2 virus","volume":"138","author":"Mishra","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Gao, Z., Xu, Y., Sun, C., Wang, X., Guo, Y., Qiu, S., and Ma, K. (2020). A systematic review of asymptomatic infections with COVID-19. J. Microbiol. Immunol. Infect.","DOI":"10.1016\/j.jmii.2020.05.001"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"105303","DOI":"10.1016\/j.cnsns.2020.105303","article-title":"Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China","volume":"88","author":"Ivorra","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_48","unstructured":"De la Sen, M., Ibeas, A., and Garrido, A.J. (2020, January 7\u201310). On the estimation of some relevant parameters in the COVID-19 pandemic. Proceedings of the 9th International Conference on Mathematical Modeling in Physical Sciences, Paper ID C01-Y20-P167, Tinos Island, Greece. Journal of Physics Conference Series."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.ijid.2020.03.020","article-title":"Estimation of the asymptomatic ratio of novel coronavirus infections (COVID- 19)","volume":"94","author":"Hiroshi","year":"2020","journal-title":"Int. J. Infect. Dis."},{"key":"ref_50","unstructured":"(2020, June 29). Percentage of COVID-19 Cases in the United States from February 12 to March 16, 2020 That Resulted in Hospitalization, by Age Group. Available online: https:\/\/www.statista.com\/statistics\/1105402\/covid-hospitalization-rates-us-by-age-group."},{"key":"ref_51","unstructured":"(2020, June 29). Distribuci\u00f3n del N\u00famero de Camas en Hospitales en Espa\u00f1a en 2019, por Comunidad Aut\u00f3noma. Available online: https:\/\/es.statista.com\/estadisticas\/578785\/numero-total-de-camas-en-hospitales-en-espana-por-comunidad-autonoma."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13662-020-02622-z","article-title":"Positive explicit and implicit computational techniques for reaction-diffusion epidemic model of dengue disease dynamics","volume":"2020","author":"Ahmed","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13662-019-2432-6","article-title":"Existence of travelling wave solutions with critical speed in a delayed diffusive epidemic model","volume":"2019","author":"Cheng","year":"2019","journal-title":"Adv. Differ. Equ."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Xu, J.H., and Geng, Y. (2017). A non-standard finite difference scheme for a multi-group epidemic model with time delay. Adv. Differ. Equ.","DOI":"10.1186\/s13662-017-1415-8"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1098\/rsif.2005.0051","article-title":"Networks and epidemic models","volume":"2","author":"Keeling","year":"2005","journal-title":"J. R. Soc. Interface"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1629","DOI":"10.1007\/s00285-017-1203-9","article-title":"The parameter identification problem for SIR epidemic models: Identifying unreported cases","volume":"77","author":"Magal","year":"2018","journal-title":"J. Math. Biol."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Liu, W., Yue, X.G., and Tchounwou, P.B. (2020). Response to the COVID-19. Epidemic: The chinese experience and implications for other countries. Int. J. Environ. Res. Public Health, 17.","DOI":"10.3390\/ijerph17072304"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/10\/1646\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:17:14Z","timestamp":1760177834000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/10\/1646"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,7]]},"references-count":57,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["sym12101646"],"URL":"https:\/\/doi.org\/10.3390\/sym12101646","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,10,7]]}}}