{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T10:03:10Z","timestamp":1779789790561,"version":"3.53.1"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T00:00:00Z","timestamp":1779753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Epidemiologia"],"abstract":"<jats:p>Introduction: This study quantifies excess mortality in Spain during and after the COVID-19 pandemic and assesses whether mortality levels are returning to pre-pandemic patterns. Methods: Expected mortality was estimated using stochastic forecasting models calibrated on pre-pandemic data (1990\u20132019) and compared with observed mortality over the period 2020\u20132023. The analysis relies on a multi-model framework including the Lee\u2013Carter, Cairns\u2013Blake\u2013Dowd, and age\u2013period\u2013cohort models. Results: The results show a substantial excess mortality during the pandemic years, with the proportion of ages exhibiting punctual excess mortality increasing from around 65% before the pandemic to approximately 85% during 2020\u20132022. Excess mortality declined sharply in 2023, when indicators returned to levels comparable to those observed prior to COVID-19, suggesting a transition toward near-normal mortality. The Lee\u2013Carter model showed superior short-term performance in detecting abrupt mortality deviations, while APC and CBD models captured longer-term structural patterns. Conclusions: These findings highlight the usefulness of multi-model stochastic approaches for monitoring excess mortality and assessing recovery trajectories following major epidemiological shocks.<\/jats:p>","DOI":"10.3390\/epidemiologia7030074","type":"journal-article","created":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T08:16:08Z","timestamp":1779783368000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Is Excess Mortality Returning to Pre-Pandemic Levels? A Multi-Model Stochastic Approach for COVID-19: The Spanish Case"],"prefix":"10.3390","volume":"7","author":[{"given":"Julio","family":"Ib\u00e1\u00f1ez-Soriano","sequence":"first","affiliation":[{"name":"Departamento d\u2019Economia Aplicada, Universitat de Val\u00e8ncia, Avda Tarongers s\/n, 46022 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4204-906X","authenticated-orcid":false,"given":"Francisco G.","family":"Morillas-Jurado","sequence":"additional","affiliation":[{"name":"Departamento d\u2019Economia Aplicada, Universitat de Val\u00e8ncia, Avda Tarongers s\/n, 46022 Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e2031756","DOI":"10.1001\/jamanetworkopen.2020.31756","article-title":"Household Transmission of SARS-CoV-2: A Systematic Review and Meta-analysis","volume":"3","author":"Madewell","year":"2020","journal-title":"JAMA Netw. Open"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1080\/15321819.2021.1904414","article-title":"An overview of COVID-19 pandemic: Immunology and pharmacology","volume":"42","author":"Arif","year":"2021","journal-title":"J. Immunoass. Immunochem."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1017\/S1748499522000045","article-title":"The impact of mortality shocks on modelling and insurance valuation as exemplified by COVID-19","volume":"16","author":"Kleinow","year":"2022","journal-title":"Ann. Actuar. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1017\/dem.2023.9","article-title":"Accounting for COVID-19-type shocks in mortality modeling: A comparative study","volume":"89","author":"Kleinow","year":"2023","journal-title":"J. Demogr. Econ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.ijforecast.2020.11.010","article-title":"COVID-19: Forecasting confirmed cases and deaths with a simple time series model","volume":"38","author":"Petropoulos","year":"2022","journal-title":"Int. J. Forecast."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1007\/s10203-024-00434-4","article-title":"Modeling and forecasting mortality with economic, environmental and lifestyle variables","volume":"48","author":"Dimai","year":"2024","journal-title":"Decis. Econ. Finan."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"10","DOI":"10.5709\/ce.1897-9254.496","article-title":"Forecasting commercial vehicle production using quantitative techniques","volume":"17","author":"Toppur","year":"2023","journal-title":"Contemp. Econ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"321","DOI":"10.5709\/ce.1897-9254.540","article-title":"To survive in the COVID-19 pandemic: The financial aspects of NGOs","volume":"18","author":"Leitoniene","year":"2024","journal-title":"Contemp. Econ."},{"key":"ref_9","first-page":"1073","article-title":"The impact of COVID-19 on health and health systems","volume":"31","author":"Haileamlak","year":"2021","journal-title":"Ethiop. J. Health Sci."},{"key":"ref_10","unstructured":"OECD\/European Union (2020). Health at a Glance: Europe 2020: State of Health in the EU Cycle, OECD Publishing."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1056\/NEJMp2005492","article-title":"Facing COVID-19 in Italy\u2014Ethics, Logistics, and Therapeutics on the Epidemic\u2019s Front Line","volume":"382","author":"Rosenbaum","year":"2020","journal-title":"N. Engl. J. Med."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1038\/s41586-020-2521-4","article-title":"Factors associated with COVID-19-related death using OpenSAFELY","volume":"584","author":"Williamson","year":"2020","journal-title":"Nature"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"m1198","DOI":"10.1136\/bmj.m1198","article-title":"COVID-19: Risk factors for severe disease and death","volume":"368","author":"Jordan","year":"2020","journal-title":"BMJ"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1016\/S0140-6736(20)30566-3","article-title":"Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: A retrospective cohort study","volume":"395","author":"Zhou","year":"2020","journal-title":"Lancet"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1126\/science.abc2535","article-title":"Susceptible supply limits the role of climate in the early SARS-CoV-2 pandemic","volume":"369","author":"Baker","year":"2020","journal-title":"Science"},{"key":"ref_16","unstructured":"Centers for Disease Control and Prevention (CDC), and National Center for Health Statistics (2026, January 10). Excess Deaths Associated with COVID-19, Available online: https:\/\/www.cdc.gov\/nchs\/nvss\/vsrr\/covid19\/excess_deaths.htm."},{"key":"ref_17","unstructured":"Reynolds, C., and Dattani, A. (2026, May 17). What If Mortality Stops Improving? Introducing a Product Idea That Shares the Risks and Benefits of Changes in Mortality Rates. Milliman. Available online: https:\/\/www.milliman.com\/en\/insight\/what-if-mortality-stops-improving."},{"key":"ref_18","unstructured":"Instituto de Salud Carlos III (ISCIII) (2018). Excesos de Mortalidad Identificados por el Sistema de Monitorizaci\u00f3n de la Mortalidad Diaria (MoMo), Epidemiological National Center of Spain. Available online: https:\/\/cne.isciii.es\/documents\/d\/cne\/informe_momo_plan_de_calor2016_final."},{"key":"ref_19","unstructured":"Fundaci\u00f3n MAPFRE (2026, May 17). La Evoluci\u00f3n de la Pir\u00e1mide Invertida. Available online: https:\/\/ageingnomics.fundacionmapfre.org\/blog\/evolucion-piramide-invertida\/."},{"key":"ref_20","unstructured":"Directorate-General for Economic and Financial Affairs (2023). 2024 Ageing Report. Underlying Assumptions and Projection Methodologies, European Commission. Available online: https:\/\/economy-finance.ec.europa.eu\/publications\/2024-ageing-report-underlying-assumptions-and-projection-methodologies_en."},{"key":"ref_21","unstructured":"Ayuso, M., Corrales, H., Guillen, M., P\u00e9rez Mar\u00edn, A.M., and Rojo, J.L. (2007). Estad\u00edstica Actuarial Vida, Publicacions i Edicions de la Universitat de Barcelona."},{"key":"ref_22","first-page":"659","article-title":"Modeling and forecasting U.S. mortality","volume":"87","author":"Lee","year":"1992","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1080\/03461230802173608","article-title":"Modelling and management of mortality risk: A review","volume":"2008","author":"Cairns","year":"2008","journal-title":"Scand. Actuar. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1353\/dem.2001.0036","article-title":"Evaluating the performance of the Lee-Carter method for forecasting mortality","volume":"38","author":"Lee","year":"2001","journal-title":"Demography"},{"key":"ref_25","unstructured":"Boumezoued, A., Elfassihi, A., Germain, V., and Titon, E.-E. (2026, January 10). Modelling the Impact of Climate Risks on Mortality [White Paper]. Available online: https:\/\/www.milliman.com\/en\/insight\/modeling-the-impact-of-climate-risks-on-mortality."},{"key":"ref_26","unstructured":"Hyndman, R.J. (2026, May 17). Demography: Forecasting Mortality, Fertility, Migration and Population Data (R Package Version 1.24). Available online: https:\/\/pkg.robjhyndman.com\/demography\/."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4942","DOI":"10.1016\/j.csda.2006.07.028","article-title":"Robust forecasting of mortality and fertility rates: A functional data approach","volume":"51","author":"Hyndman","year":"2007","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.insmatheco.2005.12.001","article-title":"A cohort-based extension to the Lee\u2013Carter model for mortality reduction factors","volume":"38","author":"Renshaw","year":"2006","journal-title":"Insur. Math. Econ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1111\/j.1539-6975.2006.00195.x","article-title":"A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration","volume":"73","author":"Cairns","year":"2006","journal-title":"J. Risk Insur."},{"key":"ref_30","unstructured":"D\u00edaz Rojo, G. (2026, May 17). Ajuste y Predicci\u00f3n de la Mortalidad. Aplicaci\u00f3n a Colombia. Available online: https:\/\/dialnet.unirioja.es\/servlet\/tesis?codigo=305889."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10920277.2009.10597538","article-title":"A quantitative comparison of stochastic mortality models using data from England and Wales and the United States","volume":"13","author":"Cairns","year":"2009","journal-title":"N. Am. Actuar. J."},{"key":"ref_32","unstructured":"Columbia University Mailman School of Public Health (2025, November 10). Age-Period-Cohort Analysis. Available online: https:\/\/www.publichealth.columbia.edu\/research\/population-health-methods\/age-period-cohort-analysis."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/BF02888350","article-title":"Likelihood and the Bayes procedure","volume":"31","author":"Akaike","year":"1980","journal-title":"Trab. Estad. Investig. Oper."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v084.i03","article-title":"StMoMo: An R Package for Stochastic Mortality Modeling","volume":"84","author":"Villegas","year":"2018","journal-title":"J. Stat. Softw."},{"key":"ref_36","unstructured":"(2026, May 17). Human Mortality Database (HMD). Human Mortality Database. Available online: https:\/\/www.mortality.org\/."},{"key":"ref_37","unstructured":"Instituto Nacional de Estad\u00edstica (INE) (2026, May 17). Tablas de Mortalidad. Available online: https:\/\/www.ine.es\/dyngs\/INEbase\/es\/operacion.htm?c=Estadistica_C&cid=1254736177004&menu=ultiDatos&idp=1254735573002."},{"key":"ref_38","unstructured":"Instituto Nacional de Estad\u00edstica (INE) (2026, May 17). Edad Media de la Poblaci\u00f3n por Provincia, Seg\u00fan Sexo. Available online: https:\/\/www.ine.es\/jaxiT3\/Tabla.htm?t=3199&L=0."},{"key":"ref_39","unstructured":"Instituto Nacional de Estad\u00edstica (INE) (2026, May 17). Mortalidad. Movimiento Natural de la Poblaci\u00f3n. Available online: https:\/\/ine.es\/dynt3\/inebase\/index.htm?padre=1684&capsel=5849."},{"key":"ref_40","unstructured":"Glei, D.A., G\u00f3mez Redondo, R., Arg\u00fceso, A., and Canudas-Romo, V. (2026, May 17). About Mortality Data for Spain. Available online: https:\/\/www.mortality.org\/File\/GetDocument\/hmd.v6\/ESP\/Public\/InputDB\/ESPcom.pdf."},{"key":"ref_41","unstructured":"Posit Team (2026, May 17). RStudio: Integrated Development Environment for R. Posit, PBC. Available online: http:\/\/www.posit.co\/."},{"key":"ref_42","unstructured":"Ib\u00e1\u00f1ez-Soriano, J., and Morillas-Jurado, F.G. (2025). Data and R-Script used to Analyze the effect of COVID-19 in the mortality of Spain with stochastic models. Zenodo."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1093\/pubmed\/fdad023","article-title":"Impact of COVID-19 on Spanish mortality rates in 2020 by age and sex","volume":"45","author":"Navarro","year":"2023","journal-title":"J. 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