{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:54:15Z","timestamp":1760147655721,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003336","name":"Bulgarian National Science Fund","doi-asserted-by":"publisher","award":["KP-06-PN 46-7"],"award-info":[{"award-number":["KP-06-PN 46-7"]}],"id":[{"id":"10.13039\/501100003336","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Honeybee losses are an extensive global problem. In this study, a new compartment model of honeybee population that mainly concerns honey production is developed. The model describes the interaction of the food stock with the brood (immature bees), adult bees and produced honey. In the present paper, the issue of an adequate model recovery is addressed and the parameter identification inverse problem is solved. An adjoint equation procedure to obtain the unknown parameter values by minimizing the functional error during a period of time is proposed. Numerical simulations with realistic data are discussed.<\/jats:p>","DOI":"10.3390\/axioms12020214","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T02:29:08Z","timestamp":1676860148000},"page":"214","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Parameter Estimation Analysis in a Model of Honey Production"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4816-2837","authenticated-orcid":false,"given":"Atanas Z.","family":"Atanasov","sequence":"first","affiliation":[{"name":"Department of Agricultural Machinery, Agrarian Industrial Faculty, University of Ruse, 7004 Ruse, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9826-9603","authenticated-orcid":false,"given":"Slavi G.","family":"Georgiev","sequence":"additional","affiliation":[{"name":"Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria"},{"name":"Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 7004 Ruse, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0684-8574","authenticated-orcid":false,"given":"Lubin G.","family":"Vulkov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 7004 Ruse, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7472","DOI":"10.1073\/pnas.1103457108","article-title":"Genes involved in convergent evolution of eusociality in bees","volume":"108","author":"Woodard","year":"2011","journal-title":"Proc. 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Biol."},{"key":"ref_10","first-page":"805","article-title":"The epidemic of honey bee colony losses during the 1995\u20131996 season","volume":"136","author":"Finley","year":"1996","journal-title":"Am. Bee J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/S0022-5193(03)00121-8","article-title":"The hive bee to forager transition in honeybee colonies: The double repressor hypothesis","volume":"223","author":"Amdam","year":"2003","journal-title":"J. Theor. Biol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"100","DOI":"10.3896\/IBRA.1.51.1.12","article-title":"Managed honey bee colony losses in Canada, China, Europe, Israel and Turkey for the winters of 2008\u20132009 and 2009\u20132010","volume":"51","author":"Pisa","year":"2012","journal-title":"J. Apic. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1080\/0005772X.1964.11097032","article-title":"The \u2018Isle of Wight Disease\u2019: The Origin and Significance of the Myth","volume":"45","author":"Bailey","year":"1964","journal-title":"Bee World"},{"key":"ref_14","first-page":"189","article-title":"Disappearing disease. Part 1\u2014Effects of certain protein sources given to honey bee colonies in Florida","volume":"122","author":"Kulincevic","year":"1982","journal-title":"Am. Bee J."},{"key":"ref_15","unstructured":"Dornberger, L., Mitchell, C., Hull, B., Ventura, W., Shopp, H., Kribs-Zaleta, C., Kojouharov, H., and Grover, J. (2012). Death of the Bees: A Mathematical Model of Colony Collapse Disorder, University of Texas at Arlington Mathematics Department."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hristov, P., Shumkova, R., Palova, N., and Neov, B. (2020). Factors associated with honey bee colony losses: A mini-review. Vet. Sci., 7.","DOI":"10.3390\/vetsci7040166"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bagheri, S., and Mirzaie, M. (2019). A mathematical model of honey bee colony dynamics to predict the effect of pollen on colony failure. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0225632"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.1007\/s11538-017-0300-7","article-title":"Reproduction number and asymptotic stability for the dynamics of a honey bee colony with continuous age structure","volume":"79","author":"Betti","year":"2017","journal-title":"Bull. Math. Biol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1016\/j.scitotenv.2016.11.178","article-title":"Modelling seasonal effects of temperature and precipitation on honey bee winter mortality in a temperate climate","volume":"579","author":"Switanek","year":"2017","journal-title":"Sci. Total Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1218","DOI":"10.1007\/s11538-017-0281-6","article-title":"A mathematical model of forager loss in honeybee colonies infested with Varroa destructor and the acute bee paralysis virus","volume":"79","author":"Ratti","year":"2017","journal-title":"Bull. Math. Biol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1111\/1365-2664.12112","article-title":"Review: Towards a systems approach for understanding honeybee decline: A stocktaking and synthesis of existing models","volume":"50","author":"Becher","year":"2013","journal-title":"J. Appl. Ecol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Torres, D.J., Ricoy, V.M., and Roybal, S. (2015). Modelling honey bee populations. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0130966"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1850063","DOI":"10.1142\/S1793524518500638","article-title":"A fractional dynamical model for honeybee colony population","volume":"11","year":"2018","journal-title":"Int. J. Biomath."},{"key":"ref_24","first-page":"7","article-title":"An approach to the modeling of honey bee colonies","volume":"22","author":"Gutierrez","year":"2013","journal-title":"Web Ecol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2481","DOI":"10.1007\/s11081-021-09678-0","article-title":"Reconstruction analysis of honeybee colony collapse disorder modeling","volume":"22","author":"Atanasov","year":"2021","journal-title":"Optim. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/978-3-030-68527-0_23","article-title":"Parameter identification of Colony Collapse Disorder in honeybees as a contagion","volume":"Volume 1341","author":"Simian","year":"2021","journal-title":"Modelling and Development of Intelligent Systems"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"110002","DOI":"10.1016\/j.ecolmodel.2022.110002","article-title":"Using system equalization principle to study the effects of multiple factors to the development of bee colony","volume":"470","author":"Hong","year":"2022","journal-title":"Ecol. Model."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hundsdorfer, W., and Vermer, J. (2003). Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer.","DOI":"10.1007\/978-3-662-09017-6"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Marchuk, G.I. (1995). Adjoint Equations and Analysis of Complex Systems, Kluwer.","DOI":"10.1007\/978-94-017-0621-6"},{"key":"ref_30","unstructured":"Marchuk, G.I., Agoshkov, V.I., and Shutyaev, V.P. (1996). Adjoint Equations and Perturbation Algorithms in Nonlinear Problems, CRC Press."},{"key":"ref_31","unstructured":"Winston, W.L. (1991). The Biology of the Honey Bee, Harvard University Press."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1016\/j.amc.2006.07.004","article-title":"Some research on Levenberg\u2013Marquardt method for the nonlinear equations","volume":"184","author":"Ma","year":"2007","journal-title":"Appl. Math. 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