{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:57:21Z","timestamp":1760785041786,"version":"3.40.5"},"reference-count":40,"publisher":"Wiley","license":[{"start":{"date-parts":[[2021,10,18]],"date-time":"2021-10-18T00:00:00Z","timestamp":1634515200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Basque Government","doi-asserted-by":"crossref","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2021,10,18]]},"abstract":"<jats:p>In this study, two types of epidemiological models called \u201cwithin host\u201d and \u201cbetween hosts\u201d have been studied. The within-host model represents the innate immune response, and the between-hosts model signifies the SEIR (susceptible, exposed, infected, and recovered) epidemic model. The major contribution of this paper is to break the chain of infectious disease transmission by reducing the number of susceptible and infected people via transferring them to the recovered people group with vaccination and antiviral treatment, respectively. Both transfers are considered with time delay. In the first step, optimal control theory is applied to calculate the optimal final time to control the disease within a host\u2019s body with a cost function. To this end, the vaccination that represents the effort that converts healthy cells into resistant-to-infection cells in the susceptible individual\u2019s body is used as the first control input to vaccinate the susceptible individual against the disease. Moreover, the next control input (antiviral treatment) is applied to eradicate the concentrations of the virus and convert healthy cells into resistant-to-infection cells simultaneously in the infected person\u2019s body to treat the infected individual. The calculated optimal time in the first step is considered as the delay of vaccination and antiviral treatment in the SEIR dynamic model. Using Pontryagin\u2019s maximum principle in the second step, an optimal control strategy is also applied to an SEIR mathematical model with a nonlinear transmission rate and time delay, which is computed as optimal time in the first step. Numerical results are consistent with the analytical ones and corroborate our theoretical results.<\/jats:p>","DOI":"10.1155\/2021\/4348910","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T01:16:44Z","timestamp":1634606204000},"page":"1-27","source":"Crossref","is-referenced-by-count":8,"title":["Optimal Allocation of Vaccine and Antiviral Drugs for Influenza Containment over Delayed Multiscale Epidemic Model considering Time-Dependent Transmission Rate"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0924-1751","authenticated-orcid":true,"given":"Zohreh","family":"Abbasi","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Kashan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6795-4461","authenticated-orcid":true,"given":"Iman","family":"Zamani","sequence":"additional","affiliation":[{"name":"Electrical and Electronic Engineering Department, Shahed University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7030-884X","authenticated-orcid":true,"given":"Amir Hossein","family":"Amiri Mehra","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Kashan, Iran"},{"name":"Electrical and Electronic Engineering Department, Shahed University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asier","family":"Ibeas","sequence":"additional","affiliation":[{"name":"Departament de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Escolad\u2019Enginyeria, Universitat Aut\u00f2noma de Barcelona, Barcelona, Spain"},{"name":"Universidad de Bogot\u00e1 Jorge Tadeo Lozano, Bogot\u00e1 D.C., Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3239-8987","authenticated-orcid":true,"given":"Mohsen","family":"Shafieirad","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Kashan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.3390\/v7102875"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/386235"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2004.08.001"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1128\/iai.13.2.438-447.1976"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1006\/jtbi.1994.1074"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1128\/JVI.01623-05"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.3182\/20120829-3-HU-2029.00029"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1927.0118"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1932.0171"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1933.0106"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2019.01.037"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-018-1241-y"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2019.08.015"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.5120\/ijca2017912886"},{"volume-title":"Control Systems, Robotics and Automation\u2013Volume VIII","year":"2009","author":"A. 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