{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T19:14:03Z","timestamp":1791400443482,"version":"4.3.3"},"reference-count":94,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2022-1115"],"award-info":[{"award-number":["075-15-2022-1115"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Vaccines"],"abstract":"<jats:p>In this work, we develop mathematical models of the immune response to respiratory viral infection, taking into account some particular properties of the SARS-CoV infections, cytokine storm and vaccination. Each model consists of a system of ordinary differential equations that describe the interactions of the virus, epithelial cells, immune cells, cytokines, and antibodies. Conventional analysis of the existence and stability of stationary points is completed by numerical simulations in order to study the dynamics of solutions. The behavior of the solutions is characterized by large peaks of virus concentration specific to acute respiratory viral infections. At the first stage, we study the innate immune response based on the protective properties of interferon secreted by virus-infected cells. Viral infection down-regulates interferon production. This competition can lead to the bistability of the system with different regimes of infection progression with high or low intensity. After that, we introduce the adaptive immune response with antigen-specific T- and B-lymphocytes. The resulting model shows how the incubation period and the maximal viral load depend on the initial viral load and the parameters of the immune response. In particular, an increase in the initial viral load leads to a shorter incubation period and higher maximal viral load. The model shows that a deficient production of antibodies leads to an increase in the incubation period and even higher maximum viral loads. In order to study the emergence and dynamics of cytokine storm, we consider proinflammatory cytokines produced by cells of the innate immune response. Depending on the parameters of the model, the system can remain in the normal inflammatory state specific for viral infections or, due to positive feedback between inflammation and immune cells, pass to cytokine storm characterized by the excessive production of proinflammatory cytokines. Finally, we study the production of antibodies due to vaccination. We determine the dose\u2013response dependence and the optimal interval of vaccine dose. Assumptions of the model and obtained results correspond to the experimental and clinical data.<\/jats:p>","DOI":"10.3390\/vaccines11010127","type":"journal-article","created":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T01:33:30Z","timestamp":1672882410000},"page":"127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Modelling of the Innate and Adaptive Immune Response to SARS Viral Infection, Cytokine Storm and Vaccination"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3944-885X","authenticated-orcid":false,"given":"Cristina","family":"Leon","sequence":"first","affiliation":[{"name":"Interdisciplinary Center for Mathematical Modelling in Biomedicine, S.M. Nikol\u2019skii Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia"},{"name":"M&S Decisions, 5 Naryshkinskaya Alley, 125167 Moscow, Russia"},{"name":"Department of Foreign Languages No. 2, Plekhanov Russian University of Economics, 36 Stremyanny Lane, 115093 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3480-1813","authenticated-orcid":false,"given":"Alexey","family":"Tokarev","sequence":"additional","affiliation":[{"name":"Interdisciplinary Center for Mathematical Modelling in Biomedicine, S.M. Nikol\u2019skii Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia"},{"name":"Semenov Institute of Chemical Physics, 4 Kosygin St., 119991 Moscow, Russia"},{"name":"Bukhara Engineering Technological Institute, 15 Murtazoyeva Street, Bukhara 200100, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2729-6484","authenticated-orcid":false,"given":"Anass","family":"Bouchnita","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79902, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vitaly","family":"Volpert","sequence":"additional","affiliation":[{"name":"Interdisciplinary Center for Mathematical Modelling in Biomedicine, S.M. Nikol\u2019skii Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia"},{"name":"Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,4]]},"reference":[{"key":"ref_1","unstructured":"WHO (2022, December 20). The Top 10 Causes of Death. 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