{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T14:30:34Z","timestamp":1780410634443,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T00:00:00Z","timestamp":1611273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.<\/jats:p>","DOI":"10.3390\/sym13020166","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T12:28:31Z","timestamp":1611577711000},"page":"166","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7470-7557","authenticated-orcid":false,"given":"Irina","family":"Volinsky","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ariel University, Ariel 4076414, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6723-7019","authenticated-orcid":false,"given":"Salvo Danilo","family":"Lombardo","sequence":"additional","affiliation":[{"name":"CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Lazarettgasse 14, AKH BT 25.3, A-1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8372-4965","authenticated-orcid":false,"given":"Paz","family":"Cheredman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ariel University, Ariel 4076414, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,22]]},"reference":[{"key":"ref_1","first-page":"2835","article-title":"Analysis of a HCV model with CTL and antibody responses","volume":"3","author":"Yousdi","year":"2009","journal-title":"Appl. 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