{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:37:13Z","timestamp":1773815833043,"version":"3.50.1"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["Grant 22-11-00025"],"award-info":[{"award-number":["Grant 22-11-00025"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["Grant 22-11-00025"],"award-info":[{"award-number":["Grant 22-11-00025"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["Grant 20-01-00352"],"award-info":[{"award-number":["Grant 20-01-00352"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["Grant 20-01-00352"],"award-info":[{"award-number":["Grant 20-01-00352"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> In this work, we briefly describe our technology developed for computing periodic solutions of time-delay systems and discuss the results of computing periodic solutions for the Marchuk\u2013Petrov model with parameter values, corresponding to hepatitis B infection. We identified the regions in the model parameter space in which an oscillatory dynamics in the form of periodic solutions exists. The respective solutions can be interpreted as active forms of chronic hepatitis B. The period and amplitude of oscillatory solutions were traced along the parameter determining the efficacy of antigen presentation by macrophages for T- and B-lymphocytes in the model.. The oscillatory regimes are characterized by enhanced destruction of hepatocytes as a consequence of immunopathology and temporal reduction of viral load to values which can be a prerequisite of spontaneous recovery observed in chronic HBV infection. Our study presents a first step in a systematic analysis of the chronic HBV infection using Marchuk\u2013Petrov model of antiviral immune response. <\/jats:p>","DOI":"10.1142\/s0219720023400012","type":"journal-article","created":{"date-parts":[[2023,1,26]],"date-time":"2023-01-26T00:59:00Z","timestamp":1674694740000},"source":"Crossref","is-referenced-by-count":6,"title":["Numerical study of chronic hepatitis B infection using Marchuk\u2013Petrov model"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0391-7319","authenticated-orcid":false,"given":"Michael","family":"Khristichenko","sequence":"first","affiliation":[{"name":"Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow 119333, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuri","family":"Nechepurenko","sequence":"additional","affiliation":[{"name":"Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow 119333, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Grebennikov","sequence":"additional","affiliation":[{"name":"Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow 119333, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gennady","family":"Bocharov","sequence":"additional","affiliation":[{"name":"Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow 119333, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,3,9]]},"reference":[{"key":"S0219720023400012BIB001","doi-asserted-by":"crossref","first-page":"125","DOI":"10.24875\/AIDSRev.M17000012","volume":"20","author":"Soriano V","year":"2018","journal-title":"AIDS Rev"},{"key":"S0219720023400012BIB002","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1038\/s41577-021-00549-4","volume":"22","author":"Iannacone M","year":"2022","journal-title":"Nat Rev Immunol"},{"key":"S0219720023400012BIB003","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1038\/s41573-019-0037-0","volume":"18","author":"Fanning GC","year":"2019","journal-title":"Nat Rev Drug Discov"},{"key":"S0219720023400012BIB004","doi-asserted-by":"crossref","first-page":"434","DOI":"10.3390\/v14020434","volume":"14","author":"Chien RN","year":"2022","journal-title":"Viruses"},{"key":"S0219720023400012BIB005","doi-asserted-by":"crossref","first-page":"S8","DOI":"10.1016\/S1590-8658(10)60686-X","volume":"43","author":"Villa E","year":"2011","journal-title":"Dig Liver Dis"},{"key":"S0219720023400012BIB006","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/S0140-6736(09)60207-5","volume":"9663","author":"Liaw YF","year":"2009","journal-title":"Lancet"},{"key":"S0219720023400012BIB007","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1016\/j.jhep.2014.08.033","volume":"61","author":"Chang ML","year":"2014","journal-title":"J Hepatol"},{"key":"S0219720023400012BIB008","first-page":"1","author":"Liaw YF","year":"2022","journal-title":"Expert Rev Gastroenterol Hepatol"},{"key":"S0219720023400012BIB009","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1038\/nm.3251","volume":"19","author":"Rehermann B","year":"2013","journal-title":"Nat Med"},{"key":"S0219720023400012BIB010","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.antiviral.2015.06.008","volume":"121","author":"Gish RG","year":"2015","journal-title":"Antiviral Res"},{"key":"S0219720023400012BIB011","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.jtbi.2018.03.025","volume":"447","author":"Fatehi Chenar F","year":"2018","journal-title":"J Theor Biol"},{"key":"S0219720023400012BIB012","doi-asserted-by":"crossref","first-page":"8176","DOI":"10.3390\/app11178176","volume":"11","author":"Hews S","year":"2021","journal-title":"Appl Sci"},{"key":"S0219720023400012BIB013","doi-asserted-by":"crossref","first-page":"e0188209","DOI":"10.1371\/journal.pone.0188209","volume":"12","author":"Cangelosi Q","year":"2017","journal-title":"PLoS One"},{"key":"S0219720023400012BIB014","doi-asserted-by":"crossref","first-page":"1252","DOI":"10.1038\/s41598-021-04022-z","volume":"12","author":"Fatehi F","year":"2022","journal-title":"Sci Rep"},{"key":"S0219720023400012BIB015","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.cam.2004.08.019","volume":"184","author":"Luzyanina T","year":"2005","journal-title":"J Comput Appl Math"},{"key":"S0219720023400012BIB016","first-page":"1905","volume":"40","author":"Bocharov GA","year":"2000","journal-title":"Comput Math Math Phys"},{"key":"S0219720023400012BIB017","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8798-3","volume-title":"Mathematical Modelling of Immune Response in Infectious Diseases","author":"Marchuk GI","year":"1997"},{"key":"S0219720023400012BIB018","series-title":"Optimization Software Inc.","volume-title":"Mathematical Models in Immunology","author":"Marchuk GI","year":"1983"},{"key":"S0219720023400012BIB019","volume-title":"Practical Bifurcation and Stability Analysis","author":"Seydel R","year":"2009"},{"key":"S0219720023400012BIB020","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1515\/rnam-2021-0008","volume":"36","author":"Khristichenko MY","year":"2021","journal-title":"Russ J Numer Anal Math Model"},{"key":"S0219720023400012BIB021","first-page":"1","volume":"012036","author":"Khristichenko MY","year":"2021","journal-title":"J Phys: Conf Ser"},{"key":"S0219720023400012BIB022","volume-title":"Solving Ordinary Differential Equations I","author":"Hairer E","year":"1993"},{"key":"S0219720023400012BIB023","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0022-5193(05)80143-2","volume":"151","author":"Marchuk GI","year":"1991","journal-title":"J Theor Biol"},{"key":"S0219720023400012BIB024","first-page":"2385","volume":"13","author":"Nechepurenko YM","year":"2020","journal-title":"Discr Contin Dyn Syst"}],"container-title":["Journal of Bioinformatics and Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219720023400012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T13:28:05Z","timestamp":1683638885000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219720023400012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,9]]},"references-count":24,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10.1142\/S0219720023400012"],"URL":"https:\/\/doi.org\/10.1142\/s0219720023400012","relation":{},"ISSN":["0219-7200","1757-6334"],"issn-type":[{"value":"0219-7200","type":"print"},{"value":"1757-6334","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,9]]},"article-number":"2340001"}}