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However, in the majority of virus-infected individuals, the response is insufficient because viruses are known to use different evasion strategies to escape immune response. In this study, we use optimal control theory to investigate how to control the innate immune response. We present an optimal control model based on an ordinary-differential-equation system from a previous study, which investigated the dynamics and regulation of virus-triggered innate immune signaling pathways, and we prove the existence of a solution to the optimal control problem involving antiviral treatment or\/and interferon therapy. We conduct numerical experiments to investigate the treatment effects of different control strategies through varying the cost function and control efficiency. The results show that a separate treatment, that is, only inhibiting viral replication (u<\/mml:mi><\/mml:mrow>1<\/mml:mn><\/mml:mrow><\/mml:msub>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:math>) or enhancing interferon activity (u<\/mml:mi><\/mml:mrow>2<\/mml:mn><\/mml:mrow><\/mml:msub>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:math>), has more advantages for controlling viral infection than a mixed treatment, that is, controlling both (u<\/mml:mi><\/mml:mrow>1<\/mml:mn><\/mml:mrow><\/mml:msub>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:math>) and (u<\/mml:mi><\/mml:mrow>2<\/mml:mn><\/mml:mrow><\/mml:msub>(<\/mml:mo>t<\/mml:mi>)<\/mml:mo><\/mml:math>) simultaneously, including the smallest cost and operability. These findings would provide new insight for developing effective strategies for treatment of viral infectious diseases.<\/jats:p>","DOI":"10.1155\/2015\/386235","type":"journal-article","created":{"date-parts":[[2015,4,9]],"date-time":"2015-04-09T03:01:08Z","timestamp":1428548468000},"page":"1-16","source":"Crossref","is-referenced-by-count":12,"title":["Optimal Control Strategy for Abnormal Innate Immune Response"],"prefix":"10.1155","volume":"2015","author":[{"given":"Jinying","family":"Tan","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"},{"name":"College of Science, Huazhong Agricultural University, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiufen","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1183021"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1038\/nri2891"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1038\/srep03799"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1038\/nri1391"},{"issue":"1","key":"5","first-page":"152","volume":"17","year":"2006","journal-title":"Genome Informatics"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2013.31"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1038\/srep09283"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2015.01.008"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.2307\/1426183"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.02.004"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2010.04.003"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2334-10-32"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1142\/s0218339013400020"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1002\/oca.704"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-003-0245-3"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0048114"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.2174\/138161207782794248"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1097\/QCO.0b013e3283184245"},{"key":"19","year":"1987"},{"key":"20","year":"1975"},{"key":"21","year":"2004"},{"key":"22","year":"2009"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127413501800"},{"key":"24","volume":"707","year":"2011"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1177\/0037549703040943"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1038\/srep05764"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2015\/386235.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2015\/386235.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2015\/386235.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,27]],"date-time":"2016-07-27T06:33:27Z","timestamp":1469601207000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/cmmm\/2015\/386235\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":26,"alternative-id":["386235","386235"],"URL":"https:\/\/doi.org\/10.1155\/2015\/386235","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"value":"1748-670X","type":"print"},{"value":"1748-6718","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}