{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T05:28:44Z","timestamp":1787117324232,"version":"build-2736575974"},"reference-count":28,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MBE"],"published-print":{"date-parts":[[2026]]},"DOI":"10.3934\/mbe.2026091","type":"journal-article","created":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T05:14:57Z","timestamp":1787116497000},"page":"2489-2515","source":"Crossref","is-referenced-by-count":0,"title":["A reaction\u2013diffusion delay model for spatial tumor virotherapy with optimal control"],"prefix":"10.3934","volume":"23","author":[{"given":"Fathalla A.","family":"Rihan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"name":"Department of Mathematical Sciences, College of Science, UAE University, Al-Ain, 15551, UAE","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2026091-1","doi-asserted-by":"publisher","unstructured":"S. J. Russell, K. W. Peng, J. C. Bell, Oncolytic virotherapy, <i>Nat. Biotechnol.<\/i>, <b>30<\/b> (2012), 658\u2013670. https:\/\/doi.org\/10.1038\/nbt.2287","DOI":"10.1038\/nbt.2287"},{"key":"key-10.3934\/mbe.2026091-2","doi-asserted-by":"publisher","unstructured":"J. C. Bell, S. H. Lichty, B. D. Stojdl, Getting oncolytic virus therapies off the ground, <i>Cancer Cell<\/i>, <b>4<\/b> (2003), 7\u201311. https:\/\/doi.org\/10.1016\/s1535-6108(03)00170-3","DOI":"10.1016\/s1535-6108(03)00170-3"},{"key":"key-10.3934\/mbe.2026091-3","doi-asserted-by":"publisher","unstructured":"N. Macedo, J. T. Miller, J. Haq, D. Kaufman, Clinical landscape of oncolytic virus research in 2020, <i>J. ImmunoTher. Cancer<\/i>, <b>8<\/b> (2003), e001486. https:\/\/doi.org\/10.1136\/jitc-2020-001486","DOI":"10.1136\/jitc-2020-001486"},{"key":"key-10.3934\/mbe.2026091-4","doi-asserted-by":"publisher","unstructured":"D. Xiao, H. Zhang, Y. Liu, Y. Li, G. Li, Y. Ning, Oncolytic viruses: advanced strategies in cancer therapy, <i>Signal Transduction Targeted Ther.<\/i>, <b>11<\/b> (2026), 45. https:\/\/doi.org\/10.1038\/s41392-025-02343-3","DOI":"10.1038\/s41392-025-02343-3"},{"key":"key-10.3934\/mbe.2026091-5","doi-asserted-by":"publisher","unstructured":"R. J. Prestwich, K. J. Harrington, H. S. Pandha, R. G. Vile, A. A. Melcher, F. Errington, Oncolytic viruses: a novel form of immunotherapy, <i>Expert Rev. Anticancer Ther.<\/i>, <b>8<\/b> (2008), 1581\u20131588. https:\/\/doi.org\/10.1586\/14737140.8.10.1581","DOI":"10.1586\/14737140.8.10.1581"},{"key":"key-10.3934\/mbe.2026091-6","doi-asserted-by":"publisher","unstructured":"D. K. Bhatt, T. Daemen, Molecular circuits of immune sensing and response to oncolytic virotherapy, <i>Int. J. Mol. Sci.<\/i>, <b>25<\/b> (2024), 4691. https:\/\/doi.org\/10.3390\/ijms25094691","DOI":"10.3390\/ijms25094691"},{"key":"key-10.3934\/mbe.2026091-7","doi-asserted-by":"publisher","unstructured":"C. F. Kollmann, N. van Montfoort, P. Cordelier, J. Pol, D. Olagnier, Oncolytic virotherapy: sparking durable anti-tumor immunity through microenvironment modulation, <i>Semin. Immunol.<\/i>, <b>80<\/b> (2025), 101994. https:\/\/doi.org\/10.1016\/j.smim.2025.101994","DOI":"10.1016\/j.smim.2025.101994"},{"key":"key-10.3934\/mbe.2026091-8","unstructured":"D. Wodarz, Viruses as antitumor weapons: defining conditions for tumor remission, <i>Cancer Res.<\/i>, <b>61<\/b> (2001), 3501\u20133507."},{"key":"key-10.3934\/mbe.2026091-9","doi-asserted-by":"publisher","unstructured":"A. Friedman, J. P. Tian, G. Fulci, E. A. Chiocca, J. Wang, Glioma virotherapy: effects of innate immune suppression and increased viral replication capacity, <i>Cancer Res.<\/i>, <b>66<\/b> (2006), 2314\u20132319. https:\/\/doi.org\/10.1158\/0008-5472.CAN-05-2661","DOI":"10.1158\/0008-5472.CAN-05-2661"},{"key":"key-10.3934\/mbe.2026091-10","doi-asserted-by":"publisher","unstructured":"L. R. Paiva, C. Binny, S. C. Ferreira Jr., M. L. Martins, A multiscale mathematical model for oncolytic virotherapy, <i>Cancer Res.<\/i>, <b>69<\/b> (2009), 1205\u20131211. https:\/\/doi.org\/10.1158\/0008-5472.CAN-08-2173","DOI":"10.1158\/0008-5472.CAN-08-2173"},{"key":"key-10.3934\/mbe.2026091-11","doi-asserted-by":"publisher","unstructured":"Q. Li, Y. Xiao, Modeling the virus-induced tumor-specific immune response with delay in tumor virotherapy, <i>Commun. Nonlinear Sci. Numer. Simul.<\/i>, <b>108<\/b> (2022), 106196. https:\/\/doi.org\/10.1016\/j.cnsns.2021.106196","DOI":"10.1016\/j.cnsns.2021.106196"},{"key":"key-10.3934\/mbe.2026091-12","unstructured":"F. A. Rihan, <i>Delay Differential Equations and Applications to Biology<\/i>, Forum for Interdisciplinary Mathematics, Springer, Cham, 2nd edition, 2026. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-3-032-08645-7\">https:\/\/doi.org\/10.1007\/978-3-032-08645-7<\/ext-link>"},{"key":"key-10.3934\/mbe.2026091-13","unstructured":"F. A. Rihan, Modeling virus\u2013tumor interactions and control in oncolytic virotherapy, in <i>Bioinformatics and Computational Biology<\/i>, volume 2977 of <i>Communications in Computer and Information Science<\/i>, Springer, Cham, 2026. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-3-032-26028-4_1\">https:\/\/doi.org\/10.1007\/978-3-032-26028-4_1<\/ext-link>"},{"key":"key-10.3934\/mbe.2026091-14","doi-asserted-by":"publisher","unstructured":"D. Morselli, M. E. Delitala, F. Frascoli, Agent-based and continuum models for spatial dynamics of infection by oncolytic viruses, <i>Bull. Math. Biol.<\/i>, <b>85<\/b> (2023), 92. https:\/\/doi.org\/10.1007\/s11538-023-01192-x","DOI":"10.1007\/s11538-023-01192-x"},{"key":"key-10.3934\/mbe.2026091-15","doi-asserted-by":"publisher","unstructured":"G. E. Mahlbacher, K. C. Reihmer, H. B. Frieboes, Mathematical modeling of tumor-immune cell interactions, <i>J. Theor. Biol.<\/i>, <b>469<\/b> (2019), 47\u201360. https:\/\/doi.org\/10.1016\/j.jtbi.2019.03.002","DOI":"10.1016\/j.jtbi.2019.03.002"},{"key":"key-10.3934\/mbe.2026091-16","doi-asserted-by":"publisher","unstructured":"S. Marzban, S. Srivastava, S. Kartika, R. Bravo, R. Safriel, A. Zarski, et al., Spatial interactions modulate tumor growth and immune infiltration, <i>npj Syst. Biol. Appl.<\/i>, <b>10<\/b> (2024), 106. https:\/\/doi.org\/10.1038\/s41540-024-00438-1","DOI":"10.1038\/s41540-024-00438-1"},{"key":"key-10.3934\/mbe.2026091-17","doi-asserted-by":"publisher","unstructured":"S. Hussain, M. Sen, V. Volpert, Infection spreading in tissue as a reaction-diffusion wave, <i>Math. Med. Biol.<\/i>, <b>41<\/b> (2024), 169\u2013191. https:\/\/doi.org\/10.1093\/imammb\/dqae009","DOI":"10.1093\/imammb\/dqae009"},{"key":"key-10.3934\/mbe.2026091-18","doi-asserted-by":"publisher","unstructured":"M. El Younoussi, Z. Hajhouji, K. Hattaf, N. Yousfi, Dynamics of a reaction\u2013diffusion fractional-order model for m1 oncolytic virotherapy with ctl immune response, <i>Chaos, Solitons Fractals<\/i>, <b>157<\/b> (2022), 111957. https:\/\/doi.org\/10.1016\/j.chaos.2022.111957","DOI":"10.1016\/j.chaos.2022.111957"},{"key":"key-10.3934\/mbe.2026091-19","unstructured":"M. El Younoussi, Z. Hajhouji, K. Hattaf, N. Yousfi, A reaction\u2013diffusion fractional model for cancer virotherapy with immune response and Hattaf time-fractional derivative, in <i>Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics<\/i> (eds. R. P. Mondaini), Springer, Cham, 2023. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-3-031-33050-6_7\">https:\/\/doi.org\/10.1007\/978-3-031-33050-6_7<\/ext-link>"},{"key":"key-10.3934\/mbe.2026091-20","doi-asserted-by":"publisher","unstructured":"Z. Wang, Modeling oncolytic virus therapy with distributed delay and nonlocal diffusion, <i>Adv. Contin. Discrete Models<\/i>, <b>2024<\/b> (2024), 59. https:\/\/doi.org\/10.1186\/s13662-024-03859-8","DOI":"10.1186\/s13662-024-03859-8"},{"key":"key-10.3934\/mbe.2026091-21","doi-asserted-by":"publisher","unstructured":"D. K. Bhatt, T. Janzen, T. Daemen, F. J. Weissing, Effects of virus-induced immunogenic cues on oncolytic virotherapy, <i>Sci. Rep.<\/i>, <b>14<\/b> (2024), 28861. https:\/\/doi.org\/10.1038\/s41598-024-80542-8","DOI":"10.1038\/s41598-024-80542-8"},{"key":"key-10.3934\/mbe.2026091-22","doi-asserted-by":"publisher","unstructured":"S. Omer, H. Mambili-Mamboundou, Assessing the impact of immunotherapy on oncolytic virotherapy in the treatment of cancer, <i>J. Appl. Math. Comput.<\/i>, <b>70<\/b> (2024), 4793\u20134825. https:\/\/doi.org\/10.1007\/s12190-024-02139-8","DOI":"10.1007\/s12190-024-02139-8"},{"key":"key-10.3934\/mbe.2026091-23","doi-asserted-by":"publisher","unstructured":"K. R. Fister, J. H. Donnelly, Immunotherapy: an optimal control theory approach, <i>Math. Biosci. Eng.<\/i>, <b>2<\/b> (2005), 499\u2013510. https:\/\/doi.org\/10.3934\/mbe.2005.2.499","DOI":"10.3934\/mbe.2005.2.499"},{"key":"key-10.3934\/mbe.2026091-24","doi-asserted-by":"crossref","unstructured":"D. Henry, <i>Geometric Theory of Semilinear Parabolic Equations<\/i>, Springer, Berlin, 1981.","DOI":"10.1007\/BFb0089647"},{"key":"key-10.3934\/mbe.2026091-25","doi-asserted-by":"crossref","unstructured":"A. Pazy, <i>Semigroups of Linear Operators and Applications to Partial Differential Equations<\/i>, Springer, New York, 1983.","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"key-10.3934\/mbe.2026091-26","doi-asserted-by":"crossref","unstructured":"J. K. Hale, S. M. V. Lunel, <i>Introduction to Functional Differential Equations<\/i>, Springer, New York, 1993.","DOI":"10.1007\/978-1-4612-4342-7"},{"key":"key-10.3934\/mbe.2026091-27","unstructured":"H. L. Smith, <i>An Introduction to Delay Differential Equations with Applications to the Life Sciences<\/i>, Springer, New York, 2011."},{"key":"key-10.3934\/mbe.2026091-28","doi-asserted-by":"crossref","unstructured":"S. Lenhart, J. T. Workman, <i>Optimal Control Applied to Biological Models<\/i>, Chapman &amp; Hall\/CRC, Boca Raton, 2007.","DOI":"10.1201\/9781420011418"}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2026091?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T05:14:58Z","timestamp":1787116498000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2026091"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":28,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2026091","relation":{},"ISSN":["1551-0018"],"issn-type":[{"value":"1551-0018","type":"print"}],"subject":[],"published":{"date-parts":[[2026]]}}}