{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:41:28Z","timestamp":1776397288756,"version":"3.51.2"},"reference-count":32,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T00:00:00Z","timestamp":1743033600000},"content-version":"vor","delay-in-days":85,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    In this study, an optimal control problem is formulated to a prey\u2013predator model with disease in both species. The model is an adapted Lotka\u2013Volterra model by incorporating susceptible\u2013infected (SI) epidemic dynamics on the prey\u2013predator population. A sensitivity analysis is conducted. The result of the analysis shows that the infection rates\n                    <jats:italic>\u03b2<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    and\n                    <jats:italic>\u03b2<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    and the conversion rate\n                    <jats:italic>e<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    are critical, influencing the dynamics through interaction and efficiency. The time\u2010dependent control is implemented in the system to determine the most effective disease control strategy. The optimal control is characterized using Pontryagin\u2019s optimality principle, which involves introducing the Hamiltonian and its associated adjoint variables. The study found that separating infected populations is crucial for disease elimination. We examine numerical simulations of various system scenarios using a wide range of parameters. Simulations are performed using a forward\u2013backward sweep method with first\u2010order necessary conditions for the control problem. The optimal solution is determined through numerical methods. The findings indicate that the ideal combination of the three control strategies necessary to meet the specified objective is influenced by the relative costs associated with each control measure. A detailed discussion of the simulation results is provided.\n                  <\/jats:p>","DOI":"10.1155\/jama\/5535536","type":"journal-article","created":{"date-parts":[[2025,3,29]],"date-time":"2025-03-29T18:46:45Z","timestamp":1743274005000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal Control Strategies in a Diseased Prey\u2013Predator Model With Holling Type\u2010II Dynamics"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6072-4444","authenticated-orcid":false,"given":"Kiros G.","family":"Kebedow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4914-9022","authenticated-orcid":false,"given":"Shegaye Lema","family":"Cheru","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2110-2084","authenticated-orcid":false,"given":"Tesfaye Tadesse","family":"Ega","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,3,27]]},"reference":[{"key":"e_1_2_10_1_2","first-page":"335","article-title":"Mathematical modeling of ecological networks, structure and interaction of prey and predator","volume":"4","author":"Bhattacharya P.","year":"2015","journal-title":"Palestine Journal of Mathematics"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2003.09.020"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/974\/1\/012050"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2010.11.002"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1986.0072"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524515500151"},{"key":"e_1_2_10_7_2","volume-title":"Elements of physical biology","author":"Lotka A. J.","year":"1925"},{"key":"e_1_2_10_8_2","unstructured":"SinghK.andKaladharK. Dynamical behavior of predator-prey with allee effect on both populations and disease in predator http:\/\/arxiv.org\/abs\/2405.15448 2024."},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1086\/513188"},{"key":"e_1_2_10_10_2","first-page":"1052","article-title":"The dynamics of prey-predator model with disease in prey","volume":"2","author":"Naji R. K.","year":"2012","journal-title":"The Journal of Mathematics and Computer Science"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/201611104"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-020-01379-8"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00276947"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1093\/imammb\/dqn017"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecolmodel.2009.01.016"},{"key":"e_1_2_10_16_2","article-title":"The evolution of virulence in sterilizing pathogens","volume":"115","author":"Kermack W. O.","year":"1927","journal-title":"Pro-Royal Soc. London, A"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2013.33.5059"},{"key":"e_1_2_10_18_2","article-title":"Analysis of an eco-epidemiological model under optimal control measures for infected prey","volume":"14","author":"Hugo A.","year":"2019","journal-title":"Applications and Applied Mathematics: An International Journal (AAM)"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.08.004"},{"key":"e_1_2_10_20_2","first-page":"83","article-title":"Stability analysis and optimal measure for controlling eco-epidemiological dynamics of prey-predator model","volume":"21","author":"Ademosu J. A.","year":"2021","journal-title":"Advances in Systems Science and Applications"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1155\/2023\/4066236"},{"key":"e_1_2_10_22_2","volume-title":"Abstract and Applied Analysis","author":"Liu C.","year":"2013"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.02.038"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1155\/2024\/5444627"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.32523\/2306-6172-2020-8-2-4-27"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12591-024-00677-y"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011418"},{"key":"e_1_2_10_28_2","volume-title":"Deterministic and Stochastic Optimal Control","author":"Fleming W. H.","year":"2012"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2010.12.010"},{"key":"e_1_2_10_30_2","first-page":"119","article-title":"The mathematical theory of optimal processes and differential games","volume":"169","author":"Pontryagin L. S.","year":"1985","journal-title":"Trudy Matematicheskogo Instituta imeni VA Steklova"},{"key":"e_1_2_10_31_2","unstructured":"RodriguesH. S. F. Optimal Control and Numerical Optimization Applied to Epidemiological Models [Ph.D. Thesis] 2012 Universidade de Aveiro (Portugal)."},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.1201\/9780203749319"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/5535536","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/5535536","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/5535536","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:43:00Z","timestamp":1776393780000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/5535536"}},"subtitle":[],"editor":[{"given":"Qiankun","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/5535536"],"URL":"https:\/\/doi.org\/10.1155\/jama\/5535536","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-01-25","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-27","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5535536"}}