{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T04:52:27Z","timestamp":1773031947768,"version":"3.50.1"},"reference-count":34,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T00:00:00Z","timestamp":1760313600000},"content-version":"vor","delay-in-days":285,"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"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah Bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2025R371"],"award-info":[{"award-number":["PNURSP2025R371"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP2\/206\/46"],"award-info":[{"award-number":["RGP2\/206\/46"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100020912","name":"King Faisal University","doi-asserted-by":"publisher","award":["KFU241144"],"award-info":[{"award-number":["KFU241144"]}],"id":[{"id":"10.13039\/501100020912","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>The present study investigated the dynamics of the nonlinear stochastic pine wilt epidemic model. An extension of the stochastic to deterministic model is presented. Equilibria, positivity, boundedness, extinction, and disease persistence were studied rigorously. Standard and nonstandard numerical techniques like Euler\u2013Maruyama, stochastic Euler, stochastic Runge\u2013Kutta, and stochastic nonstandard finite difference are presented for computational analysis. Furthermore, the nonstandard method is a dynamically consistent approximation of stochastic differential equations of the pine wilt epidemic model that is efficient, low cost, and independent of time\u2010step size. The comparison section with standard methods strengthens the nonstandard method and supports the theoretical results of the model.<\/jats:p>","DOI":"10.1155\/cplx\/4099469","type":"journal-article","created":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T05:12:03Z","timestamp":1760418723000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic Analysis of Pine Wilt Epidemic Model With Dynamically Consistent Approximation"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6443-9966","authenticated-orcid":false,"given":"Ali","family":"Raza","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6124-9043","authenticated-orcid":false,"given":"Mohammed Mahyoub Ali","family":"Al-Shamiri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9701-4809","authenticated-orcid":false,"given":"Wafa F.","family":"Alfwzan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2165-3479","authenticated-orcid":false,"given":"Muhammad","family":"Rafiq","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9401-6481","authenticated-orcid":false,"given":"Emad","family":"Fadhal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1742-585X","authenticated-orcid":false,"given":"Nauman","family":"Ahmed","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,10,13]]},"reference":[{"key":"e_1_2_13_1_2","first-page":"1","article-title":"Mathematical Modelling and Stability Analysis of Pine Wilt Disease With Optimal Control","volume":"3115","author":"Khan M.","year":"2017","journal-title":"Scientific Reports"},{"key":"e_1_2_13_2_2","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/184054"},{"key":"e_1_2_13_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/s1793524518500353"},{"key":"e_1_2_13_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.09.042"},{"key":"e_1_2_13_5_2","doi-asserted-by":"publisher","DOI":"10.1080\/17513758.2016.1225828"},{"key":"e_1_2_13_6_2","doi-asserted-by":"publisher","DOI":"10.21833\/ijaas.2019.09.002"},{"key":"e_1_2_13_7_2","first-page":"189","article-title":"Analysis of a Mathematical Model for the Pine Wilt Disease Using a Graph-Theoretic Approach","volume":"22","author":"Romero J.","year":"2020","journal-title":"Applied Sciences"},{"key":"e_1_2_13_8_2","doi-asserted-by":"publisher","DOI":"10.22436\/jmcs.017.03.07"},{"key":"e_1_2_13_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.02.002"},{"key":"e_1_2_13_10_2","doi-asserted-by":"publisher","DOI":"10.1890\/0012-9658(1999)080[1691:mtsopw]2.0.co;2"},{"key":"e_1_2_13_11_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-018-1868-4"},{"key":"e_1_2_13_12_2","first-page":"200","article-title":"Dynamical Features of Pine Wilt Disease Model With Asymptotic Carrier","volume":"366","author":"Ozair M.","year":"2020","journal-title":"The European Physical Journal Plus"},{"key":"e_1_2_13_13_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/182680"},{"key":"e_1_2_13_14_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/204241"},{"key":"e_1_2_13_15_2","doi-asserted-by":"publisher","DOI":"10.1111\/1365-2656.12884"},{"key":"e_1_2_13_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2019.03.007"},{"key":"e_1_2_13_17_2","first-page":"01","article-title":"Qualitative Analysis and Sensitivity Based Optimal Control of Pine Wilt Disease","author":"Awan A.","year":"2018","journal-title":"Advances in Difference Equations"},{"key":"e_1_2_13_18_2","article-title":"A Machine Learning Approach for Detecting Pine Wilt Disease Using Airborne Spectral Imagery","author":"Iordache M. D.","year":"2020","journal-title":"Department of Earth Sciences"},{"key":"e_1_2_13_19_2","first-page":"01","article-title":"Research Advance on Esteya vermicola, a High Potential Biocontrol Agent of Pine Wilt Disease","author":"Chu W. H.","year":"2015","journal-title":"Mycological Progress"},{"key":"e_1_2_13_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10658-019-01908-7"},{"key":"e_1_2_13_21_2","volume-title":"Nonstandard Finite Difference Models of Differential Equations","author":"Mickens R. E.","year":"1994"},{"key":"e_1_2_13_22_2","doi-asserted-by":"publisher","DOI":"10.1142\/5884"},{"key":"e_1_2_13_23_2","unstructured":"CressonJ.andPierretF. Nonstandard Finite Difference Scheme Preserving Dynamical Properties 2014."},{"key":"e_1_2_13_24_2","doi-asserted-by":"publisher","DOI":"10.1080\/10236190412331334527"},{"key":"e_1_2_13_25_2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0063050"},{"key":"e_1_2_13_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.110839"},{"key":"e_1_2_13_27_2","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/abfacc"},{"key":"e_1_2_13_28_2","first-page":"16","article-title":"Investigating a Coupled System of Mittag-Leffler Type Fractional Differential Equations With Coupled Integral Boundary Conditions","volume":"1","author":"Ullah S.","year":"2024","journal-title":"Journal of Mathematical Techniques in Modeling"},{"key":"e_1_2_13_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40819-024-01690-z"},{"key":"e_1_2_13_30_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/s13360-025-06108-3"},{"key":"e_1_2_13_31_2","first-page":"191","article-title":"Effect of SOF\/VEL Antiviral Therapy for HCV Treatment: A Control Theoretic Approach","volume":"8","author":"Mondal J.","year":"2021","journal-title":"Letters in Biomathematics"},{"key":"e_1_2_13_32_2","doi-asserted-by":"publisher","DOI":"10.1080\/07362990701857129"},{"key":"e_1_2_13_33_2","first-page":"01","article-title":"Analysis of the Stochastic Model for Predicting the Novel Coronavirus Disease","volume":"20","author":"Sene N.","year":"2020","journal-title":"Advances in Difference Equations"},{"key":"e_1_2_13_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0378-4754(01)00356-1"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/cplx\/4099469","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/cplx\/4099469","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/cplx\/4099469","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T03:55:00Z","timestamp":1773028500000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/cplx\/4099469"}},"subtitle":[],"editor":[{"given":"Pramita","family":"Mishra","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/cplx\/4099469"],"URL":"https:\/\/doi.org\/10.1155\/cplx\/4099469","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-03-10","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-08","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-10-13","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"4099469"}}