{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T13:05:40Z","timestamp":1779195940684,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T00:00:00Z","timestamp":1779148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"\u201cAI + Education\u201d Course Project in Wannan Medical University","award":["2025aikc02"],"award-info":[{"award-number":["2025aikc02"]}]},{"name":"Student Innovation Training Program in Anhui Province","award":["202410368070"],"award-info":[{"award-number":["202410368070"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Accurate prediction of invasive species diffusion is essential for effective management and ecological conservation. Existing spatio-temporal Cox process models face limitations due to the separability assumption, which fails to capture spatio-temporal coupling dynamics inherent in biological diffusion processes. This study proposes a Spatio-Temporal Interaction Kernel Cox (STIK-Cox) model that constructs a non-separable conditional intensity function integrating baseline intensity, spatial and temporal proximity kernels, seasonal fluctuation, and a spatio-temporal interaction term. The model employs maximum likelihood estimation with Limited-memory Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno with Bounds (L-BFGS-B) optimisation and incorporates SHapley Additive exPlanations (SHAP) for interpretability analysis. Using the Vespa mandarinia (Hymenoptera, Vespidae) monitoring dataset from Washington State, the model achieves a comprehensive accuracy score of 0.957, a capture rate of 98.74% at a 0.5\u00b0 threshold, and a mean prediction error of 0.0802\u00b0. K-function analysis confirms effective capture of spatial clustering patterns, while SHAP analysis reveals longitude as the primary predictive driver. The non-separable design outperforms conventional methods including inverse distance weighting and Poisson point processes. This framework demonstrates the potential of non-separable spatio-temporal point processes for invasive species early warning, providing a scientific basis for targeted monitoring and resource allocation in ecological management.<\/jats:p>","DOI":"10.3390\/a19050408","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T11:53:10Z","timestamp":1779191590000},"page":"408","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interpretable Non-Separable Spatio-Temporal Interaction Cox Model for Diffusion Prediction in Invasive Species Management"],"prefix":"10.3390","volume":"19","author":[{"given":"Yantao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Medical Information, Wannan Medical University, Wuhu 241000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yangyang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Medical Information, Wannan Medical University, Wuhu 241000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-4174-9391","authenticated-orcid":false,"given":"Shuxin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Medical Information, Wannan Medical University, Wuhu 241000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingxuan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Public Health, Anhui Medical University, Hefei 230032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1673-1946","authenticated-orcid":false,"given":"Robail","family":"Yasrab","sequence":"additional","affiliation":[{"name":"MRC Biostatistics Unit, University of Cambridge, Cambridge CB2 1TN, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinli","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Medical Information, Wannan Medical University, Wuhu 241000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.ecolecon.2004.10.002","article-title":"Update on the environmental and economic costs associated with alien-invasive species in the United States","volume":"52","author":"Pimentel","year":"2005","journal-title":"Ecol. 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