{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,4]],"date-time":"2026-11-04T19:30:11Z","timestamp":1793820611090,"version":"4.6.1"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T00:00:00Z","timestamp":1791936000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000270","name":"UK Research and Innovation Natural Environment Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000270","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Biosciences"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.mbs.2026.109824","type":"journal-article","created":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T15:10:10Z","timestamp":1791990610000},"page":"109824","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Reaction-diffusion models of invasive tree pest spread: Quantifying the expansion of oak processionary moth in the UK"],"prefix":"10.1016","volume":"402","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-8130-5737","authenticated-orcid":false,"given":"Jamie P.","family":"McKeown","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7355-2023","authenticated-orcid":false,"given":"Laura E.","family":"Wadkin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7238-8492","authenticated-orcid":false,"given":"Nick G.","family":"Parker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6730-1279","authenticated-orcid":false,"given":"Andrew","family":"Golightly","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6813-2443","authenticated-orcid":false,"given":"Andrew W.","family":"Baggaley","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"10","key":"10.1016\/j.mbs.2026.109824_bib0001","doi-asserted-by":"crossref","first-page":"3265","DOI":"10.1007\/s10530-023-03107-2","article-title":"An updated assessment of the direct costs of invasive non-native species to the United Kingdom","volume":"25","author":"Eschen","year":"2023","journal-title":"Biol. Invasions"},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0002","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10530-008-9318-y","article-title":"Ecological effects of invasive alien insects","volume":"11","author":"Kenis","year":"2008","journal-title":"Biol. Invasions"},{"key":"10.1016\/j.mbs.2026.109824_bib0003","series-title":"Technical Report","article-title":"State of the UK\u2019s Woods and Trees 2025","author":"Downey","year":"2025"},{"key":"10.1016\/j.mbs.2026.109824_bib0004","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.forpol.2016.06.024","article-title":"Tree disease and pest epidemics in the Anthropocene: a review of the drivers, impacts and policy responses in the UK","volume":"79","author":"Potter","year":"2017","journal-title":"For. Policy Econ."},{"issue":"9","key":"10.1016\/j.mbs.2026.109824_bib0005","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1016\/j.puhe.2012.06.007","article-title":"The arrival of oak processionary moth, a novel cause of itchy dermatitis, in the UK: experience, lessons and recommendations","volume":"126","author":"Mindlin","year":"2012","journal-title":"Public Health"},{"key":"10.1016\/j.mbs.2026.109824_bib0006","doi-asserted-by":"crossref","unstructured":"S. Blaser, M. Guetg, M. Bader, B. Wermelinger, S. Studhalter, V. Queloz, The oak processionary moth. Background knowledge and recommended action, 2022. 10.55419\/wsl:31198.","DOI":"10.55419\/wsl:31198"},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0007","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1159\/000075051","article-title":"Caterpillar dermatitis in two siblings due to the larvae of Thaumetopoea processionea L., the oak processionary caterpillar","volume":"208","author":"Maier","year":"2004","journal-title":"Dermatology"},{"issue":"2","key":"10.1016\/j.mbs.2026.109824_bib0008","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.ufug.2015.02.009","article-title":"Managing tree pests and diseases in urban settings: the case of oak processionary moth in London, 2006\u20132012","volume":"14","author":"Tomlinson","year":"2015","journal-title":"Urban for. Urban Green."},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0009","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1111\/afe.12468","article-title":"Estimating expansion of the range of oak processionary moth (Thaumetopoea processionea) in the UK from 2006 to 2019","volume":"24","author":"Suprunenko","year":"2021","journal-title":"Agric. for. Entomol."},{"issue":"2","key":"10.1016\/j.mbs.2026.109824_bib0010","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/s10530-019-02108-4","article-title":"Current and future distribution of the invasive oak processionary moth","volume":"22","author":"Godefroid","year":"2019","journal-title":"Biol. Invasions"},{"key":"10.1016\/j.mbs.2026.109824_bib0011","first-page":"3","article-title":"Thaumetopoea processionea in the Netherlands: present status and management perspectives (Lepidoptera: Notodontidae)","volume":"8","author":"Stigter","year":"1997","journal-title":"Proc. Sect. Exp. Appl. Entomol. Neth. Entomol. Soc."},{"key":"10.1016\/j.mbs.2026.109824_bib0012","series-title":"The Population Ecology of Oak Processionary Moth","author":"Sands","year":"2017"},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0013","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1564\/v24_feb_10","article-title":"Oak processionary moth in the United Kingdom","volume":"24","author":"Townsend","year":"2013","journal-title":"Outlooks Pest Manag."},{"issue":"5","key":"10.1016\/j.mbs.2026.109824_bib0014","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1007\/s10980-015-0168-6","article-title":"Using electric network theory to model the spread of oak processionary moth, Thaumetopoea processionea, in urban woodland patches","volume":"30","author":"Cowley","year":"2015","journal-title":"Landsc. Ecol."},{"issue":"4","key":"10.1016\/j.mbs.2026.109824_bib0015","doi-asserted-by":"crossref","first-page":"496","DOI":"10.3390\/d15040496","article-title":"Quantifying invasive pest dynamics through inference of a two-node epidemic network model","volume":"15","author":"Wadkin","year":"2023","journal-title":"Diversity"},{"issue":"6","key":"10.1016\/j.mbs.2026.109824_bib0016","doi-asserted-by":"crossref","DOI":"10.1007\/s11222-023-10311-6","article-title":"Accelerating Bayesian inference for stochastic epidemic models using incidence data","volume":"33","author":"Golightly","year":"2023","journal-title":"Stat. Comput."},{"issue":"5","key":"10.1016\/j.mbs.2026.109824_bib0017","doi-asserted-by":"crossref","DOI":"10.1002\/ece3.8871","article-title":"Inference for epidemic models with time-varying infection rates: tracking the dynamics of oak processionary moth in the UK","volume":"12","author":"Wadkin","year":"2022","journal-title":"Ecol. Evol."},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0018","doi-asserted-by":"crossref","DOI":"10.1098\/rsos.240763","article-title":"Predicting the effect of landscape structure on epidemic invasion using an analytical estimate for infection rate","volume":"12","author":"Suprunenko","year":"2025","journal-title":"R. Soc. Open Sci."},{"issue":"2","key":"10.1016\/j.mbs.2026.109824_bib0019","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s13595-013-0287-7","article-title":"Potential spread of the pine processionary moth in France: preliminary results from a simulation model and future challenges","volume":"71","author":"Robinet","year":"2013","journal-title":"Ann. for. Sci."},{"issue":"3","key":"10.1016\/j.mbs.2026.109824_bib0020","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.bulm.2004.08.005","article-title":"Mathematical models for the dispersal dynamics: travelling waves by wing and wind","volume":"67","author":"Takahashi","year":"2005","journal-title":"Bull. Math. Biol."},{"key":"10.1016\/j.mbs.2026.109824_bib0021","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1011627","article-title":"Imaging with spatio-temporal modelling to characterize the dynamics of plant-pathogen lesions","volume":"19","author":"Leclerc","year":"2023","journal-title":"PLoS Comput. Biol."},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0022","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.86.016105","article-title":"Bayesian inference for a wave-front model of the neolithization of Europe","volume":"86","author":"Baggaley","year":"2012","journal-title":"Phys. Rev. E"},{"issue":"5","key":"10.1016\/j.mbs.2026.109824_bib0023","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1007\/s00466-020-01888-0","article-title":"Diffusion\u2013reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study","volume":"66","author":"Viguerie","year":"2020","journal-title":"Comput. Mech."},{"key":"10.1016\/j.mbs.2026.109824_bib0024","series-title":"Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition","author":"Gamerman","year":"2006"},{"issue":"4","key":"10.1016\/j.mbs.2026.109824_bib0025","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1111\/j.1469-1809.1937.tb02153.x","article-title":"The wave of advance of advantageous genes","volume":"7","author":"Fisher","year":"1937","journal-title":"Ann. Eugen."},{"key":"10.1016\/j.mbs.2026.109824_bib0026","first-page":"1","article-title":"\u00c9tude de l\u2019\u00e9quation de la diffusion avec croissance de la quantit\u00e9 de mati\u00e8re et son application \u00e0 un probl\u00e8me biologique","volume":"1","author":"Kolmogorov","year":"1937","journal-title":"Moscow Univ. Bull. Math."},{"issue":"4","key":"10.1016\/j.mbs.2026.109824_bib0027","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1002\/ece3.2661","article-title":"Abundance distributions for tree species in Great Britain: a two-stage approach to modeling abundance using species distribution modeling and random forest","volume":"7","author":"Hill","year":"2017","journal-title":"Ecol. Evol."},{"key":"10.1016\/j.mbs.2026.109824_bib0028","series-title":"Mathematical Biology: I. An Introduction","author":"Murray","year":"2002"},{"issue":"2","key":"10.1016\/j.mbs.2026.109824_bib0029","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10340-012-0457-7","article-title":"Temporal synchrony of Thaumetopoea processionea egg hatch and Quercus robur budburst","volume":"86","author":"Wagenhoff","year":"2013","journal-title":"J. Pest Sci."},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0030","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/0021-9991(80)90033-9","article-title":"Low-storage Runge-Kutta schemes","volume":"35","author":"Williamson","year":"1980","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.mbs.2026.109824_bib0031","unstructured":"W. Dobler, A. Brandenburg, The pencil code: a high-order MPI code for MHD turbulence (2010). https:\/\/pencil-code.nordita.org\/doc\/manual.pdf."},{"issue":"2","key":"10.1016\/j.mbs.2026.109824_bib0032","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1111\/j.1461-9563.2011.00552.x","article-title":"Historical distribution of the oak processionary moth Thaumetopoea processionea in Europe suggests recolonization instead of expansion","volume":"14","author":"Groenen","year":"2011","journal-title":"Agric. for. Entomol."},{"issue":"6","key":"10.1016\/j.mbs.2026.109824_bib0033","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","article-title":"Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images","volume":"PAMI-6","author":"Geman","year":"1984","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"2","key":"10.1016\/j.mbs.2026.109824_bib0034","doi-asserted-by":"crossref","first-page":"223","DOI":"10.2307\/3318737","article-title":"An adaptive Metropolis algorithm","volume":"7","author":"Haario","year":"2001","journal-title":"Bernoulli"},{"issue":"4","key":"10.1016\/j.mbs.2026.109824_bib0035","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1214\/ss\/1015346320","article-title":"Optimal scaling for various Metropolis-Hastings algorithms","volume":"16","author":"Roberts","year":"2001","journal-title":"Stat. Sci."},{"issue":"2","key":"10.1016\/j.mbs.2026.109824_bib0036","doi-asserted-by":"crossref","DOI":"10.1007\/s11222-022-10080-8","article-title":"Optimal scaling of random walk Metropolis algorithms using Bayesian large-sample asymptotics","volume":"32","author":"Schmon","year":"2022","journal-title":"Stat. Comput."},{"issue":"4","key":"10.1016\/j.mbs.2026.109824_bib0037","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1111\/1467-9868.00353","article-title":"Bayesian measures of model complexity and fit","volume":"64","author":"Spiegelhalter","year":"2002","journal-title":"J. R. Stat. Soc. B: Stat. Methodol."},{"key":"10.1016\/j.mbs.2026.109824_bib0038","doi-asserted-by":"crossref","first-page":"249","DOI":"10.14411\/eje.2018.024","article-title":"Weather-dependent fluctuations in the abundance of the oak processionary moth, Thaumetopoea processionea (Lepidoptera: Notodontidae)","volume":"115","author":"Csoka","year":"2018","journal-title":"Eur. J. Entomol."},{"key":"10.1016\/j.mbs.2026.109824_bib0039","series-title":"Natural History of the Processionary Moths (Thaumetopoea spp.): New Insights in Relation to Climate Change","first-page":"15","author":"Battisti","year":"2015"},{"issue":"1","key":"10.1016\/j.mbs.2026.109824_bib0040","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1111\/j.1365-2656.2004.00896.x","article-title":"The effect of propagule size on the invasion of an alien insect","volume":"74","author":"Memmott","year":"2005","journal-title":"J. Anim. Ecol."},{"issue":"8","key":"10.1016\/j.mbs.2026.109824_bib0041","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/S0169-5347(02)02554-5","article-title":"Evolutionary genetics of invasive species","volume":"17","author":"Lee","year":"2002","journal-title":"Trends Ecol. Evol."},{"key":"10.1016\/j.mbs.2026.109824_bib0042","series-title":"Proceedings of the 2nd International RILEM Workshop on Testing and Modelling the Chloride Ingress into Concrete","first-page":"225","article-title":"Time-dependent diffusivities: possible misinterpretation due to spatial dependence","author":"Bentz","year":"2001"},{"issue":"7","key":"10.1016\/j.mbs.2026.109824_bib0043","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1111\/ddi.12212","article-title":"Dendrochronological reconstruction of the epicentre and early spread of emerald ash borer in North America","volume":"20","author":"Siegert","year":"2014","journal-title":"Divers. Distrib."},{"key":"10.1016\/j.mbs.2026.109824_bib0044","series-title":"Bayesian Inference for Models of Collective Behaviour","author":"Walton","year":"2021"},{"key":"10.1016\/j.mbs.2026.109824_bib0045","doi-asserted-by":"crossref","unstructured":"R. Nartallo-Kaluarachchi, R. Lambiotte, A. Goriely, From reductionism to realism: holistic mathematical modelling for complex biological systems (2025). 10.48550\/arXiv.2503.20511.","DOI":"10.1098\/rsif.2025.0468"},{"key":"10.1016\/j.mbs.2026.109824_bib0046","unstructured":"L. Hill, Predicted abundance maps for british trees, 201610.10615287\/bodleian:mNq8GpgZ8."},{"key":"10.1016\/j.mbs.2026.109824_bib0047","doi-asserted-by":"crossref","unstructured":"J.P. McKeown, Software for \u2019Reaction-diffusion models of invasive tree pest spread: quantifying the expansion of oak processionary moth in the UK\u2019, 2025, 10.25405\/data.ncl.30437849.","DOI":"10.1016\/j.mbs.2026.109824"}],"container-title":["Mathematical Biosciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0025556426002142?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0025556426002142?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,11,4]],"date-time":"2026-11-04T19:10:57Z","timestamp":1793819457000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0025556426002142"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":47,"alternative-id":["S0025556426002142"],"URL":"https:\/\/doi.org\/10.1016\/j.mbs.2026.109824","relation":{},"ISSN":["0025-5564"],"issn-type":[{"value":"0025-5564","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Reaction-diffusion models of invasive tree pest spread: Quantifying the expansion of oak processionary moth in the UK","name":"articletitle","label":"Article Title"},{"value":"Mathematical Biosciences","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.mbs.2026.109824","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"109824"}}