{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T17:13:09Z","timestamp":1790097189403,"version":"4.0.1"},"reference-count":99,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,4,23]],"date-time":"2023-04-23T00:00:00Z","timestamp":1682208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,23]],"date-time":"2023-04-23T00:00:00Z","timestamp":1682208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Margaret Chase Smith Policy Center"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s11538-023-01148-1","type":"journal-article","created":{"date-parts":[[2023,4,23]],"date-time":"2023-04-23T16:01:50Z","timestamp":1682265710000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Modeling Opioid Abuse: A Case Study of the Opioid Crisis in New England"],"prefix":"10.1007","volume":"85","author":[{"given":"Cole","family":"Butler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5162-4951","authenticated-orcid":false,"given":"Peter","family":"Stechlinski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,4,23]]},"reference":[{"issue":"4","key":"1148_CR1","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1111\/add.15698","volume":"117","author":"GC Alexander","year":"2021","unstructured":"Alexander GC, Ballreich J, Mansour O et al (2021) Effect of reductions in opioid prescribing on opioid use disorder and fatal overdose in the United States: a dynamic Markov model. Drug Alcohol Depend 117(4):969\u201376. https:\/\/doi.org\/10.1111\/add.15698","journal-title":"Drug Alcohol Depend"},{"key":"1148_CR2","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1016\/j.jsat.2013.04.002","volume":"45","author":"GL Bailey","year":"2013","unstructured":"Bailey GL, Herman DS, Stein MD (2013) Perceived relapse risk and desire for medication assisted treatment among persons seeking inpatient opiate detoxification. J Subst Abus Treat 45:302\u20135. https:\/\/doi.org\/10.1016\/j.jsat.2013.04.002","journal-title":"J Subst Abus Treat"},{"issue":"11","key":"1148_CR3","doi-asserted-by":"publisher","first-page":"e2023677","DOI":"10.1001\/jamanetworkopen.2020.23677","volume":"3","author":"J Ballreich","year":"2020","unstructured":"Ballreich J, Mansour O, Hu E et al (2020) Modeling mitigation strategies to reduce opioid-related morbidity and mortality in the US. JAMA Netw Open 3(11):e2023677\u2013e2023677. https:\/\/doi.org\/10.1001\/jamanetworkopen.2020.23677","journal-title":"JAMA Netw Open"},{"key":"1148_CR4","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1515\/jiip-2015-0090","volume":"24","author":"HT Banks","year":"2016","unstructured":"Banks HT, Catepacci J, Hu S (2016) Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems. J Inverse Ill Posed Probl 24:413\u2013433. https:\/\/doi.org\/10.1515\/jiip-2015-0090","journal-title":"J Inverse Ill Posed Probl"},{"key":"1148_CR5","volume-title":"Modeling and inverse problems in the presence of uncertainty","author":"HT Banks","year":"2016","unstructured":"Banks HT, Hu S, Thompson WC (2016) Modeling and inverse problems in the presence of uncertainty. CRC Press, Boca Raton"},{"issue":"6","key":"1148_CR6","doi-asserted-by":"publisher","first-page":"1254","DOI":"10.1007\/s11538-017-0282-5","volume":"79","author":"HT Banks","year":"2017","unstructured":"Banks HT, Bekele-Maxwell K, Everett RA et al (2017) Dynamic modeling of problem drinkers undergoing behavioral treatment. Bull Math Model 79(6):1254\u20131273. https:\/\/doi.org\/10.1007\/s11538-017-0282-5","journal-title":"Bull Math Model"},{"issue":"7","key":"1148_CR7","doi-asserted-by":"publisher","first-page":"2258","DOI":"10.1007\/s11538-019-00605-0","volume":"81","author":"NA Battista","year":"2019","unstructured":"Battista NA, Pearcy LB, Strickland WC (2019) Modeling the prescription opioid epidemic. Bull Math Biol 81(7):2258\u20132289. https:\/\/doi.org\/10.1007\/s11538-019-00605-0","journal-title":"Bull Math Biol"},{"issue":"3","key":"1148_CR8","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1287\/mnsc.46.3.333.12068","volume":"46","author":"DA Behrens","year":"2000","unstructured":"Behrens DA, Caulkins JP, Tragler G et al (2000) Optimal control of drug epidemics: Prevent and treat\u2013but not at the same time? Manage Sci 46(3):333\u201347. https:\/\/doi.org\/10.1287\/mnsc.46.3.333.12068","journal-title":"Manage Sci"},{"key":"1148_CR9","unstructured":"Butler C (2020) A mathematical model of the opioid epidemic in the state of Maine. Honors College, University of Maine https:\/\/digitalcommons.library.umaine.edu\/honors\/630\/"},{"issue":"10","key":"1148_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2019.110003","volume":"108","author":"WK Caldwell","year":"2019","unstructured":"Caldwell WK, Freedman B, Settles L et al (2019) The Vicodin abuse problem: a mathematical approach. J Theor Biol 108(10):110003. https:\/\/doi.org\/10.1016\/j.jtbi.2019.110003","journal-title":"J Theor Biol"},{"key":"1148_CR11","unstructured":"CDC (2020) Multiple cause of death 1999\u20132018 on CDC wonder online database, released in 2020. URL: http:\/\/wonder.cdc.gov\/mcd-icd10.html"},{"key":"1148_CR12","unstructured":"CDC (2021a) Drug overdose deaths in the U.S. top 100,000 annually. URL: https:\/\/www.cdc.gov\/nchs\/pressroom\/nchs_press_releases\/2021\/20211117.html. Accessed 18 Sep 2022"},{"key":"1148_CR13","unstructured":"CDC (2021b) U.S. opioid dispensing rate maps. URL: https:\/\/www.cdc.gov\/drugoverdose\/rxrate-maps\/index.html. Accessed 18 Sep 2022"},{"key":"1148_CR14","unstructured":"CDC (2022a) CDC WONDER (database). https:\/\/wonder.cdc.gov. Accessed 01 Sep 2022"},{"key":"1148_CR15","unstructured":"CDC (2022b) Overdose death rates. URL: https:\/\/nida.nih.gov\/research-topics\/trends-statistics\/overdose-death-rates. Accessed 18 Sep 2022"},{"issue":"2","key":"1148_CR16","doi-asserted-by":"publisher","first-page":"e187621","DOI":"10.1001\/jamanetworkopen.2018.7621","volume":"2","author":"Q Chen","year":"2019","unstructured":"Chen Q, Larochelle MR, Weaver DT et al (2019) Prevention of prescription opioid misuse and projected overdose deaths in the United States. JAMA Netw Open 2(2):e187621\u2013e187621. https:\/\/doi.org\/10.1001\/jamanetworkopen.2018.7621","journal-title":"JAMA Netw Open"},{"issue":"2","key":"1148_CR17","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1177\/002204261104100207","volume":"41","author":"TJ Cicero","year":"2011","unstructured":"Cicero TJ, Kurtz SP, Surratt HL et al (2011) Multiple determinants of specific modes of prescription opioid diversion. J Drug Issues 41(2):283\u2013304. https:\/\/doi.org\/10.1177\/002204261104100207","journal-title":"J Drug Issues"},{"key":"1148_CR18","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1056\/NEJMc1204141","volume":"367","author":"T Cicero","year":"2012","unstructured":"Cicero T, Ellis M, Surratt H (2012) Effect of abuse-deterrent formulation of oxycontin. N Engl J Med 367:187\u2013189. https:\/\/doi.org\/10.1056\/NEJMc1204141","journal-title":"N Engl J Med"},{"key":"1148_CR19","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1001\/jamapsychiatry.2014.366","volume":"71","author":"TJ Cicero","year":"2014","unstructured":"Cicero TJ, Ellis MS, Surratt HL et al (2014) The changing face of heroin use in the United States: a retrospective analysis of the past 50 years. JAMA Psychiat 71:821\u20136. https:\/\/doi.org\/10.1001\/jamapsychiatry.2014.366","journal-title":"JAMA Psychiat"},{"issue":"12","key":"1148_CR20","doi-asserted-by":"publisher","first-page":"244","DOI":"10.2105\/AJPH.2019.305412","volume":"110","author":"TJ Cicero","year":"2020","unstructured":"Cicero TJ, Ellis MS, Kasper ZA (2020) Polysubstance use: a broader understanding of substance use during the opioid crisis. Am J Public Health 110(12):244\u201350. https:\/\/doi.org\/10.2105\/AJPH.2019.305412","journal-title":"Am J Public Health"},{"issue":"5","key":"1148_CR21","doi-asserted-by":"publisher","first-page":"e0232538","DOI":"10.1371\/journal.pone.0232538","volume":"15","author":"PO Coffin","year":"2020","unstructured":"Coffin PO, Rowe C, Oman N et al (2020) Illicit opioid use following changes in opioids prescribed for chronic non-cancer pain. PLOS One 15(5):e0232538. https:\/\/doi.org\/10.1371\/journal.pone.0232538","journal-title":"PLOS One"},{"issue":"4","key":"1148_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11538-022-01002-w","volume":"84","author":"S Cole","year":"2022","unstructured":"Cole S, Wirkus S (2022) Modeling the dynamics of heroin and illicit opioid use disorder, treatment, and recovery. Bull Math Biol 84(4):1\u201349. https:\/\/doi.org\/10.1007\/s11538-022-01002-w","journal-title":"Bull Math Biol"},{"key":"1148_CR23","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/j.ypmed.2015.04.003","volume":"80","author":"WM Compton","year":"2015","unstructured":"Compton WM, Boyle M, Wargo E (2015) Prescription opioid abuse: problems and responses. Prev Med 80:5\u20139. https:\/\/doi.org\/10.1016\/j.ypmed.2015.04.003","journal-title":"Prev Med"},{"issue":"2","key":"1148_CR24","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1056\/NEJMra1508490","volume":"374","author":"WM Compton","year":"2016","unstructured":"Compton WM, Jones CM, Baldwin GT (2016) Relationship between nonmedical prescription-opioid use and heroin use. N Engl J Med 374(2):154\u201363. https:\/\/doi.org\/10.1056\/NEJMra1508490","journal-title":"N Engl J Med"},{"issue":"3","key":"1148_CR25","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1080\/02791072.2014.916833","volume":"46","author":"R Daniulaityte","year":"2014","unstructured":"Daniulaityte R, Russel F, Carlson RG (2014) Sources of pharmaceutical opioids for non-medical use among young adults. J Pyschoactive Drugs 46(3):198\u2013207. https:\/\/doi.org\/10.1080\/02791072.2014.916833","journal-title":"J Pyschoactive Drugs"},{"issue":"3","key":"1148_CR26","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1056\/NEJMsa1406143","volume":"372","author":"RC Dart","year":"2015","unstructured":"Dart RC, Surratt HL, Cicero TJ et al (2015) Trends in opioid analgesic abuse and mortality in the United States. N Engl J Med 372(3):241\u2013248. https:\/\/doi.org\/10.1056\/NEJMsa1406143","journal-title":"N Engl J Med"},{"key":"1148_CR27","unstructured":"DHHS M (2015) Substance abuse trends in Maine: state epidemiological profile 2015. URL: http:\/\/www.fpddev.com\/staging\/ctn\/wp-content\/uploads\/2016\/11\/SA-Trends-in-ME-2015.pdf. Accessed 25 Sep 2022"},{"key":"1148_CR28","unstructured":"DHHS M (2016) Substance abuse trends in Maine: atate epidemiological profile 2016. URL: https:\/\/vdocuments.net\/substance-abuse-trends-in-maine-maine-seow-epiprofile-2016-finalpdfsubstance.html?page=1. Accessed 25 Sep 2022"},{"key":"1148_CR29","unstructured":"DHHS M (2017) Substance abuse trends in Maine: atate epidemiological profile 2017. URL: https:\/\/static1.squarespace.com\/static\/60b00f2b0884962f72a32db5\/t\/60e5eb0d0990c24a70620288\/1625680655311\/SEOW+EpiProfile+2017+FINAL+09292017.pdf. Accessed 25 Sep 2022"},{"key":"1148_CR30","unstructured":"DHHS M (2018) Substance use trends in Maine: state epidemiological profile 2018. URL: https:\/\/static1.squarespace.com\/static\/60b00f2b0884962f72a32db5\/t\/60e5e3d47612d607a368e716\/1625678806106\/SEOW+EpiProfile+2018+with+sub+state+data+11302018.pdf. Accessed 25 Sep 2022"},{"key":"1148_CR31","unstructured":"DHHS M (2019) Substance use trends in Maine: State epidemiological profile 2019. URL: https:\/\/static1.squarespace.com\/static\/60b00f2b0884962f72a32db5\/t\/60e5e3b7a6110f30d7c5f209\/1625678777496\/SEOW+EpiProfile+2019+Final+092419.pdf. Accessed 25 Sep 2022"},{"key":"1148_CR32","doi-asserted-by":"crossref","unstructured":"Doleac J, Mukherjee A (2018) The moral hazard of lifesaving innovations: naloxone access, opioid abuse, and crime. URL: https:\/\/ideas.repec.org\/p\/iza\/izadps\/dp11489.html. Accessed 18 Sep 2022","DOI":"10.2139\/ssrn.3135264"},{"issue":"10","key":"1148_CR33","doi-asserted-by":"publisher","first-page":"1876","DOI":"10.1377\/hlthaff.2016.0448","volume":"35","author":"D Dowell","year":"2016","unstructured":"Dowell D, Zhang K, Noonan RK et al (2016) Mandatory provider review and pain clinic laws reduce the amounts of opioids prescribed and overdose death rates. Health Aff 35(10):1876\u201383. https:\/\/doi.org\/10.1377\/hlthaff.2016.0448","journal-title":"Health Aff"},{"issue":"2","key":"1148_CR34","doi-asserted-by":"publisher","first-page":"85","DOI":"10.7326\/0003-4819-152-2-201001190-00006","volume":"152","author":"KM Dunn","year":"2010","unstructured":"Dunn KM, Saunders KW, Rutter CM et al (2010) Opioid prescriptions for chronic pain and overdose: a cohort study. Ann Intern Med 152(2):85\u201392. https:\/\/doi.org\/10.7326\/0003-4819-152-2-201001190-00006","journal-title":"Ann Intern Med"},{"key":"1148_CR35","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.drugalcdep.2010.05.017","volume":"112","author":"MJ Edlund","year":"2010","unstructured":"Edlund MJ, Martin BC, Fan MY et al (2010) Risks for opioid abuse and dependence among recipients of chronic opioid therapy: results from the TROUP study. Drug Alcohol Depend 112:90\u20138. https:\/\/doi.org\/10.1016\/j.drugalcdep.2010.05.017","journal-title":"Drug Alcohol Depend"},{"key":"1148_CR36","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1097\/AJP.0000000000000021","volume":"30","author":"MJ Edlund","year":"2014","unstructured":"Edlund MJ, Martin BC, Russo JE et al (2014) The role of opioid prescription in incident opioid abuse and dependence among individuals with chronic noncancer pain: the role of opioid prescription. Clin J Pain 30:557\u201364. https:\/\/doi.org\/10.1097\/AJP.0000000000000021","journal-title":"Clin J Pain"},{"issue":"143","key":"1148_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12889-020-8205-z","volume":"20","author":"B Fischer","year":"2020","unstructured":"Fischer B, Jones W, Tyndall M et al (2020) Correlations between opioid mortality increases related to illicit\/synthetic opioids and reductions of medical opioid dispensing\u2013exploratory analysis from Canada. BMC Public Health 20(143):1\u20137. https:\/\/doi.org\/10.1186\/s12889-020-8205-z","journal-title":"BMC Public Health"},{"issue":"26","key":"1148_CR38","doi-asserted-by":"publisher","first-page":"697","DOI":"10.15585\/mmwr.mm6626a4","volume":"66","author":"GP Guy Jr","year":"2017","unstructured":"Guy GP Jr, Zhang K, Bohm MK et al (2017) Vital signs: changes in opioid prescribing in the United States 2006\u20132015. Morb Mortal Wkly Rep 66(26):697\u2013704","journal-title":"Morb Mortal Wkly Rep"},{"issue":"16","key":"1148_CR39","doi-asserted-by":"publisher","first-page":"1615","DOI":"10.1001\/jama.2020.18543","volume":"324","author":"DF Haley","year":"2020","unstructured":"Haley DF, Saitz R (2020) The opioid epidemic during the COVID-19 pandemic. JAMA 324(16):1615\u20137. https:\/\/doi.org\/10.1001\/jama.2020.18543","journal-title":"JAMA"},{"key":"1148_CR40","unstructured":"HHS (2019) The opioid epidemic by the numbers. URL: https:\/\/www.hhs.gov\/opioids\/sites\/default\/files\/2019-11\/Opioids%20Infographic_letterSizePDF_10-02-19.pdf. Accessed 18 Sep 2022"},{"key":"1148_CR41","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/j.drugalcdep.2018.02.010","volume":"186","author":"S Hulme","year":"2018","unstructured":"Hulme S, Bright D, Nielsen S (2018) The source and diversion of pharmaceutical drugs for non-medical use: a systematic review and meta-analysis. Drug Alcohol Depend 186:242\u201356. https:\/\/doi.org\/10.1016\/j.drugalcdep.2018.02.010","journal-title":"Drug Alcohol Depend"},{"issue":"2","key":"1148_CR42","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1111\/j.1526-4637.2006.00255.x","volume":"8","author":"JA Inciardi","year":"2007","unstructured":"Inciardi JA, Surratt HL, Kurtz SP et al (2007) Mechanisms of prescription drug diversion among drug-involved club- and street-based populations. Pain Med 8(2):171\u201383. https:\/\/doi.org\/10.1111\/j.1526-4637.2006.00255.x","journal-title":"Pain Med"},{"issue":"3","key":"1148_CR43","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1111\/j.1526-4637.2009.00603.x","volume":"10","author":"JA Inciardi","year":"2009","unstructured":"Inciardi JA, Surratt HL, Cicero TJ et al (2009) Prescription opioid abuse and diversion in an urban community: the results of an ultrarapid assessment. Pain Med 10(3):537\u201348. https:\/\/doi.org\/10.1111\/j.1526-4637.2009.00603.x","journal-title":"Pain Med"},{"key":"1148_CR44","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1111\/j.1526-4637.2011.01126.x","volume":"12","author":"EM Johnson","year":"2011","unstructured":"Johnson EM, Porucznik CA, Anderson JW et al (2011) State-level strategies for reducing prescription drug overdose deaths: Utah\u2019s prescription safety program. Pain Med 12:66\u201372. https:\/\/doi.org\/10.1111\/j.1526-4637.2011.01126.x","journal-title":"Pain Med"},{"issue":"26","key":"1148_CR45","first-page":"719","volume":"64","author":"CM Jones","year":"2015","unstructured":"Jones CM, Logan J, Gladden RM et al (2015) Vital signs: demographic and substance use trends among heroin users\u2013United States, 2002\u20132013. Morb Mortal Wkly Rep 64(26):719\u201325","journal-title":"Morb Mortal Wkly Rep"},{"key":"1148_CR46","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.addbeh.2017.03.008","volume":"71","author":"J Jones","year":"2017","unstructured":"Jones J, Campbell A, Metz V et al (2017) No evidence of compensatory drug use risk behavior among heroin users after receiving take-home naloxone. Addict Behav 71:104\u20136. https:\/\/doi.org\/10.1016\/j.addbeh.2017.03.008","journal-title":"Addict Behav"},{"issue":"2","key":"1148_CR47","first-page":"41","volume":"6","author":"K Kenan","year":"2012","unstructured":"Kenan K, Mack K, Paulozzi L (2012) Trends in prescriptions for oxycodone and other commonly used opioids in the United States, 2000\u20132010. Open Med 6(2):41\u201347","journal-title":"Open Med"},{"key":"1148_CR48","first-page":"1","volume":"178","author":"KD Kochanek","year":"2014","unstructured":"Kochanek KD, Murphy SL, Xu J et al (2014) Mortality in the United States, 2013. NCHS Data Brief 178:1\u20138","journal-title":"NCHS Data Brief"},{"key":"1148_CR49","first-page":"1","volume":"293","author":"KD Kochanek","year":"2017","unstructured":"Kochanek KD, Murphy SL, Xu J et al (2017) Mortality in the United States, 2016. NCHS Data Brief 293:1\u20138","journal-title":"NCHS Data Brief"},{"key":"1148_CR50","first-page":"1","volume":"395","author":"KD Kochanek","year":"2020","unstructured":"Kochanek KD, Xu J, Arias E (2020) Mortality in the United States, 2019. NCHS Data Brief 395:1\u20138","journal-title":"NCHS Data Brief"},{"key":"1148_CR51","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1151\/spp021113","volume":"1","author":"T Kosten","year":"2002","unstructured":"Kosten T, George T (2002) The neurobiology of opioid dependence: implications for treatment. Sci Pract Perspect 1:13\u201320. https:\/\/doi.org\/10.1151\/spp021113","journal-title":"Sci Pract Perspect"},{"key":"1148_CR52","doi-asserted-by":"publisher","first-page":"1450","DOI":"10.1038\/nn1583","volume":"8","author":"MJ Kreek","year":"2005","unstructured":"Kreek MJ, Nielsen DA, Butelman ER et al (2005) Genetic influences on impulsivity, risk taking, stress responsivity and vulnerability to drug abuse and addiction. Nat Neurosci 8:1450\u20137. https:\/\/doi.org\/10.1038\/nn1583","journal-title":"Nat Neurosci"},{"issue":"2","key":"1148_CR53","doi-asserted-by":"publisher","DOI":"10.1001\/jamanetworkopen.2020.36687","volume":"4","author":"B Lee","year":"2021","unstructured":"Lee B, Zhao W, Yang K et al (2021) Systematic evaluation of state policy interventions targeting the US opioid epidemic. JAMA Netw Open 4(2):e2036687. https:\/\/doi.org\/10.1001\/jamanetworkopen.2020.36687","journal-title":"JAMA Netw Open"},{"issue":"10","key":"1148_CR54","doi-asserted-by":"publisher","first-page":"1685","DOI":"10.1016\/j.aml.2011.04.019","volume":"24","author":"J Liu","year":"2011","unstructured":"Liu J, Zhang T (2011) Global behaviour of a heroin epidemic model with distributed delays. Appl Math Lett 24(10):1685\u201392. https:\/\/doi.org\/10.1016\/j.aml.2011.04.019","journal-title":"Appl Math Lett"},{"issue":"2","key":"1148_CR55","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.drugpo.2013.10.004","volume":"25","author":"SG Mars","year":"2014","unstructured":"Mars SG, Bourgois P, Karandinos G et al (2014) \u201cEvery \u2018never\u2019 i ever said came true\u2019\u2019: transitions from opioid pills to heroin injecting. Int J Drug Policy 25(2):257\u201366. https:\/\/doi.org\/10.1016\/j.drugpo.2013.10.004","journal-title":"Int J Drug Policy"},{"key":"1148_CR56","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.addbeh.2018.03.014","volume":"86","author":"C McClellan","year":"2018","unstructured":"McClellan C, Lambdin B, Ali M et al (2018) Opioid-overdose laws association with opioid use and overdose mortality. Addict Behav 86:90\u20135. https:\/\/doi.org\/10.1016\/j.addbeh.2018.03.014","journal-title":"Addict Behav"},{"key":"1148_CR57","first-page":"1","volume":"229","author":"SL Murphy","year":"2015","unstructured":"Murphy SL, Kochanek KD, Xu J et al (2015) Mortality in the United States, 2014. NCHS Data Brief 229:1\u20138","journal-title":"NCHS Data Brief"},{"key":"1148_CR58","first-page":"1","volume":"328","author":"SL Murphy","year":"2018","unstructured":"Murphy SL, Xu J, Kochanek KD et al (2018) Mortality in the United States, 2017. NCHS Data Brief 328:1\u20138","journal-title":"NCHS Data Brief"},{"issue":"16","key":"1148_CR59","doi-asserted-by":"publisher","first-page":"1673","DOI":"10.1001\/jama.2020.17477","volume":"324","author":"TA Ochalek","year":"2020","unstructured":"Ochalek TA, Cumpston KL, Wills BK et al (2020) Nonfatal opioid overdoses at an urban emergency department during the COVID-19 pandemic. JAMA 324(16):1673\u20134. https:\/\/doi.org\/10.1001\/jama.2020.17477","journal-title":"JAMA"},{"key":"1148_CR60","doi-asserted-by":"publisher","DOI":"10.1016\/j.drugalcdep.2020.108416","volume":"218","author":"JN Park","year":"2021","unstructured":"Park JN, Rashidi E, Foti K et al (2021) Fentanyl and fentanyl analogs in the illicit stimulant supply: results from U.S. drug seizure data, 2011\u20132016. Drug Alcohol Depend 218:108416. https:\/\/doi.org\/10.1016\/j.drugalcdep.2020.108416","journal-title":"Drug Alcohol Depend"},{"issue":"10","key":"1148_CR61","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11538-021-00925-0","volume":"83","author":"T Phillips","year":"2021","unstructured":"Phillips T, Lenhart S, Strickland WC (2021) A data-driven mathematical model of the heroin and fentanyl epidemic in Tennessee. Bull Math Biol 83(10):1\u201327. https:\/\/doi.org\/10.1007\/s11538-021-00925-0","journal-title":"Bull Math Biol"},{"issue":"4","key":"1148_CR62","doi-asserted-by":"publisher","first-page":"556","DOI":"10.15288\/jsad.2016.77.556","volume":"77","author":"BJ Piper","year":"2016","unstructured":"Piper BJ, Desrosiers CE, Lipovsky JW et al (2016) Use and misuse of opioids in Maine: results from pharmacists, the prescription monitoring, and the diversion alert programs. J Stud Alcohol Drugs 77(4):556\u201365. https:\/\/doi.org\/10.15288\/jsad.2016.77.556","journal-title":"J Stud Alcohol Drugs"},{"issue":"10","key":"1148_CR63","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.2105\/AJPH.2018.304590","volume":"108","author":"AL Pitt","year":"2018","unstructured":"Pitt AL, Humphreys K, Brandeau ML (2018) Modeling health benefits and harms of public policy responses to the US opioid epidemic. Am J Public Health 108(10):1394\u20131400. https:\/\/doi.org\/10.2105\/AJPH.2018.304590","journal-title":"Am J Public Health"},{"key":"1148_CR64","unstructured":"Rabin RC (2021) Overdose deaths reached record high as the pandemic spread. URL: https:\/\/www.nytimes.com\/2021\/11\/17\/health\/drug-overdoses-fentanyl-deaths.html. Accessed 18 Sep 2022"},{"key":"1148_CR65","doi-asserted-by":"publisher","DOI":"10.1186\/s12913-019-4642-8","author":"E Rhodes","year":"2019","unstructured":"Rhodes E, Wilson M, Robinson A et al (2019) The effectiveness of prescription drug monitoring programs at reducing opioid-related harms and consequences: a systematic review. BMC Health Serv Res. https:\/\/doi.org\/10.1186\/s12913-019-4642-8","journal-title":"BMC Health Serv Res"},{"key":"1148_CR66","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s12630-015-0502-0","volume":"63","author":"P Rose","year":"2016","unstructured":"Rose P, Sakai J, Argue R et al (2016) Opioid information pamphlet increases postoperative opioid disposal rates: a before versus after quality improvement study. Can J Anesth 63:31\u20137. https:\/\/doi.org\/10.1007\/s12630-015-0502-0","journal-title":"Can J Anesth"},{"key":"1148_CR67","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s12190-009-0349-z","volume":"35","author":"GP Samanta","year":"2011","unstructured":"Samanta GP (2011) Dynamic behaviour for a nonautonomous heroin epidemic model with time delay. J Appl Math Comput 35:161\u2013178. https:\/\/doi.org\/10.1007\/s12190-009-0349-z","journal-title":"J Appl Math Comput"},{"key":"1148_CR68","unstructured":"SAMHSA (2002) Office of Applied Studies, results from the 2001 national household survey on drug abuse: volume I. summary of national findings. (Office of Applied Studies, NHSDA Series h-17, DHHS Publication no. SMA 02-3758). Substance Abuse and Mental Health Services Administration"},{"key":"1148_CR69","unstructured":"SAMHSA (2014a) 2011\u20132012 NSDUH state prevalence estimates. Substance Abuse and Mental Health Services Administration, https:\/\/www.samhsa.gov\/data\/report\/2011-2012-nsduh-state-prevalence-estimates-pdf-tables"},{"key":"1148_CR70","unstructured":"SAMHSA (2014b) 2012\u20132013 NSDUH state prevalence estimates. Substance Abuse and Mental Health Services Administration, https:\/\/www.samhsa.gov\/data\/report\/2012-2013-nsduh-state-prevalence-estimates-pdf-tables-printing"},{"key":"1148_CR71","unstructured":"SAMHSA (2015) 2013\u20132014 NSDUH state prevalence estimates. Substance Abuse and Mental Health Services Administration, https:\/\/www.samhsa.gov\/data\/report\/2013-2014-nsduh-state-prevalence-estimates-pdf-tables-printing"},{"key":"1148_CR72","unstructured":"SAMHSA (2017a) 2013\u20132014 NSDUH state prevalence estimates. Substance Abuse and Mental Health Services Administration, https:\/\/www.samhsa.gov\/data\/report\/2014-2015-nsduh-state-prevalence-estimates-pdf-tables-printing"},{"key":"1148_CR73","unstructured":"SAMHSA (2017b) 2015\u20132016 NSDUH state prevalence estimates. Substance Abuse and Mental Health Services Administration, https:\/\/www.samhsa.gov\/data\/report\/2015-2016-nsduh-state-prevalence-estimates-pdf-tables-printing"},{"key":"1148_CR74","unstructured":"SAMHSA (2018) 2016\u20132017 NSDUH state prevalence estimates. Substance Abuse and Mental Health Services Administration, https:\/\/www.samhsa.gov\/data\/report\/2016-2017-nsduh-state-prevalence-estimates"},{"key":"1148_CR75","unstructured":"SAMHSA (2019) 2017\u20132018 national survey on drug use and health: model-based prevalence estimates (50 states and the District of Columbia). Substance Abuse and Mental Health Services Administration, https:\/\/www.samhsa.gov\/data\/report\/2017-2018-nsduh-state-prevalence-estimates"},{"key":"1148_CR76","doi-asserted-by":"publisher","first-page":"67","DOI":"10.36076\/ppj.2012\/15\/ES67","volume":"15","author":"N Sehgal","year":"2012","unstructured":"Sehgal N, Machikanti L, Smith HS (2012) Prescription opioid abuse in chronic pain: a review of opioid abuse predictors and strategies to curb opioid abuse. Pain Physician 15:67\u201392","journal-title":"Pain Physician"},{"key":"1148_CR77","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1177\/1178221819866211","volume":"13","author":"N Sharareh","year":"2019","unstructured":"Sharareh N, Sabounchi SS, McFarland M et al (2019) Evidence of modeling impact in development of policies for controlling the opioid epidemic and improving public health: a scoping review. Subst Abuse Res Treat 13:1\u201310. https:\/\/doi.org\/10.1177\/1178221819866211","journal-title":"Subst Abuse Res Treat"},{"issue":"1","key":"1148_CR78","doi-asserted-by":"publisher","first-page":"1615","DOI":"10.1016\/j.drugalcdep.2020.108176","volume":"214","author":"S Slavova","year":"2020","unstructured":"Slavova S, Rock P, Bush HM et al (2020) Signal of increased opioid overdose during COVID-19 from emergency medical services data. Drug Alcohol Depend 214(1):1615\u20137. https:\/\/doi.org\/10.1016\/j.drugalcdep.2020.108176","journal-title":"Drug Alcohol Depend"},{"key":"1148_CR79","first-page":"176","volume":"103","author":"BP Smyth","year":"2010","unstructured":"Smyth BP, Barry J, Keenan E et al (2010) Lapse and relapse following inpatient treatment of opiate dependence. Ir Med J 103:176\u20139","journal-title":"Ir Med J"},{"key":"1148_CR80","unstructured":"Sorg MH (2017) Expanded Maine drug death report for 2016. Health & Public Safety 5. https:\/\/digitalcommons.library.umaine.edu\/mcspc_healthsafety\/5\/"},{"key":"1148_CR81","unstructured":"Sorg MH (2018) Expanded Maine drug death report for 2017. Health & Public Safety 6. https:\/\/digitalcommons.library.umaine.edu\/mcspc_healthsafety\/6\/"},{"key":"1148_CR82","unstructured":"Sorg MH (2019) Expanded Maine drug death report for 2018. Health & Public Safety 8. https:\/\/digitalcommons.library.umaine.edu\/mcspc_healthsafety\/8\/"},{"key":"1148_CR83","unstructured":"Sorg MH (2020) Maine drug death report for 2019. Health & Public Safety 7. https:\/\/digitalcommons.library.umaine.edu\/mcspc_healthsafety\/7\/"},{"key":"1148_CR84","unstructured":"Sorg MH (2021) Maine drug death report for 2020. Maine Office of Attorney General, https:\/\/mainedrugdata.org\/wp-content\/uploads\/2021\/06\/2020_Annual_ME_Drug_Death_Rpt_Final.pdf"},{"key":"1148_CR85","unstructured":"Sorg MH (2022) Maine\u2019s overdose data and the fentanyl epidemic. Margaret Chase Smith Policy Center, URL: https:\/\/legislature.maine.gov\/doc\/7889. Accessed 25 Sep 2022"},{"issue":"4","key":"1148_CR86","doi-asserted-by":"publisher","first-page":"665","DOI":"10.2105\/AJPH.2012.301209","volume":"103","author":"R Spoth","year":"2013","unstructured":"Spoth R, Trudeau L, Shin C et al (2013) Longitudinal effects of universal preventive intervention on prescription drug misuse: three randomized controlled trials with late adolescents and young adults. Am J Public Health 103(4):665\u201372. https:\/\/doi.org\/10.2105\/AJPH.2012.301209","journal-title":"Am J Public Health"},{"key":"1148_CR87","doi-asserted-by":"publisher","first-page":"65","DOI":"10.2105\/AJPH.2014.302207","volume":"105","author":"H Stewart","year":"2015","unstructured":"Stewart H, Malinowski A, Ochs L et al (2015) Inside Maine\u2019s medicine cabinet: findings from the drug enforcement administration\u2019s medication take-back events. Am J Public Health 105:65\u201371. https:\/\/doi.org\/10.2105\/AJPH.2014.302207","journal-title":"Am J Public Health"},{"issue":"3","key":"1148_CR88","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1002\/pds.3553","volume":"23","author":"HL Surratt","year":"2013","unstructured":"Surratt HL, O\u2019Grady C, Kurtz SP et al (2013) Reductions in prescription opioid diversion following recent legislative interventions in Florida. Pharmacoepidemiol Drug Saf 23(3):314\u201320. https:\/\/doi.org\/10.1002\/pds.3553","journal-title":"Pharmacoepidemiol Drug Saf"},{"issue":"1","key":"1148_CR89","doi-asserted-by":"publisher","first-page":"175","DOI":"10.3934\/mbe.2008.5.175","volume":"5","author":"KL Sutton","year":"2008","unstructured":"Sutton KL, Banks HT, Castillo-Chavez CC (2008) Estimation of invasive pneumococcal disease dynamics parameters and the impact of conjugate vaccination in Australia. Math Biosci Eng 5(1):175\u2013204. https:\/\/doi.org\/10.3934\/mbe.2008.5.175","journal-title":"Math Biosci Eng"},{"issue":"1\u20132","key":"1148_CR90","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Van den Driessche","year":"2002","unstructured":"Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1\u20132):29\u201348. https:\/\/doi.org\/10.1016\/S0025-5564(02)00108-6","journal-title":"Math Biosci"},{"key":"1148_CR91","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/978-3-540-78911-6_6","volume-title":"Further notes on the basic reproduction number","author":"P van den Driessche","year":"2008","unstructured":"van den Driessche P, Watmough J (2008) Further notes on the basic reproduction number. Springer Berlin Heidelberg, Berlin, pp 159\u2013178. https:\/\/doi.org\/10.1007\/978-3-540-78911-6_6"},{"issue":"13","key":"1148_CR92","doi-asserted-by":"publisher","first-page":"1346","DOI":"10.1001\/jama.2011.369","volume":"305","author":"ND Volkow","year":"2011","unstructured":"Volkow ND, McLellan TA (2011) Curtailing diversion and abuse of opioid analgesics without jeopardizing pain treatment. JAMA 305(13):1346\u20137. https:\/\/doi.org\/10.1001\/jama.2011.369","journal-title":"JAMA"},{"issue":"4","key":"1148_CR93","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1097\/01.j.pain.0000460357.01998.f1","volume":"156","author":"KE Vowles","year":"2015","unstructured":"Vowles KE, McEntee ML, Julnes PS et al (2015) Rates of opioid misuse, abuse, and addiction in chronic pain: a systematic review and data synthesis. Pain 156(4):569\u201376. https:\/\/doi.org\/10.1097\/01.j.pain.0000460357.01998.f1","journal-title":"Pain"},{"key":"1148_CR94","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1111\/j.1533-2500.2008.00222.x","volume":"8","author":"M Walid","year":"2008","unstructured":"Walid M, Donahue S, Darmohray D et al (2008) The fifth vital sign\u2013What does it mean? Pain Pract 8:417\u201322. https:\/\/doi.org\/10.1111\/j.1533-2500.2008.00222.x","journal-title":"Pain Pract"},{"issue":"1","key":"1148_CR95","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1016\/j.mbs.2006.10.008","volume":"208","author":"E White","year":"2007","unstructured":"White E, Comiskey C (2007) Heroin epidemics, treatment and ODE modeling. Math Biosci 208(1):312\u201324. https:\/\/doi.org\/10.1016\/j.mbs.2006.10.008","journal-title":"Math Biosci"},{"key":"1148_CR96","first-page":"1","volume":"168","author":"J Xu","year":"2014","unstructured":"Xu J, Kochanek KD, Murphy SL et al (2014) Mortality in the United States, 2012. NCHS Data Brief 168:1\u20138","journal-title":"NCHS Data Brief"},{"key":"1148_CR97","first-page":"1","volume":"267","author":"J Xu","year":"2017","unstructured":"Xu J, Murphy SL, Kochanek KD et al (2017) Mortality in the United States, 2015. NCHS Data Brief 267:1\u20138","journal-title":"NCHS Data Brief"},{"key":"1148_CR98","first-page":"1","volume":"355","author":"J Xu","year":"2020","unstructured":"Xu J, Murphy SL, Kochanek KD et al (2020) Mortality in the United States, 2018. NCHS Data Brief 355:1\u20138","journal-title":"NCHS Data Brief"},{"key":"1148_CR99","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/s0376-8716(03)00003-6","volume":"69","author":"J Zacny","year":"2003","unstructured":"Zacny J, Bigelow G, Compton P et al (2003) College on problems of drug dependence taskforce on prescription opioid non-medical use and abuse: position statement. Drug Alcohol Depend 69:215\u2013232. https:\/\/doi.org\/10.1016\/s0376-8716(03)00003-6","journal-title":"Drug Alcohol Depend"}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-023-01148-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11538-023-01148-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-023-01148-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T00:58:44Z","timestamp":1744160324000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11538-023-01148-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,23]]},"references-count":99,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["1148"],"URL":"https:\/\/doi.org\/10.1007\/s11538-023-01148-1","relation":{},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,23]]},"assertion":[{"value":"25 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Statements and Declarations"}},{"value":"The authors have no competing interests to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"45"}}