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zY5kncWc4-dSL4F^o^u=X?pm2o2`hF872$dI>{-~`)wLnwCg!2Pv)6{sb(ZWGz2c^x zcgfCC^-99ft1&xk^`gUdJuMwUyUiC(n` zKS(PC-fW*x2U@2jUCat8#$lQoO*jRvEaRMZ8F>_zfr(>De8U2>zsF+GJ1D+PEL$_1 zo^C;NBih0tSntJSGJ|98sMCj8s6TO;SN`}|Z&+BESmaUg5?5G!gSu@_+8_QiCw-k8 V`fJ{NHwFd<22WQ%mvv4FO#p(qNa_Fp literal 0 HcmV?d00001 diff --git a/m3c.bib b/m3c.bib index fee5865..d280dfc 100644 --- a/m3c.bib +++ b/m3c.bib @@ -11,4 +11,292 @@ month = jan, year = {2019}, file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\XTD7E5SV\\report-americans-are-now-more-likely-to-die-of-an-opioid-overdose-than-on-the-ro.html:text/html} +} + +@article{humensky_are_2010, + title = {Are adolescents with high socioeconomic status more likely to engage in alcohol and illicit drug use in early adulthood?}, + volume = {5}, + issn = {1747-597X}, + url = {https://substanceabusepolicy.biomedcentral.com/articles/10.1186/1747-597X-5-19}, + doi = {10.1186/1747-597X-5-19}, + abstract = {Background: Previous literature has shown a divergence by age in the relationship between socioeconomic status (SES) and substance use: adolescents with low SES are more likely to engage in substance use, as are adults with high SES. However, there is growing evidence that adolescents with high SES are also at high risk for substance abuse. The objective of this study is to examine this relationship longitudinally, that is, whether wealthier adolescents are more likely than those with lower SES to engage in substance use in early adulthood. +Methods: The study analyzed data from the National Longitudinal Survey of Adolescent Health (AddHealth), a longitudinal, nationally-representative survey of secondary school students in the United States. Logistic regression models were analyzed examining the relationship between adolescent SES (measured by parental education and income) and substance use in adulthood, controlling for substance use in adolescence and other covariates. +Results: Higher parental education is associated with higher rates of binge drinking, marijuana and cocaine use in early adulthood. Higher parental income is associated with higher rates of binge drinking and marijuana use. No statistically significant results are found for crystal methamphetamine or other drug use. Results are not sensitive to the inclusion of college attendance by young adulthood as a sensitivity analysis. However, when stratifying by race, results are consistent for white non-Hispanics, but no statistically significant results are found for non-whites. This may be a reflection of the smaller sample size of non-whites, but may also reflect that these trends are driven primarily by white non-Hispanics. +Conclusions: Previous research shows numerous problems associated with substance use in young adults, including problems in school, decreased employment, increases in convictions of driving under the influence (DUI) and accidental deaths. Much of the previous literature is focused on lower SES populations. Therefore, it is possible that teachers, parents and school administrators in wealthier schools may not perceive as great to address substance abuse treatment in their schools. This study can inform teachers, parents, school administrators and program officials of the need for addressing drug abuse prevention activities to this population of students.}, + language = {en}, + number = {1}, + urldate = {2019-03-03}, + journal = {Substance Abuse Treatment, Prevention, and Policy}, + author = {Humensky, Jennifer L}, + month = dec, + year = {2010}, + file = {Humensky - 2010 - Are adolescents with high socioeconomic status mor.pdf:C\:\\Users\\tynan\\Zotero\\storage\\A3I8G5NH\\Humensky - 2010 - Are adolescents with high socioeconomic status mor.pdf:application/pdf} +} + +@misc{abuse_monitoring_nodate, + title = {Monitoring the {Future} {Study}: {Trends} in {Prevalence} of {Various} {Drugs}}, + shorttitle = {Monitoring the {Future} {Study}}, + url = {https://www.drugabuse.gov/trends-statistics/monitoring-future/monitoring-future-study-trends-in-prevalence-various-drugs}, + abstract = {[tabular\_data types=1 drugs=* periods=* grades=1,2,3 years=2011,@ range=1][/tabular\_data] * Data in brackets indicate statistically significant change from the previous year. The use of any prescription drug includes use of any of the following: amphetamines, sedatives (barbiturates), narcotics other than heroin, or tranquilizers “…without a doctor telling you to use them.”}, + language = {en}, + urldate = {2019-03-03}, + author = {Abuse, National Institute on Drug}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\GZ436WV5\\monitoring-future-study-trends-in-prevalence-various-drugs.html:text/html} +} + +@misc{cdctobaccofree_2016_2017, + title = {2016 {SGR}: {E}-{Cigarette} {Use} {Among} {Youth} and {Young} {Adults}}, + shorttitle = {2016 {SGR}}, + url = {https://www.cdc.gov/tobacco/data_statistics/sgr/e-cigarettes/index.htm}, + abstract = {Browse through resources related to and links to the 2016 Surgeon General's Report: E-Cigarette Use Among Youth and Young Adults.}, + language = {en-us}, + urldate = {2019-03-03}, + journal = {Centers for Disease Control and Prevention}, + author = {CDCTobaccoFree}, + month = jul, + year = {2017}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\9AMHZ795\\e-cigarettes.html:text/html} +} + +@article{miech_what_2017, + title = {What are kids vaping? {Results} from a national survey of {US} adolescents}, + volume = {26}, + issn = {0964-4563, 1468-3318}, + shorttitle = {What are kids vaping?}, + url = {http://tobaccocontrol.bmj.com/lookup/doi/10.1136/tobaccocontrol-2016-053014}, + doi = {10.1136/tobaccocontrol-2016-053014}, + abstract = {Objective To examine what substances US youth vape. +Methods Data come from Monitoring the Future, an annual, nationally representative survey of USA 12th-grade, 10th-grade and 8th-grade students. Respondents reported what substance they vaped the last time they used a vaporiser such as an e-cigarette. +Results Among students who had ever used a vaporiser, 65–66\% last used ‘just flavouring’ in 12th, in 10th and in 8th grade, more than all other responses combined. In all three grades, the percentage using ‘just flavouring’ was above 57\% for males, females, AfricanAmericans, Hispanics, Whites, and students both with and without a parent with a college degree. Nicotine use came in a distant second, at about 20\% in 12th and 10th grade and 13\% in 8th grade. Taking into account youth who vaped nicotine at last use increases national estimates of tobacco/nicotine prevalence in the past 30 days by 24–38\% above and beyond cigarette smoking, which is substantial but far less than estimates that assume all vaporiser users inhale nicotine. +Conclusions These results challenge the common assumption that all vaporiser users inhale nicotine. They (a) call into question the designation of vaporisers and e-cigarettes as ENDS (‘Electronic Nicotine Delivery System’), (b) suggest that the recent rise in adolescent vaporiser use does not necessarily indicate a nicotine epidemic, and (c) indicate that vaporiser users can be candidates for primary prevention programmes. Finally, the results suggest the importance of developing different rationales for the regulation of vaporiser devices as compared to the regulation of substances marketed for vaporiser use.}, + language = {en}, + number = {4}, + urldate = {2019-03-03}, + journal = {Tobacco Control}, + author = {Miech, Richard and Patrick, Megan E and O'Malley, Patrick M and Johnston, Lloyd D}, + month = jul, + year = {2017}, + pages = {386--391}, + file = {Miech et al. - 2017 - What are kids vaping Results from a national surv.pdf:C\:\\Users\\tynan\\Zotero\\storage\\DTM8PSUQ\\Miech et al. - 2017 - What are kids vaping Results from a national surv.pdf:application/pdf} +} + +@misc{noauthor_association_nodate, + title = {Association of {Electronic} {Cigarette} {Use} {With} {Initiation} of {Combustible} {Tobacco} {Product} {Smoking} in {Early} {Adolescence}. {\textbar} {Adolescent} {Medicine} {\textbar} {JAMA} {\textbar} {JAMA} {Network}}, + url = {https://jamanetwork.com/journals/jama/fullarticle/2428954?resultClick=3}, + urldate = {2019-03-03}, + file = {Association of Electronic Cigarette Use With Initiation of Combustible Tobacco Product Smoking in Early Adolescence. | Adolescent Medicine | JAMA | JAMA Network:C\:\\Users\\tynan\\Zotero\\storage\\7JARVDSZ\\2428954.html:text/html} +} + +@misc{noauthor_vital_nodate, + title = {Vital {Signs}: {Exposure} to {Electronic} {Cigarette} {Advertising} {Among} {Middle} {School} and {High} {School} {Students} — {United} {States}, 2014}, + url = {https://www.cdc.gov/mmwr/preview/mmwrhtml/mm6452a3.htm}, + urldate = {2019-03-03}, + file = {Vital Signs\: Exposure to Electronic Cigarette Advertising Among Middle School and High School Students — United States, 2014:C\:\\Users\\tynan\\Zotero\\storage\\JHZX728M\\mm6452a3.html:text/html} +} + +@article{redonnet_tobacco_2012, + title = {Tobacco, alcohol, cannabis and other illegal drug use among young adults: {The} socioeconomic context}, + volume = {121}, + issn = {03768716}, + shorttitle = {Tobacco, alcohol, cannabis and other illegal drug use among young adults}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0376871611003887}, + doi = {10.1016/j.drugalcdep.2011.09.002}, + language = {en}, + number = {3}, + urldate = {2019-03-03}, + journal = {Drug and Alcohol Dependence}, + author = {Redonnet, Bertrand and Chollet, Aude and Fombonne, Eric and Bowes, Lucy and Melchior, Maria}, + month = mar, + year = {2012}, + pages = {231--239}, + file = {Submitted Version:C\:\\Users\\tynan\\Zotero\\storage\\X2SWPUBH\\Redonnet et al. - 2012 - Tobacco, alcohol, cannabis and other illegal drug .pdf:application/pdf} +} + +@article{mcmillen_trends_2015, + title = {Trends in {Electronic} {Cigarette} {Use} {Among} {U}.{S}. {Adults}: {Use} is {Increasing} in {Both} {Smokers} and {Nonsmokers}}, + volume = {17}, + issn = {1462-2203, 1469-994X}, + shorttitle = {Trends in {Electronic} {Cigarette} {Use} {Among} {U}.{S}. {Adults}}, + url = {https://academic.oup.com/ntr/article-lookup/doi/10.1093/ntr/ntu213}, + doi = {10.1093/ntr/ntu213}, + language = {en}, + number = {10}, + urldate = {2019-03-03}, + journal = {Nicotine \& Tobacco Research}, + author = {McMillen, Robert C. and Gottlieb, Mark A. and Shaefer, Regina M. Whitmore and Winickoff, Jonathan P. and Klein, Jonathan D.}, + month = oct, + year = {2015}, + pages = {1195--1202}, + file = {McMillen et al. - 2015 - Trends in Electronic Cigarette Use Among U.S. Adul.pdf:C\:\\Users\\tynan\\Zotero\\storage\\T5ELXFSD\\McMillen et al. - 2015 - Trends in Electronic Cigarette Use Among U.S. Adul.pdf:application/pdf} +} + +@article{noauthor_social_2004, + title = {Social determinants of drug use}, + issn = {0733422446 9780733422447}, + language = {English}, + journal = {Social determinants of drug use}, + year = {2004}, + note = {OCLC: 224475482} +} + +@article{taylor_08_socioeconomic_2008, + title = {Socioeconomic {Factors} and {Illicit} {Drug} {Demand}}, + volume = {16}, + url = {https://digitalcommons.iwu.edu/parkplace/vol16/iss1/17}, + number = {1}, + journal = {The Park Place Economist}, + author = {Taylor '08, Elizabeth}, + month = jan, + year = {2008}, + file = {Taylor '08 - 2008 - Socioeconomic Factors and Illicit Drug Demand.pdf:C\:\\Users\\tynan\\Zotero\\storage\\AQYLYE3Z\\Taylor '08 - 2008 - Socioeconomic Factors and Illicit Drug Demand.pdf:application/pdf} +} + +@misc{fogoros_pot_nodate, + title = {Pot {Can} {Sometimes} {Be} {Experimental} or a {Gateway} {Drug}}, + url = {https://www.verywellmind.com/does-marijuana-lead-to-the-use-of-other-drugs-63530}, + abstract = {Many young people who smoke marijuana never progress to using other drugs, but some do go on to abuse other harder, illegal substances.}, + language = {en}, + urldate = {2019-03-03}, + journal = {Verywell Mind}, + author = {Fogoros, Richard N. and {MD}}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\6UVB2DCX\\does-marijuana-lead-to-the-use-of-other-drugs-63530.html:text/html} +} + +@article{torabi_cigarette_1993, + title = {Cigarette {Smoking} as a {Predictor} of {Alcohol} and {Other} {Drug} {Use} by {Children} and {Adolescents}: {Evidence} of the “{Gateway} {Drug} {Effect}”}, + volume = {63}, + issn = {00224391, 17461561}, + shorttitle = {Cigarette {Smoking} as a {Predictor} of {Alcohol} and {Other} {Drug} {Use} by {Children} and {Adolescents}}, + url = {http://doi.wiley.com/10.1111/j.1746-1561.1993.tb06150.x}, + doi = {10.1111/j.1746-1561.1993.tb06150.x}, + language = {en}, + number = {7}, + urldate = {2019-03-03}, + journal = {Journal of School Health}, + author = {Torabi, Mohammad R. and Bailey, William J. and Majd-Jabbari, Massoumeh}, + month = sep, + year = {1993}, + pages = {302--306}, + file = {Torabi et al. - 1993 - Cigarette Smoking as a Predictor of Alcohol and Ot.pdf:C\:\\Users\\tynan\\Zotero\\storage\\A858ZU5W\\Torabi et al. - 1993 - Cigarette Smoking as a Predictor of Alcohol and Ot.pdf:application/pdf} +} + +@book{american_psychiatric_association_diagnostic_2013, + edition = {Fifth Edition}, + title = {Diagnostic and {Statistical} {Manual} of {Mental} {Disorders}}, + isbn = {978-0-89042-555-8 978-0-89042-557-2}, + url = {https://psychiatryonline.org/doi/book/10.1176/appi.books.9780890425596}, + language = {en}, + urldate = {2019-03-03}, + publisher = {American Psychiatric Association}, + author = {{American Psychiatric Association}}, + month = may, + year = {2013}, + doi = {10.1176/appi.books.9780890425596} +} + +@misc{noauthor_economic_nodate, + title = {Economic {Status} and {Abuse}}, + url = {https://www.dualdiagnosis.org/drug-addiction/economic-status/}, + abstract = {Economic status refers to the bracket or class a person or household falls into based on their income production level. In 2012, around 122,459,000 households had income during the year, and 4.5 percent of them brought in more than \$200,000.[1] Those who made between \$39,736 and \$104,087 that year were considered to be of middle …}, + language = {en-US}, + urldate = {2019-03-03}, + journal = {Dual Diagnosis}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\5DYIRR75\\economic-status.html:text/html} +} + +@misc{noauthor_juulpods_nodate, + title = {{JUULpods} and {E}-{Liquid} {FAQs} - {JUUL} {Support}}, + url = {https://support.juul.com/home/learn/faqs/juulpod-basics}, + urldate = {2019-03-03}, + file = {JUULpods and E-Liquid FAQs - JUUL Support:C\:\\Users\\tynan\\Zotero\\storage\\YU4SH5UX\\juulpod-basics.html:text/html} +} + +@misc{noauthor_e-cigarette_2014, + title = {E-{Cigarette} {Use}: {The} {Fallacy} of {Puff} {Counts} {\textbar} {White} {Cloud}}, + shorttitle = {E-{Cigarette} {Use}}, + url = {https://www.whitecloudelectroniccigarettes.com/blog/fallacy-puff-counts/}, + abstract = {Because vaping has evolved, it’s no longer accurate to make blanket claims about puff counts or longevity, which are still used by many e-cig companies.}, + language = {en}, + urldate = {2019-03-03}, + journal = {Electronic Cigarette Blog {\textbar} White Cloud}, + month = jul, + year = {2014}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\EH3TM8MQ\\fallacy-puff-counts.html:text/html} +} + +@misc{matthews_how_2017, + title = {How {Much} {Nicotine} {Is} in a {Cigarette} and a {Pack}?}, + url = {https://vapingdaily.com/nicotine-in-cigarette/}, + abstract = {You cannot just say all cigarettes contain such and such amounts of nicotine. It depends on different things we covered in this article for you.}, + language = {en-US}, + urldate = {2019-03-03}, + journal = {Vaping Daily}, + author = {Matthews, Christina}, + month = oct, + year = {2017}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\R9BMQTMG\\nicotine-in-cigarette.html:text/html} +} + +@article{benowitz_daily_1984, + title = {Daily intake of nicotine during cigarette smoking}, + volume = {35}, + issn = {0009-9236, 1532-6535}, + url = {http://doi.wiley.com/10.1038/clpt.1984.67}, + doi = {10.1038/clpt.1984.67}, + number = {4}, + urldate = {2019-03-03}, + journal = {Clinical Pharmacology and Therapeutics}, + author = {Benowitz, Neal L and Iii, Peyton Jacob}, + month = apr, + year = {1984}, + pages = {499--504}, + file = {Benowitz and Iii - 1984 - Daily intake of nicotine during cigarette smoking.pdf:C\:\\Users\\tynan\\Zotero\\storage\\4VLFELUC\\Benowitz and Iii - 1984 - Daily intake of nicotine during cigarette smoking.pdf:application/pdf} +} + +@misc{noauthor_juul_nodate, + title = {{JUUL} {Slate} {Device} {Kit} {\textbar} {Free} {Shipping} {\textbar} {JUUL}}, + url = {https://www.juul.com/shop/devices/basic-kit}, + abstract = {Shop the JUUL Device Kit. The kit includes a rechargeable JUUL device, a USB charger and a 1 year limited device warranty.}, + language = {en}, + urldate = {2019-03-03}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\XGJCRJMK\\basic-kit.html:text/html} +} + +@article{zeb_dynamical_2018, + title = {Dynamical analysis of cigarette smoking model with a saturated incidence rate}, + volume = {8}, + issn = {2158-3226}, + url = {http://aip.scitation.org/doi/10.1063/1.5028157}, + doi = {10.1063/1.5028157}, + language = {en}, + number = {4}, + urldate = {2019-03-03}, + journal = {AIP Advances}, + author = {Zeb, Anwar and Bano, Ayesha and Alzahrani, Ebraheem and Zaman, Gul}, + month = apr, + year = {2018}, + pages = {045317}, + file = {Full Text:C\:\\Users\\tynan\\Zotero\\storage\\JDVYWBB7\\Zeb et al. - 2018 - Dynamical analysis of cigarette smoking model with.pdf:application/pdf} +} + +@misc{noauthor_buy_nodate, + title = {Buy {JUUL} {Pods} ({Pack} of 4) {\textbar} {Official} {Store} {\textbar} {All} {JUUL} {Flavors} {\textbar} {JUUL}}, + url = {https://www.juul.com/shop/pods}, + abstract = {Shop all JUULpods here. Discover your favorite flavor today.}, + language = {en}, + urldate = {2019-03-03}, + file = {Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\HYF5ENWZ\\pods.html:text/html} +} + +@misc{noauthor_college-age_2018, + type = {Government}, + title = {College-{Age} \& {Young} {Adults}}, + url = {https://www.drugabuse.gov/related-topics/college-age-young-adults}, + abstract = {While daily marijuana use has been steadily increasing in prevalence among young adults over the past decade, the level has reached an all-time high in non-college young adults to nearly three times that of their college peers. The biggest division between the groups, however, was seen in annual , past month, and daily cigarette smoking rates.}, + language = {en}, + urldate = {2019-03-03}, + journal = {National Institute on Drug Abuse}, + month = feb, + year = {2018}, + file = {2018 - College-Age & Young Adults.pdf:C\:\\Users\\tynan\\Zotero\\storage\\VDELDDRW\\2018 - College-Age & Young Adults.pdf:application/pdf;Snapshot:C\:\\Users\\tynan\\Zotero\\storage\\GD8A6RT5\\college-age-young-adults.html:text/html} } \ No newline at end of file diff --git a/m3c.pdf b/m3c.pdf index 84c71a5c0034ff4b781003f97d2abe80b9f9d0e5..037ae9a7f2a5ce9c2377fd95c94fe136a0c4711c 100644 GIT binary patch literal 386561 zcmY!laBR8|4K7o21p|frq%1BQ8!mmH)V%bP39- z(09v8EJ<}qP0mkA<+8KmDlREXP0Z!0xK(=2n%l{chxNhVe_ajU`Zs1Q$-K3@i(lZ* zuFk_>_wM-dpFLlfgU>H=U$Gy@JBJN#U!0GfmbWpHSa3OZ0YO?u!~?nMXSI?d?#C znER@x#h7EY!+kyP47R`x>WQZ{)OQ@noTwpvO7Qj#`(uY|cHhx{Y7w?|*U_^!zQ12@ zzBTo$e->Mr!SZuH_j)wcKlSX&)h%5m@AGfoz83MM9EGcxKCv*t^ogmV1<^iv8)ln- 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+\usepackage[backend=biber,style=ieee,natbib=true]{biblatex} \usepackage{subcaption} +\usepackage{hyperref} +\usepackage{enumitem} \geometry{letterpaper, portrait, margin=1in} \doublespace \title{Dab} \author{Team \#11745} \graphicspath{{./imgs/}} +\addbibresource{m3c.bib} + +\hypersetup{ + colorlinks=true, + linkcolor=black, + filecolor=magenta, + urlcolor=cyan, + citecolor=blue, +} \definecolor{codegreen}{rgb}{0,0.6,0} \definecolor{codegray}{rgb}{0.5,0.5,0.5} \definecolor{codepurple}{rgb}{0.58,0,0.82} -\definecolor{backcolor}{rgb}{0.95,0.95,0.92} +\definecolor{backcolor}{rgb}{0.95,0.95,0.95} \lstdefinestyle{scheme}{ backgroundcolor=\color{backcolor}, - commentstyle=\color{codegreen}, + commentstyle=\color{codegray}, keywordstyle=\color{blue}, numberstyle=\tiny\color{codegray}, - stringstyle=\color{codepurple}, + stringstyle=\color{red}, basicstyle=\footnotesize\ttfamily, breakatwhitespace=false, breaklines=true, @@ -58,22 +68,154 @@ \tableofcontents \newpage -\section{Section} - -\subsection{Assumptions} - -\section{Section} - -\subsection{Assumptions} - -\section{Section} - -\subsection{Assumptions} +\section{Global Assumptions} + +\begin{itemize} + \item Sources of information, data, and models in this investigation pertain only to the United States population. + \item Differences in factors between genders will be ignored because the input data is gender agnostic and any gender-based lurking variables will equalize within the sample size of data and simulations. + \item One year is equal to 365 days. + \item A high school is a closed-system, besides socioeconomic factors. +\end{itemize} + +\section{Darth Vapor} + +\begin{figure}[H] + \centering + \begin{subfigure}[t]{.3\linewidth} + \includegraphics[width=\linewidth]{percentUsers8} + \end{subfigure} + \begin{subfigure}[t]{.3\linewidth} + \includegraphics[width=\linewidth]{percentUsers10} + \end{subfigure} + \begin{subfigure}[t]{.3\linewidth} + \includegraphics[width=\linewidth]{percentUsers12} + \end{subfigure} + + \begin{subfigure}[t]{.4\linewidth} + \includegraphics[width=\linewidth]{percentUsersYA} + \end{subfigure} + \begin{subfigure}[t]{.4\linewidth} + \includegraphics[width=\linewidth]{percentUsersCo} + \end{subfigure} + \caption{Vape vs. Cigarette Usage by Age Group \citep{noauthor_college-age_2018}} +\end{figure} + +\subsection{Local Assumptions} +\begin{itemize} + \item One cigarette contains 12 mg of nicotine \citep{matthews_how_2017} + \item The rate of absorption of nicotine from one cigarette is 1 mg per cigarette because there is loss from the combustion of the cigarette and filtering. Our unit of 1 cigarette of nicotine indicates the rate of nicotine intake, 1 mg per cigarette, and not nicotine content, 12 mg per cigarette. \citep[501]{benowitz_daily_1984} + \item One cigarette is worth 10 puffs. \citep{noauthor_e-cigarette_2014} + \item One pack of cigarettes costs \$5 and contains 20 cigarettes. + \item The current smoking rate among adults in the US is 14\%. + \item Our model assumes JUULs as the unit of vape consumption and encapsulates e-cigarettes for this model. + \item The JUUL device kit costs \$35 for the device and charger and is the base cost of entry for JUUL. \citep{noauthor_juul_nodate} + \item Four JUUL pods cost \$16. \citep{noauthor_buy_nodate} + \item A JUUL pod has negligible nicotine waste becasue there is no combustion or filter. + \item One JUUL pod 41 mg or approximately 41 cigarettes worth of nicotine absorption. \citep{noauthor_juulpods_nodate} + \item Our model only considers a death directly from overdose of nicotine, which is so unlikely that we have not accounted for it in our model. +\end{itemize} + +\subsection{Cost Analysis of JUULs vs. Cigarettes} +To determine which nicotine vector is more cost effective over time, two linear equations were constructed for each, where $y$ is the total cost and $x$ is each additional cigarette (synonymous with each additional intake of 1 mg of nicotine). + +\begin{figure}[H] + \centering + \includegraphics[width=.8\linewidth]{JUULs-vs-Cigarettes-Cost} + \caption{JUULs vs. Cigarettes Cost} + \label{fig:cigcosts} + JUUL: $y = \frac{16}{160} x + 35$ + \begin{itemize} + \item Slope $\frac{16}{160}$ = cost per each additional cigarette, aka each additional cigarette worth of nicotine intake (1 mg). + \subitem 16 = the cost of four JUUL pods; JUUL pods are sold in packs of four for \$15.99. + \subitem 160 = the number of milligrams of nicotine in 4 pods (approximately 40 milligrams of nicotine per pod). + \item 35 = cost of device kit (\$34.99), which includes a JUUL device and charger. + \end{itemize} + Cigarette: $y = \frac{5}{20} x$ + \begin{itemize} + \item Slope $\frac{5}{20}$ = Cost per each additional cigarette, aka each additional cigarette’s worth of nicotine intake (1 mg). + \subitem 5 = simplified cost per pack of cigarette. + \subitem 20 = number of milligrams of nicotine absorbed per pack. + \end{itemize} +\end{figure} + +\subsection{Model} + +\begin{figure}[H] + \centering + \includegraphics[width=.8\linewidth]{PSR} + \caption{PSR for the total US population} + \label{fig:PSR} +\end{figure} + +\begin{singlespace} +\begin{small} +\begin{equation} +\label{eq:1} +\begin{aligned} +\frac{dP}{dt} &= \beta \frac{PS}{N} + \alpha ( 1 - \epsilon )S \\ +\frac{dS}{dt} &= \beta \frac{PS}{N} - \alpha S \\ +\frac{dQ}{dt} &= \alpha \epsilon S +\end{aligned} +\end{equation} +\begin{itemize}[label=] + \item $S$ = Smokers + \item $P$ = Potential smokers + \item $\beta$ = Rate of transmission + \item $\alpha$ = Rate of recovery + \item $1 - \epsilon$ = Rate of relapse + \item $Q$ = Smoking quitters + \item $N$ = Total population +\end{itemize} +\end{small} +\end{singlespace} + +\section{Above or Under the Influence?} + +\subsection{Local Assumptions} + +\begin{itemize} + \item The proportion of deaths caused by opium overdose is negligible. + \item The gateway nature of ateway nature of marijuana doesn’t need to be identified as its own variable because the reasons (behind why marijuana leads to opioid usage) can be woven into the other variables. +\end{itemize} + +\subsection{Model} + +\paragraph{Variables} +\begin{itemize}[label=] + \item $S$ = Socioeconomic factors + \item $P$ = People (social circles) + \item $\beta$ = Baseline (derived from previous years) + \item $N$ = Population + \item $h$ = Health + \item $x$ = Number of people + \item $D$ = Death constant +\end{itemize} +\section{Ripples} + +\subsection{Variables} + +\begin{itemize}[label=] + \item $C$ = Total cost of drug + \item $T$ = Tax + \item $c_j$ = Cost of jail + \item $p_j$ = Percent of drug users in jail + \item $p_r$ = Percent in rehab + \item $c_r$ = Cost of rehab + \item $M$ = Medical costs +\end{itemize} + +\subsection{Local Assumptions} + +\subsection{Conclusion} + +\begin{enumerate} + \item +\end{enumerate} \newpage -\bibliography{m3c} -\bibliographystyle{apa} +\printbibliography +% \bibliographystyle{IEEEtran} \newpage \appendix

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