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Honors Theses

Modeling the opioid crisis in virginia: a differential equations model assessing the impact of medication-assisted treatment on the addicted population.

Maniha Zehra Akram

Date of Award

Document type, degree name.

Bachelor of Science

Mathematics

First Advisor

Dr. Joanna Wares

Second Advisor

Dr. Saif Mehkari

The opioid epidemic is prevalent in countless communities throughout the United States and has yet to be mitigated. Treatments for OUD (opioid use disorder) include Medication-Assisted Treatment (MAT) and treatment without medication (non-MAT), with the former being judged as more effective in terms of lower relapse rates, death rates, and criminal activity (U.S. Food & Drug Administration, 2023; SAMHSA, 2024). Motivated by the promising research on MAT, this paper models the relationship

between the treatment and addicted populations using a system of ordinary differential equations. In addition to producing closed-form equilibrium solutions, the model leads to the conclusion that expanding access to MAT, while important for decreasing the addicted population, is not a sufficient policy measure in isolation. Instead, policymakers should endeavor to increase access to all forms of treatment. Furthermore, varying the rate of addiction to prescription opioids causes significantly different equilibrium populations, indicating that the prescription of opioids requires further monitoring.

Recommended Citation

Akram, Maniha Zehra, "Modeling the Opioid Crisis in Virginia: A Differential Equations Model Assessing the Impact of Medication-Assisted Treatment on the Addicted Population" (2024). Honors Theses . 1751. https://scholarship.richmond.edu/honors-theses/1751

Since May 07, 2024

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Legacy Theses & Dissertations (2009 - 2024)

The Legacy ETD collection includes all theses or dissertations submitted to ProQuest electronically between 2008 and 2022.

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Theses/Dissertations from 2022 2022

The simulated sensitivity of the North American monsoon at convection-permitting scales , Brendan Wallace

Dynamic instance-wise decision-making for machine learning , Yasitha Warahena Liyanage

The Long Island Opt-Out Movement and local politics in four school districts , Raymond James Webb

AB42 alters glutamatergic transmission in the CA1 region of the mouse hippocampus , Patrick Harry Wehrle

The dark figure of wrongful convictions : how intake decisions impact exonerations , Jennifer Weintraub

Understanding sense of belonging of students of color attending a liberal arts college , Jessica Wenger

Women's work history and mental well-being : evidence from the Indonesian family life survey , Nurul Widyaningrum

Relationships of teacher perceptions and racially diverse third grade student achievement : an analysis of ECLS-K:2011 data University at Albany , Lynnette Renee Williams

New York city micronet : comprehensive site metadata and classifications and characteristics of the urban heat island , Ashley Williamson

Computational methods for propagation of optical fields with the angle-impact Wigner function , Jeremy Wittkopp

Spatio-temporal analyses of the relationships between stop, question and frisk and crime in New York City , Haemi Won

Examining the relationship between admission requirements and program outcome variables in a special education teacher preparation program , Emily Woofenden

Adolescent maltreatment, substance use, and self-efficacy : a test of General Strain Theory among a sample of clinical youth , Sonya Worthington

Sampling distribution of non-overlap indices using bootstrapping procedure : a monte carlo simulation study and empirical demonstration , Xinyun Xu

Stability and differential privacy of stochastic gradient methods , Zhenhuan Yang

Probing the stability and solution processability of metal chalcogenide semiconducting materials , Mengwen Yan

High-capacity and interpretable temporal point process models for user activity sequence modeling , Mengfan Yao

"We are the stories" : narrative competence and cognitive mapping as a culturally sustaining pedagogy in the education of emergent bilinguals , Sepideh Yasrebi

Applications of search and matching to international trade and unemployment insurance , Kai You

Innovation capacity in local government organizations : a comparative case study of three innovation labs in the U.S , Qianli Yuan

Contrapuntal readings of the exilic consciousness : reading Yehuda Amichai and Mahmoud Darwish together , Sarah Brooks Zahed

Theses/Dissertations from 2021 2021

Novel functional proteomics techniques for multiplex and single cell cytokines detection , Mohammed Abdullah

Statistical and variational modeling and analysis of passive integrated photonic devices , Norbert Dinyi Agbodo

Black bisexual women's experiences of growth following gendered racism and biphobia , Alexandra Agiliga

Development of bioaffinity based assays for forensic applications , Juliana Maria Agudelo Cano

Graduate students' intrinsic motivation in fully online courses , Ahmed Alahmari

Long noncoding RNA AK001796 as a mediator of epithelial-to-mesenchymal transition in metastatic breast cancer , Sumayya Adib Alchalabi

Arabic-speaking students' responses to children's literature about the Middle East , Amal Aldaej

Evaluating the impact of tobacco retailer density on smoking among patients with serious mental illness and diabetes in New York State , Amani Alharthy

Graduate students' understanding, perception, and preference of time management in online learning , Majed Ali

Isolating oral bacterial species from a single donor through a multi-step detection method , Khalid Al-Lakhen

Flexible lives on engineering's 'Bleeding edge' : gender, migration and belonging in the semiconductor industry , Sarah E. Appelhans

Mass spectral and chemometric analysis for the detection and identification of forensically relevant materials , Meghan Grace Appley

Change and continuity in biology , Gunnar O'Neill Babcock

The time course and interaction of emoji and text processing during natural reading : evidence from eye movements , Eliza Barach

Utilizing raman spectroscopy to determine the time since deposition of heated bloodstains , Alexis Pearl Barber

Supporting highly mobile literacy learners : examining how an elementary school provided support to mobile students in an urban school district , Rebecca L. Benjamin

Factors influencing psychotherapy completion in children exposed to adverse childhood experiences , Cheryl Kayleen Best

An examination of the Arctic environment and Arctic cyclones during periods of low and high forecast skill of the synoptic-scale flow , Kevin Biernat

Role of RNA helicases in the drosophila germline , Patrick Blatt

Feasibility of acceptance-based health coaching targeting food cravings in pregnancy , Lauren Blau

A cross cultural comparison of Asian college students' well-being : exploring the impact of cultural factors in a social cognitive framework , Jennifer Joy Bordon

Belonging and bias : how diatonicity and response bias affect pitch memory in a probe tone task , Jeff Bostwick

Novel sensing concept for organophosphate monitoring , Cheyenne Bowman

Legacy and emerging per- and polyfluoroalkyl substances : analysis, environmental distribution, and bioconcentration , Richard Anthony Brase

Using machine learning to predict super-utilizers of healthcare services , Kevin Paul Buchan Jr.

Disrupting the school-to-prison pipeline : implementing alternative education programs to reduce student disciplinary issues , Michael M. Burns

The sensitivity of convection to boundary layer parameterization in hurricanes Harvey and Irma 2017 , Dylan Card

The foundations of inference and its application to fundamental physics , Nicholas Matthew Carrara

Crime and safety in United States schools : selected findings regarding the relationship of interventions on the rate of student removal from the educational setting for disciplinary reasons , Heather Chadwell Dennis

Modulation of Rho termination : expectation vs reality , Kavya Sri Sai Chegireddy

Navigating racial discrimination as transnational actors : racial experiences of Asian international students in the U.S. under the Covid-19 pandemic , Chen Chen

Higher education under market forces how the "transnational shadow education" industry emerged and persisted to help Taiwanese students to study in the U.S , Kenneth Han Chen

The acquisition of variation in future time expression by high school student learners of Spanish in Upstate New York , Erika E. Clarkin

The effect of mindfulness on autonomic nervous system coordination in individuals with interparental conflict exposure , Rachel Clegg

Critical media literacy in social studies : a case study , Lauren Collet-Gildard

Sex differences in context fear neural circuitry and behavior across development , Lorianna Marie Colon

Black women social workers : a qualitative exploration of stress and coping , Collina D. Cooke

Exploring the roles of school business officials through the lens of financial transparency reporting requirements in New York State , Colette Crawfordmack

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Intrabodies reveal critical steps involved in ricin's interactions with the ribosome , Timothy Francis Czajka

Substance abuse policies, prescribing behaviors, and health outcomes , Huy Do Dang

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Uncle Tom's women : slavery and Black female sexuality , Natalia Davila

Examining the benefits of a sustained balance and fall prevention programming for independent older adults living in a community setting , Noah Davis

Courtland Street, Lake George : a bioarchaeological study of the skeletal foot morphology of early Revolutionary War soldiers , Alexandra Grace Decarlo

Inverse problems for topological summaries in topological data analysis , Jordan Desha

The materiality of metaphor in Mayan hieroglyphic texts : metaphor in changing political climates , Rebecca Ann Dinkel

Properties of curriculum-based measurement for mathematics : an investigation of the average growth, variability, and precision of three forms , Arianna Doss

Social identities at work : how do multiple social identities influence organizational attraction? , Aileen Dowden

Emotion regulation and executive functioning : a comparison of collegiate taekwondo athletes, other athletes, and non-athletes , Rae Danett Drach

Aerosol and terrain effects on winter cloud and precipitation over New York State , Yuyi Du

Addressing the development of reading comprehension in students with ASD : a meta-analysis , Halley Eacker

Molecular simulation of RNA conformational dynamics : an example of Micro-RNA targeting messenger RNA : Mir-34a-MSIRT1 , Parisa Ebrahimi

Cuerpos femeninos en concursos de mujeres o 'reinados' en Colombia, 1991-2018 , Ernesto L. Ebratt

19th century exam, 21st century policing : an examination of the New York State Civil Service and police officer recruitment: , Amani Edwards

Diagnosing high sinuosity regimes associated with anomalous Greenland ice-melt events using self-organizing maps , Mansour El Riachy

Kinetic characterization of two C-family polymerases from the gram-positive bacterium staphylococcus aureus , Sean P. Fagan

Seasonal differences in the impacts of IPO and AMO on temperature and precipitation over South America , Thomas Favata

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A comparison of implicit and explicit error detection and their effects on purchase intention and judgments of quality , Rachel Fernandes

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Intergenerational risk of maternal childhood maltreatment on infant health concerns in low-income Mexican American mother-child dyads , Amanda Flagg

An exploration of undergraduates' intercultural development : a case study of an internship abroad program , Jennifer Fong

Against empathy bias : the moral value of equitable empathy , Zoe Fowler

Exploring environmental and methodological sensitivities of forecasted and observed surface winds and gusts using underutilized datasets , Alex Roslyn Gallagher

Epitranscriptomic writer regulation of gene expression in Escherichia coli , William Eugene Gasperi

Identifying the microphysical sensitivities of mesoscale and synoptic precipitation using an ensemble framework , Lauriana Gaudet

Applications of mass spectrometry to forensic entomology : calliphoridae species determination, monitoring of decomposition volatiles, and discovery of chemical cues , Justine Elizabeth Giffen-Lemieux

Mining subgroups from temporal data : from the parts to the whole , Alexander Gorovits

Mechanical analysis of a heterogeneously integrated silicon photonic interposer , Erica Charlene Graham

The case of environmental education of children , Mary Greagan

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The circulatory process and user-data , Matthew Greene

Are there individual differences in the foreign language effect? , Rita Gross

Dominican Spanish in New York : language attitudes and variation of final /ɾ/ and /l/ , Gabriel Valentín Guadalupe

Simulation analysis of the snowball chamber , Thomas Guile

Student teachers' TPACK development and technology integration in the shared collective lesson planning , Chen Guo

The role of school and district leaders in discipline systems in positive outlier high schools , Catherine E. Guthrie

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