Technical Reports

Every summer QRLSSP, formerly MTBI, offers sequential research experiences for undergraduate students. The program, which has been held in conjunction with Cornell University (1996-2003), Los Alamos National Laboratory (2003-2005), and Arizona State University (2004-present) focuses on the field of applied mathematics and its applications to the biological and social sciences.

The online research archives are a collection of the technical papers produced by the participants of the QRLSSP summer REU. Following four weeks of intensive coursework, homework and lectures, participants work in self-selected groups on projects of their own choosing in collaboration with faculty, visiting scholars and graduate students. Participants then attend and present their work at national conferences such as the Society for Industrial and Applied Mathematics (SIAM) conference on the life sciences, the National Meetings of the Society for the Advancement of Chicanos and Native Americans in Science (SACNAS), the AMS/MAA Joint Mathematics Meetings and at their respective institutions.

This research has been made possible over 19 years through funding provided by the National Science Foundation (NSF), the National Security Agency (NSA), the Alfred P. Sloan Foundation and the Office of the Executive Vice President and Provost of Arizona State University. MTBI funding was provided by Cornell University and Los Alamos National Laboratory (T-Division) from 1996-2004.


  1. Computational Methods for Electrical Impedance Tomography: 
  2. Effect of Methane Mitigation on Global Temperature under a Permafrost Feedback: 
  3. Malaria Early Warning Application for Individual Risk Assessment: 
  4. A mathematical model to determine which pathway of castration resistance the patient will develop: 


  1. Controlling Recidivism Among Released Inmates: How Can Education Programs Be Better Used to Reduce Their Rates?:   
  2. Resistance Dynamics in Chronic Lymphocytic Leukemia: 
  3. In-nest information flow analysis of social ant colonies.: 
  4. Modeling climate change’s impact on Macrocystis pyrifera through population dynamics.: 
  5. Mathematics of the dynamics of multidrug resistant TB (MDR-TB) in India: Role of timely identification and treatment.: 


  1. Analyzing the Control Measures for the Homeless Population and Quantifying their Impact on the COVID-19 Epidemic in New York City: 
  2. Quantifying the impact of chronic lead toxicity on the American Bald Eagle (Haliaeetus leucocephalus) population in the Great Lakes Region: 


1. Minimizing Drug Resistant Cases of Gonorrhea through Cost-Effective Treatment Plans: 

2. Evaluating the Impact of Vocational Training and Housing Assistance Programs on the Spread and Control of Homelessness in Los Angeles, California: 

3. Topography and Behavior Based Movement Modeling for Missing Hikers in Land-Wilderness Settings: 

4. Dynamics of Prion Proliferation Under Combined Treatment of Pharmacological Chaperones and Interferons: 

5. The Impact of Temperature-Dependent Sex Determination on the Population Dynamics of Green Sea Turtles (Chelonia mydas): 

6. The Role of Preferential Mating and Wolbachia Infection on the Aedes Aegypti Population Dynamics: 


1. Controlling Foodborne Infections in Lettuce: Testing and Cleaning Methods for Curbing the Spread of E.Coli O157:H7

2. Spatial Dynamics of Myeloid-Tumor Cell Interactions during Early Non-Small Adenocarcinoma Development: 

3. A Cost-Effective Analysis of Treatment Strategies for the Control of HSV-2 Infection in the US

4. Modeling an Anthrax Plume: Prioritizing the Delivery of Antibiotics After an Anthrax Bioterrorism Event: 

5. Modeling the Dynamics and Control of Lyme Disease in Tick-Mouse System Subject to Vaccination of Mice Populations

6. The Effect of Gonadotropin-Releasing Hormone (GnRH) on the Regulation of Hormones in the Menstrual Cycle

7. Comparison of screening for methicillin-resistant Staphylococcus aureus (MRSA) at hospital admission and discharge

8. Economics of Prison: Modeling the Dynamics of Recidivism: 


1.Cheating the Cheaters: Spatial Dynamics In the Evolutionarily Stability of Antibiotic Resistance: 

2. A Household Model of Blatella Germanica Infestation and their Effects on Atopic Asthma Symptom

3. A Stage Structured Model of the Impact of Buffelgrass on Saguaro Cacti and their Nurse Trees

4. Transportation Networks Optimized for Various Income Groups and their Impact on the Spread of Airborne Disease.

5. The Dynamics of Math Anxiety as it is Transferred through Peer and Teacher Interactions

6. A Mathematical Study to Gout Symptoms

7. Evaluating Cost Effective Control Strategies for Dealing with Beaver Infestation in Tierra del Fuego


  1. The Impact of Preferred Mixing on the Sexual Transmission of ZIKV at the 2016 Summer Olympics.: 

  2. The Effects of Culling and Quarantine on Reducing Antibiotic Resistance in a Cohort of Beef Cattle.: 

  3. A Mathematical Model of Coral Reef Response to Destructive Fishing Practices with Predator-Prey Interactions.: 

  4. Assessing the Impact of Treatment Delays on the Prevalence of HIV Drug Resistant Cases: Modeling Case Study in Ecuador.: 

  5. The Spatial-Temporal Dynamics of Chikungunya in Most Affected Ecuadorian Provinces.: 

  6. Modeling Voting Dynamics in a Two-Party System: Person-To-Person Interactions and Media Effect.: 

  7. Dynamics of Cutaneous Leishmaniasis Infection in the Presence of Bird Reservoirs as a Tool for Vector Surveillance in Ecuador.: 

  8. Mathematically Modeling the Role of Triglyceride Production on Leptin Resistance.:

  9. Modeling Neuroinflammation in Individuals with Parkinson's Disease.: 

  10. The effect of rain seasonality and migration on the emergence of Dengue in the Northwestern Argentina.: 

  11. A Continuous-risk Model with Heterogeneous Mixing for Understanding Impact of Condom Use on Spread of Sexually Transmitted Infections Among Adolescents.: 


  1. A Mathematical Model to Study the Joint Effects of Genetics and Diet on Obesity

  2. Minimizing recidivism by optimizing profit: a theoretical case study of incentivized reform in a Louisiana prison

  3. Modeling the Interaction Dynamics between Honeybees and Food Availability

  4. Female Centered Mate Selections as an Explanatory Mechanism for Dimorphic Solutions in a Rock-Paper-Scissors Game

  5. Mathematical Model for Time to Neuronal Apoptosis Due to Accrual of DNA DSBs

  6. Global Analysis of a Multi-scale HIV/AIDS Model with Different Treatment Strategies

  7. The impact of multiple transmission pathways and movement of vector reservoirs on the dynamics of Dengue



  1. The Effects of Rural/Urban Movement on Dengue Transmission Dynamics

  2. The Impact of the Effectiveness of Needle Exchange Programs on Addiction-Treatment Dynamics

  3. The Effects of Regional Vaccination Heterogeneity on Measles Outbreaks with France as a Case Study

  4. A Model for Stripe Rust Growth with Two Fungicidal Effects

  5. Dynamics of Glial Cell Defense Mechanisms in Response to Ischemic Hypoxia in the Brain

  6. Political Recruitment via Television Ads in a Two-Party System

  7. Population Dynamics of Wolves and Coyotes at Yellowstone National Park

  8. Dynamical Modeling of Toxic and Non-toxic Phytoplankton Competition


  1. Asymmetric Intraguild Predation Between Protoperidinium and Heterocapsa in the Presence of a Mutual Predator

  2. Substance Abuse via Legally Prescribed Drugs: The Case of Vicodin in the United States

  3. Dynamics and Control of an Invasive Species: The Case of the Rasberry Crazy Ant Colonies

  4. The Dynamics of Offensive Messages in the World of Social Media: the Control of Cyberbullying on Twitter

  5. Ticks, Deer, Mice, and a Touch of Sensitivity: A Recipe for Controlling Lyme Disease

  6. A Model of Plant-Herbivore Interaction with Size Structure in Plants Using Toxin-Determined Functional Response

  7. A bifurcation study on epidemic models with density-dependent treatments

  8. A Study of Gravity-Linked Metapopulation Models for the Spatial Spread of Dengue Fever


  1. Competition Model between the Invasive Sahara Mustard and Native Plants in the Sonoran Desert

  2. Mitochondrial Iron: A Mathematical Model for Iron Regulatory Disease

  3. Dynamics of Triatomine Infestation in a Population of Houses

  4. Secondary Aneurysm Formation due to the Effect of a Primary Aneurysm

  5. Evolution of Within-Host Antibiotic Resistance in Gonorrhea

  6. Prison Reform Programs, and their Impact on Recidivism

  7. The Effects of Epidemic Dynamics on MHC Diversity

  8. Eternal Sunshine of the Solar Panel

  9. Modeling Tuberculosis Contact Tracing and the Role of Social Cluster

  10. Interior Point Methods for a Two-Group Discrete Time Influenza Model

  11. Effects of Natural Acquired Immunity in an Age-Structured Malaria Model


  1. Short and Long Range Population Dynamics of the Monarch Butterfly (Danaus plexippus)

  2. Determination of Tucson, Arizona as an Ecological Trap for Cooper's Hawks (Accipiter cooperii)

  3. Analysis and Optimal Control of an HIV Model with Immune Response

  4. My βIG Fat Math Model: β-Cell Compensation and Type 2 Diabetes

  5. Assessing the levels of unreporting in the 2009 A-H1N1 influenza epidemic in Lima, Peru

  6.  A Symmetric Intraguild Predation Model for the Invasive Lionfish and Native Grouper

  7. A Mathematical Model of the Emission and Optimal Control of Photochemical Smog

  8. Social Dynamics of Gang Involvement: A Mathematical Approach


  1. Extensions of the Cable Equation Incorporating Spatial Dependent Variations in Nerve Cell Diameter

  2. A New Perspective on Modeling Forest Fires

  3. The Effect of Localized Oil Spills on the Atlantic Loggerhead Turtle Population Dynamics

  4. Optimal Treatment Strategies for Tuberculosis with Exogenous Reinfection

  5. Effects of Temperature on Membrane Electrodiffusion

  6. Immigration Laws and Immigrant Health: Modeling the Spread of Tuberculosis in Arizona

  7. A Note on the Use of Optimal Control on a Discrete Time Model of Influenza Dynamics

  8. An Agent-Based Model with Drift and Cross-Immunity for Influenza

  9.  A Note on the Dynamics of an SAIQR Influenza Model

  10. Modeling the Impact of Batrachochytrium Dendrobatidis in the Life History Dynamics of Eleutherodactylus Coqui Under Seasonality


  1. Vaccination Strategy and Optimal Control for Seasonal and H1N1 Influenza Outbreak

  2. Static Behavioral Effects On Gonorrhea Transmission Dynamics

  3. Time-since-infection Immunological Model for Hepatitis C and Observed Treatment Profiles

  4. The Dynamics of a Spatial Cyclic Competition System

  5. A Minimal Biophysical Model of Phase Precession

  6. Comparing Treatment and Social Distancing Strategies in two Connected Cities, the case of 2009 Flu Pandemic in Mexico

  7. Two strain competition: Trypanosoma cruzi


  1. A Mechanism For Stabilization of Dynamics in Nonlinear Systems with Different Time Scales

  2. The Effects of Clustered Unvaccinated Individuals on Epidemic Outbreak

  3. The Effects of Maternal Age on the Prevalence of Autism

  4. Evaluating Treatment of Hepatitis C Infection with Respect to Resulting Hemolytic Anemia

  5. A Tale of Two Regions: A Mathematical Model for Chagas' Disease

  6. The Effects of Estrogen and Chemotherapy on the Dynamics of Invasive Carcinoma of Breast Cancer Patients

  7. A Cyclic Compartmental Model Approach to the Nemesis of Consciousness: Alzheimer's


  1. Dynamics of Targeted Treatment

  2. The Effects of Cycling on Drug Resistance HIV

  3. A Cost Analysis of Human Papillomavirus: Individual Education vs. Mass-Media Campaign

  4. Modeling Transmission Dynamics for the Fall Wave of the 1918-1919 Influenza Pandemic in Montreal and Winnipeg

  5. A Mathematical Model of Nosocomial Infection and Antibiotic Resistance: Evaluating the Efficacy of Antimicrobial Cycling Programs and Patient Isolation on Dual Resistance

  6. A mathematical model of HIV and Malaria Co-Infection in Sub-Saharan Africa

  7. A Dynamical Interpretation of the Three-Strikes Law

  8. The Cursed Duet: Dynamics of HIV-TB Co-infection in South Africa

  9. Modeling B Cell Dysfunction in HIV Infection

  10. A Model of the Drosphila Heart

  11. Cats Protecting Birds Revisited with a Spatial Approach

  12. The New American University: Mentorship in the Mathematical Sciences


  1. The Effects of Myeloid Cells on Tumor-Immune System Interaction in Different Time Scales

  2. An Epidemiological Approach to the Dynamics of Chytidiomycosis on a Harlequin Fog Population

  3. Estimation of Within-Host Reproductive Number Distributions from HIV-1 Viral Load Data

  4. The Impacts of the Sleeper Effect and Relapse on the Dynamics of Cigarette Smoking Among Adolescents

  5. A Theoretical Framework for a Three-state Spatial Population model with applications

  6. Mathematical Modeling of the Sex Worker Industry as a Supply and Demand System

  7. OCD Therapeutic Dynamics: Markovian Based Simulations


  1. Disease Spread as a Function of Socioeconomic Status in Manhattan

  2. An Epidemiological Approach to the Spread of Political Third Parties

  3. Epidemiology as Related to the Phylogenetic Analysis of the Evolution of the Influenza Virus

  4. An Epidemic Model of HSV-1 with Vaccination

  5. The Effects of Migration and Connectivity upon Initial Behavior of Multi-City Endemic Models

  6. Effects of Lifestyle Choices on Atherosclerosis: A Mathematical Approach

  7. Understanding Immigration and Policy Change from a Mathematical Perspective

  8. The Dynamics of Poverty and Crime

  9. Ring Vaccination as a Control Strategy for Foot-and-Mouth Disease

  10. Two Mathematical Models for the Tympanic Membrane

  11. The Effect of Immune Response and Combination Drug Treatment on the Progression of Multi-Strain HIV

  12. Differential Behavior of Vectors Infected with Chagas' disease

  13. The Role of Transactional Sex in the Spread of HIV/AIDS: A Modeling Perspective

  14. An Interspecies Competition Model with Multiscale Interpretations


  1. Cellular Noise and the Aging Process

  2. Agent based modeling of Eciton burchelli swarm patterns

  3. USA the Fast Food Nation: Obesity as an Epidemic

  4. Does gravitational gossip weigh heavy on your local area network (LAN)?

  5. The Role of Vaccination in the Control of SARS

  6. Modeling of Tumor Growth and its Control via Paclitaxel Using a Delay Differential Equation

  7. HIV and Its Impact on the Infant Immune System

  8. The Impact of Mosquito-Bird Interaction on the Spread of West Nile Virus to Human Populations


  1. Change in Host Behavior and its Impact on the Co-evolution of Dengue

  2. A Mathematical Model for Photoreceptor Interaction

  3. Modeling a Novel Method to Control Human Malaria: Insecticide Treated Cattle

  4. A Deterministic Approach to the Spread of Rumors

  5. The Role of Network Topology on the Initial Growth Rate of Influenza Epidemic

  6. Scaling Laws and Dynamics of Sexual Activity with Interracial and Multi-Ethnic Mixing

  7. The Effects of Student-Teacher Ratio and Interactions on Student/Teacher Performance in High School Scenarios


  1. The Effect of the HIV/AIDS Epidemic on the Population of Truck Drivers in South Africa and its Economic Impact

  2. Models of Negatively Damped Harmonic Oscillators: the Case of Bipolar Disorder

  3. A Stochastic Approach for Modeling Treatment and Diagnosis of Attention Deficit Disorder

  4. Intraspecific Competition in the Population of Danaus plexippus (L.)

  5. A Mathematical Model of Depression in Young Women as a Function of the Pressure to be "Beautiful"

  6. Chronic Wasting Disease: The Effects of Environmental Prion Density and Interactions between Populations on Disease Dynamics

  7. The Effects of Mass Transportation during a Deliberate Release of Smallpox

  8. The Demographic Effects of Increasing Anthropogenic Noise on Mysticeti Whales

  9. A Critical Response Stochastic Model for Foot-and-Mouth Disease Epidemics

  10. A Two-Gender Human Papillomavirus Model with an Investigation of the Effects of Male Screening

  11. The Effects of Environmental Pressure and Genetic Predisposition to Temperamental Behavior

  12. Preventing Crack Babies: Different Approaches of Prevention


  1. The Role of Time Delay in the Fitzhugh-Nagumo Equations: The Impact of Alcohol on Neuron Firing

  2. Am I Too Fat?: Bulimia as an Epidemic

  3. A Model of β-cell Mass, Insulin, Glucose, and Receptor Dynamics with Applications to Diabetes

  4. Different Strokes for Different Folks: The Evolution of the Distribution of Traits within Heterogeneous Populations

  5. Raves, Clubs, and Ecstasy: The Impact of Peer Pressure

  6. To Bt or Not to Bt? Balancing Spatial Genetic Heterogeneity to Control the Evolution of Ostrinia nubilalis

  7. Compressive Failure of Single Fiber Composites

  8. Metapopulation Models with Age Structure

  9. Mouse in the House: Looking at the Spread of Hantavirus in Houses Through the Deer Mouse Population

  10. Who Says We R0 Ready for Change?

  11. Effects of Education, Vaccination and Treatment on HIV Transmission in Homosexuals with Genetic Heterogeneity

  12. Disease Dynamics on Small-World and Other Networks

  13. Social Mobility and the Evolution of Tuberculosis


  1. A Mathematical Model for Lung Cancer: The Effects of Second-Hand Smoke and Education

  2. A Socially Transmitted Disease: Teacher Qualifications and High School Drop-Out Rates

  3. Do we really have to take all our medicine? Predicting the Consequences of Large-Scale Antibiotic Misuse

  4. Evolution of Fluconazole Resistance in Candida albicans

  5. The Effects of a Potential National Campaign and a VEI Type Vaccine on an HIV-1 Infected Homosexually Active Population

  6. Dynamics of Two-Strain Influenza with Isolation and Cross-Immunity

  7. Dispersal between Two Patches in a Discrete Time SEIS Model

  8. Deterministic and Stochastic Reaction-Diffusion Models in a Ring

  9. Discrete-Time S-E-I-S Models with Exogerous Re-infection and Dispersal between Two Patches


  1. Competitive Exclusion in a Discrete-Time Epidemic Model with Two Competing Strains

  2. Scramble Versus Contest Competition in a Two Patch System

  3. Numerical Solution of a Model of Influenza with Two Strains

  4. Dynamics of the Spruce Budworm Population under the Action of Predation and Insecticides

  5. Dynamics of a Two-Dimensional Discrete-Time SIS Model

  6. The Ebola Virus: Factors Affecting the Dynamics of the Disease

  7. Interactions between Dispersal and Dynamics: Coupled Ricker's Equations

  8. Urn, Baby, Urn: A Simpler Approach to Studying Epidemic Models and the Efficacy of Disease-Prevention Policies

  9. Differential Equation Models of Neoadjuvant Chemotherapeutic Treatment Strategies for Stage III Breast Cancer

  10. Probability of False Prostate Cancer Diagnosis Using a Logistic Function Given Age and f/t PSA Ratio

  11. An S-I-S Model of Streptococcal Disease with a Class of Beta-Hemolytic Carriers


  1. A Mathematical Model for Assessing Genetic Damage on HIV Populations after Anti-Retroviral Therapy

  2. The Effects of Condom Distribution with Education on Chlamydia Rates in High Schools

  3. A Stochastic Study of Incarceration Times for Narcotic Distributors in a City under "The Three Strikes Law"

  4. Discussion of Difference Equation Model of Ventricular Parasystole as an Interaction between Cardiac Pacemakers Based on the Phase Response Curve

  5. Dynamical Results of Discrete Pioneer and Climax Species Models

  6. The Effect of Purse Seine Vessel Harvesting in the Eastern Tropical Pacific Yellowfin Tuna Stock

  7. Estimation of the Population Vaccination Effectiveness Using Urn Models

  8. The Recovery and Ecological Succession of the Tropical Montserrat Flora from Periodic Volcanic Eruptions


  1. A Competition Model for Advertised Companies

  2. Mean Time to Extinction of Source-Sink Metapopulation for Different Spatial Considerations

  3. Can We Get a Head Start on Head Lice?

  4. Dynamics of Rubella Virus in Populations with Different Vaccination Policies

  5. Tumor Growth Dynamics: A Deterministic and Stochastic Analysis of the Interaction Between Normal and Abnormal Cells

  6. Models for the Transmission Dynamics of Gonorrhea in a Homosexually-Active Population

  7. Dynamics of HIV/AIDS in Core Groups in the Presence of a Transient Population

  8. Three Models for Measles Control

  9. Macrophage-Activating and Tissue-Damaging Imune Responses to M.tuberculosis

  10. Analysis of an Age-structured Epidemic Model with a Chronic State

  11. Delinquency Dynamics

  12. Mathematical Models for the Dynamics of Tobacco Use, Recovery, and Relapse


  1. A Model Describing the Response of the Immune System to Mycobacterum Tuberculosis

  2. Mathematical Models to Study the Outbreaks of Ebola

  3. Stochastic Simulations of a Saptial SIR Model

  4. HIV-1 Replication Rate

  5. The Effects of Vaccination in a Core Group

  6. A Mathematical Model of the Dynamics of Rickettsia rickettsii in Tick-Host Interactions