From MathBio

Welcome to the Mathematical Biology Wiki hosted by the Applied Mathematics Department at the University of Colorado. Below are general topics in mathematical biology.

For any significant errors in these pages, please contact David Bortz.

Contents 1 Cancer 2 Ecology 3 Evolution 4 Immunology 5 Metabolism 6 Microbiology 7 Neuroscience 8 Physiology 9 Population Dynamics 10 Reaction/Diffusion 11 Chaotic Dynamics 12 Templates 13 Acknowledgments

Cancer

• Tumor Modeling Jason Hammond, Sekson Sirisubtawee, and Michael Kochen
• Optimal Chemotherapy Strategies Sigmund Stoerset
• A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth Steven Van Buskirk
• Inducing Catastrophe in Malignant Growth Emily Schuck
• A Reaction-Diffusion Model of Cancer Invasion Nicole Look
• Modeling of Oxygen Transport Across Tumor Multicellular Layers Kumar Thurimella and Nik Kauffman
• MBW:Modeling Stem/ Progenitor Cell-induced Neovascularization and Oxygenation Around Solid Implants Matthew Cullen, Caitlin Lowe,and Sam Verplanck

Ecology

• Effect of Seasonal Growth On Delayed Prey-Predator Model Asghar Ali and Rashida Hussain
• Gypsy moth population dynamics Stephan Kupsa
• Host-Parasitoid Models Geoffrey Peterson
• Modelling the dynamics of a complex life-cycle parasite Sara Hellmuth and Sarah Orlofske
• Robustness Analysis of an Observer-Based Controller in a Food Web Jay Brasch and Kirk Nichols
• Three Species Food Chain Modeling William Dowling, Toni Klopfenstein, and Lucas Koepke
• Computer Modeling of the Biotic Cycle Formation in a Closed Ecological System Matt Reisman, Brayden Hass and Kumar Thurimella
• Epizootics of the Plague in Prairie Dog Populations Ashley Patchen and Phillip Lenzini
• Prairie Dog Plague Transmission (Project 3) Ashley Patchen and Phillip Lenzini
• Observability of Trophic Food Chains Josh Kelly
• Agent Based Model of Fish Populations Steele Jones and Josh Kelly
• Island Biogeographic Model for Designing Nature Reserves Lee Stanish
• Habitat heterogentiy-area tradeoffs and species diversity Maxwell Joseph

Evolution

• Evolution and Distribution of Species Body Size Dan Larremore

Immunology

• Complement Modeling Colin Peterson, Matanya Horowitz
• Immune Complement Matanya Horowitz
• Mathematical Immunology Michael Kochen
• When to Initiate HIV Therapy Lucas Koepke
• HIV Dynamics Meg Noble, Tiana Stastny
• Dynamics of Drug-Resistant HIV Mutants Jessica Moton
• Two-Phase Approximate Solution to an Acute Viral Infection Model Zach Vaughan and JaeAnn Dwulet
• Estimation of HIV/AIDS Parameters Alexandra Zelinskaya
• Modelling Viral Dynamics and Immune System Dynamics Steel Jones
• Delayed Production and Viral Dynamics of the HIV-1 Virus Sai'd Azzam and John Nelson Kane
• A Two-Strain Tuberculosis Model with Age of Infection Shivani Ehrenfeucht
• Immunological Memory Ash Same
• The Impact of information transmission on epidemic outbreaks Inom Mirzaev and Ash Same
• Fundamental Mathematics of the Delay Differential Equation in the HIV-1 Virus Model Sai'd Azzam and John Nelson Kane
• Comparison of Deterministic and Stochastic SIS and SIR Models in Discrete Time Shivani Ehrenfeucht

Metabolism

• A mathematical model comparing solute kinetics in low- and high-BMI hemodialysis patients Mohammad Munir
• Biological Clocks and Switches William Dowling and Toni Klopfenstein
• Kinetic investigations of methane co-fermentation Natalia Taupe
• Modelling Components of a Lunar Life Support System Alex Fletcher
• Modelling the Tryptophan Operon Eric Greenwald and Scott Tatum
• Timescales in Metabolic Pathways Henry Romero
• MBW:Nonlinear Control for Algae Growth Models Christine Fanchiang
• Nonlinear Control For Algae Growth Models Part II Christine Fanchiang
• Singular value decomposition of stoichiometric matrices Steven VanBuskirk, Andrew Erickson and Brian Strathman
• The (Right) Null Space of the Stoichiometric Matrix Keesha Erickson
• Oscillatory behavior in enzymatic control processes Scott Hoch
• Oscillatory behavior in enzymatic control processes, rights and wrongs Scott Hoch and Sigmund Stoerset
• Dissipative Structures for an Allosteric Model JaeAnn Dwulet and Zach Vaughan
• MBW: Determining Metabolic Constants from Gas Uptake Data Tyler Janes
• MBW: PBPK Modeling of Metabolic Pathways of Bromochloromethane in Rats Tyler Janes

Microbiology

• Big Bacteria Brayden Hass and Matt Reisman
• Bacterial Aggregates in the Bloodstream Erin Byrne
• Bacterial Community Aggregation Erin Byrne
• Dynamical System Analysis Of Staphylococcus Epidermidis Bloodstream Infection Gerald Feichtinger
• Senescence Can Explain Microbial Persistence Ryan Brown
• Role of Biofilm Matrix in Structural Development Alexandra Zelinskaya
• A Dynamic Global Model for Planktonic Foraminifera Mariah Walton and Nick Levine
• Effects of Persister Formation on Bacterial Response to Dosing Jessica Moton
• Approximating free energy profiles from single-molecule measurements George Emanuel
• Coagulation-Fragmentation Models Dustin Keck
• Flocculation Dynamics - a PDE Model Dustin Keck

Neuroscience

• Hodgkin-Huxley Jay Brasch and Kirk Nichols
• Modelling Sleep Regulation Sara Bessman, Ben Brown
• Noise in the Nervous System Alex Fletcher
• Mathematical neuroscience: from neurons to circuits to systems Nick Levine
• MBW:The Morris-Lecar Model for Excitable Systems Ian Mathieson
• Period Doubling and other Phenomena in the Hodgkin-Huxley equations Ian Mathieson
• Network Models: Firing Rate, Feedforward, Recurrent and Stochastic Models Graham Annetty
• Mathematical Modeling of Alzheimer's Disease Joseph Parks
• Extension to Mathematical Modeling of Alzheimer's Disease Victoria Gershuny and Joseph Parks
• MBW: Analysis and Application of Early Concussion Research in American Football Zachary Sajevic

Physiology

• Describing the Pumping Heart as a Pressure Source Mustafa Habib and Mark Sommer
• Glucose-Insulin Regulatory System Cody Cichowitz and Stephen Kissler
• Extensions to a 2-Delay Glucose-Insulin Regulatory Model Cody Cichowitz and Stephen Kissler
• Interaction Between the Thyroid and Pituitary Glands Paul VaughanMiller
• Correcting the analysis for Interaction Between the Thyroid and Pituitary Glands Paul VaughanMiller
• Optimum Design of Blood Vessels Kristina Callaghan
• Womersley Arterial Flow Tracey Morland
• Gravitational Effects on Blood Flow Tracey Morland

Population Dynamics

• A Crocodilian Population Model using Delay Differential Equations Andreas Schober and Christof Zwanziger
• A New Model for Age-Size Structure of a Population James W. Sinko and William Streifer
• Age Structured Populations in Seasonal Environments Andrew Erickson and Brian Strathman
• Density Dependence in Single-Species Populations Eric Greenwald and Scott Tatum
• Pod-Specific Demography of Killer Whales Meg Noble, Emily Schuck, and Tiana Stastny
• Population Biology of Infectious Diseases Sara Hellmuth and Sarah Orlofske
• Population Dynamics of Pathogens with Multiple Host Species Maxwell Joseph and James Balasalle
• Predator-prey models with delay and prey harvesting Aurelio de los Reyes
• Spatial Genetics Jason Hammond and Sekson Sirisubtawee
• Stage-Based Population Model Luke Pederson
• Stage-Based Population ModelAnalysis Luke Pederson
• Stochastic Epidemic Modeling Ted Galanthay and Steve Chestnut
• Modeling the coupling of ocean ecology and biogeochemistry Mariah Walton
• The dynamics of hierarchical age-structured populations J.M. Cushing
• The Dynamics of Arthropod Predator-Prey Systems Justin Baacke and Brit Schneiders
• Extensions to The Dynamics of Arthropod Predator-Prey Systems Justin Baacke, Nicole Look and Brit Schneiders
• Resource Competition Between Algae Lee Stanish
• Equations for the Age Structure of Growing Populations Victoria Gershuny
• Effects Of Human Decision On Infectious Diseases Colleen Courtney
• Stochastic Models for Bacterial Development of Multidrug Resistance Colleen Courtney and Keesha Erickson
• MBW: Stochastic modeling of Pseudomonos syringae growth Graham Annett

Reaction/Diffusion

• MBW:Gas Exchange in Animal Burrows Kenneth Pratt
• MBW: Particle Tracking Model for Simulation of Advection and Diffusion in Prairie Dog Burrows Kenneth Pratt
• Traveling Waves in Excitable Media Henry Romero
• Pre-Pattern Formation Mechanisms for Animal Coat Markings Jonathan Varkovitzky and Ryan Brown
• Cooperativity between Cell Contractility and Adhesion Louis Foucard
• Wolf Territoriality, Wolf-Deer Interaction and Survival Takako Hirokawa
• Stress Fibers Formation and sensitivity Louis Foucard
• Geometry of Multisite Phosphorylation George Emanuel
• Finger Formation in Biofilm Layers Kristina Callaghan
• Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion Inom Mirzaev

• Dynamic Biodegradation model with Flocculation Robert Hale and Theodore Eberts
• Locust Phase Change and Swarming Amy Le
• Two Models of Locust Phase Change Amy Le
• Models of Diffusion-Mediated Gas Exchange in Animal Burrows Matthew Cullen
• Governing Fluid Dynamics of Non-Motile Bacteria in Varying Gravitational Domains Robert Hale and Theodore Eberts

Chaotic Dynamics

• MBW:Chaotic Heart Rate James Balasalle

Templates

• Project 2
• Project 3

Acknowledgments

The majority of this wiki has been constructed over several years by students from the APPM 4390/5390 class. During the summer 2009, I also gave a summer school on mathematical biology at the University of Graz and those students have also contributed to this wiki. Without these contributions, this wiki would not have been possible. Thank you.