1. Let’s Get Graphical: Understanding Differential Equations with Random Initial Values 

Charles Brookshire and Thomas Benton

Abstract 

This mathematical analysis examines how the solutions of differential equations will change with randomly changing initial values. Graphs are constructed as a solutions of system of coupled differential equations modeling the spring mass systems. The system of differential equations will be solved using the Runge- Kutta Method and animated in MATLAB to show how the solutions change.

2. Its Presence Poisons our Bodies: A Mathematical Study of Lead in Living Tissues

Marlys Bridgham and Matthew Schmidt

Abstract

This mathematical study investigates the chronic biological problems that have evolved due to high levels of lead in living tissues. Bone, blood, and soft tissue are three types of tissues that will be identified in this mathematical model. This model uses the basic idea that the rate of change of lead in a tissue is equal to the difference between the rate of lead entering and leaving the body. We will explore the solution using a system of three differential equations. It is essential to understand the nature of the elements that enter and exit our bodies, so why not use mathematics to explore this biological study?

3. Measles Epidemic, the Next Big Thing?

Robert DeTorres and Vignesh Krishnaraja

Abstract

This study utilizes mathematical models in order to path and predict measles epidemics in the future. Records from New York measles epidemic, along with the factors of susceptibility and infectiousness, with respect to time, are used in this model. These factors are in the form of three primary differential equations. All this information will be used to predict the future viability of another measles epidemic by using numerical techniques.

4. A Mathematical Model to Quit Smoking:The Decline of Cigarette Smoking

Alexis Wingfield and Alison Gaines

Abstract

Mathematical models are often used to track the spread of diseases. Smoking can be tracked using a similar model. Numerical results will be presented here according to the Non-standard finite difference method (NSFD). These results will be compared with the ones obtained using the Runge-Kutta methods of order 2 and 4. We will use MATLAB built-in functions ode23 and ode45.

5. Zombie Mathpocolypse

Claire Shannon and James Gallagher

Abstract:

Do you watch zombie movies? Have you ever wondered what will be the climax? Now you can use mathematics to figure out who will win. In this work we consider a mathematical model for zombie infection from the literature. The model consists of three ordinary differential equations for three classes Susceptible, Zombie and Removed. We will solve the model using numerical techniques such as the Euler's method and the Runge-Kutta methods.

6.  Numerical Techniques to Study Transmission Dynamics of Zika Virus

Benjamin Hansen and Chris O’Brien

Abstract

Mathematics can be used for infectious diseases modeling. Mathematical modeling helps us to understand the spread of a disease as well as its control. In this work we consider a system of coupled differential equations that model the Zika virus dynamics. We will use numerical techniques to model a simulation in order to better understand the Zika virus transmission.

7. Nonlinear Duffing Systems may be Chaotic, but Math Definitely isn’t

Sam Jacobi and Michael Molchan

Abstract 

There are many chaotic physical things that occur in our world. The differential equations in this model are used to simulate things that are hard to determine through normal mathematical techniques. These chaotic phenomenon are things such as navigation in the ocean, the movement of rockets or other planets, and the flection of dynamic machines. This model will be solved using different numerical solving methods such as Euler's Method and the Runge-Kutta Methods.

8. Mathematical Models of Dumping Atomic Waste Drums

David Kreinar and Belal Yoldash

Abstract

We can use mathematical models to determine the velocity of objects falling through a liquid. This model, described by differential equations, is a convenient way to understand the danger of disposing atomic waste into the ocean. Our team is analyzing these differential equations with a numerical method in order to determine the velocity of the drums as a function of distance.

9. Meteors get Meatier with Mathematics!

Andrew Albers and James Lenard

Abstract

With the help of mathematics, one is able to compute and model the behaviors of meteors as they penetrate the earth’s atmosphere. Given the numerical values of mass, drag, atmospheric density and velocity, we will be able to model the trajectory of a meteor throughout its path towards earth. With these values in differential equations, we will be able to determine the mass required for the meteor to penetrate the atmosphere and impact the earth’s surface. 

10. Is Your Computer Sick? It Might Have a Virus? See Dr. Math

Owen Miller and Dylan Niese

Abstract

Computers, just like humans are susceptible to illness and spreadable viruses. Since computer viruses act in the same manner as human viruses, researchers developed models to study the propagation of worms/viruses. In this work, we consider a model for such a computer worm consisting of differential equations. We will use the numerical methods learned in the differential equation class to solve this model numerically to understand the phenomena.

11. A Numerical Solution of a Model of Diabetes

Malle Schilling and Nathan Volk

Abstract

Many researchers use mathematical models to understand and predict the behavior of biological systems. In this work we consider a mathematical model for diabetes mellitus presented by Hussain and Zadeng to study a metabolic disease for the regulation of glucose in the body by pancreatic insulin. The mathematical models consists of two ordinary differential equations for glucose concentration and insulin concentration. In particular, this study attempts to numerically solve the model using the Runge-Kutta methods of order 2 and 4, and the Adams-Bashforth Method. A qualitative analysis of the system was also performed. Through the numerical simulations, it was shown that the Runge-Kutta methods and Adams-Bashforth method correctly simulate the model by Hussain and Zadeng. A nullcline of the model was also created which demonstrated the asymptotic stability of the system.

12. Type 1 + Type 1 = Type 2 (not in terms of Diabetes, just mathematical funny!)

Tom Krokey and Stephanie Townsend

Abstract 

Diabetes is a common disease that can be difficult to diagnose simply by human observation alone. We will consider a mathematical model developed for the blood glucose regulatory system that focuses on one or two criteria of a common glucose tolerance test (GTT) in order to distinguish and detect the severity of diabetes in patients. Several differential equation techniques and methods such as Euler’s and Runge-Kutta of order two and four will be used to solve this model.

13. Global Worming: A mathematical model of the spread of computer worm attacks 

Dan Lenz and  Dakota Waller

Abstract 

This mathematical model provides a series of equations by considering the rate of reproduction (R0), as to whether or not the virus will remain asymptotically above or below a global epidemic state. The group will analyze the model presented by using the Runge-Kutta methods of orders two and four in order to find the numerical solution of the initial equations.

14. The Models of how Persistent Viruses Resist Immune Responses

Yuhang Lin and Xinkai Ma

Abstract:

The goal of this study was to use population models to study the interactions between virus and immune cells. This offers a way to understand the dynamics of immune responses and to test various hypotheses uses, comparing infected cells and uninfected cells, and how the immune system responses to persistent viruses.

15. Mathematical Telescope for Star Formation in the Galaxy 

Taylor Curtis and Conor Pausche

Abstract

One can use mathematics to locate where star formation takes place, using the location of luminous blue stars. The three components used in this model are the total mass of active stars, total mass of molecular clouds, and total mass of atomic clouds. The two differential equations used explain that the rate of changes of two of the masses will lead you to find the mass of all three components, which indicates whether or not star formation will occur.

16. The Walking Dead: Don’t Run, Use Math!

David Fink and Theodore Stitzel

Abstract

To study the effect of a zombie outbreak, our team used several differential equations and techniques learned in class to predict the population of humans and zombies during a zombie outbreak. It is important to be able to study the population of both humans and zombie to understand the odds of getting infected and to predict how long the outbreak will last for. This information could then be given to the Center of Disease Control for proper defensive measures to ensure the survival of humans. If there is an outbreak, it is best to be prepared. 

17. Mathematical Study of Ebola Outbreak  in West Africa

Derek McGrew and Keegan McCafferty

Abstract 

 The purpose of using mathematical models is to determine the rate at which the Ebola virus is spread. The infection rate and total infected will be measured with the numerical solutions. The model will be based on how people are infected and how the virus is spread. We will come up with numerical solutions for system of ODEs in order to determine how the virus will spread in the population for West Africa. The numerical solutions will come from using data that exist and using Euler's Method and Runge -Kutta methods (RK2 and RK4) to determine the numerical solutions of the model.