MATH495 - Special Topics in Mathematical Modeling
Presentation Abstracts
Presentation Title: Reservoir Models
Team Members: Jessica Jones, Joshua Rainville, Michael Souza
Abstract: In this project we create a continuous model to predict the volume of water in a reservoir over a period of time. This type of model is useful in various urban and agricultural situations. We use compartmental analysis and differential equations to model the flow of water into and out of the reservoir for scenarios including a drought and a storm. Our storm model has a constant outflow, and a time-dependent inflow. Our drought model has a constant inflow, and a time-dependent outflow.
Presentation Title: Modeling the Population of Barren Ground Caribou
Team Members: Jen Eckrote, Rebekah Puig, Zach Zigrang
Abstract: In our project we are asked to assume that we are part of a biological modeling team hired by the Canadian Wildlife Service to address the following questions. 1) What is expected from an unmanaged caribou population under normal circumstances? 2) What is the effect of harsh springs and winters? 3) What is the effect of the current hunting strategy under normal circumstances and with weather effects? 4) What is the effect of a revised hunting plan under both normal and extreme weather effects? We will explore these dynamics by creating a matrix model to express the stages and states of the Caribou in Excel to predict future populations. In our presentation, we will deliver our results and conclusions from the influence of weather severity and hunting on the caribou population.
Presentation Title: Black-Capped Chickadees
Team Members: Amanda Barnes, Tennant Brastow, Joseph Gordon, Adam Reeves
Abstract: We take up the problem of predicting the long term population of a Black-Capped Chickadee population. We initially model the population as being deterministic. We also create a population model with demographic stochasticity. Afterwards we fit regression curves to our population data to model the population survival and recruitment rates. We use these regression curves to refine our deterministic model. Later we add stochasticity to the trend curves of our refined model and examine whether this complication is justified.
Presentation Title: Stock Market Predictions Based on Historical Market Trends
Team Members: Kim Bowman, Samantha Soukup, Ashley Swandby
Abstract: Throughout recent history the stock market has reflected the health of the economy. By observing past trends in the stock market we attempt to predict the behavior of the future market. The stock market appears to follow an exponential trend in its values. In order to verify this we consider four major indices, individually, that indicate the behavior of major stocks. First we plot an exponential model to each index and determine how well this model predicts the values of the index. We then use this model to predict what the stock market values will be in thirty years and determine the value of a $1000 investment. We also create a new model where we include a stochastic rate of change of the stock market value. Again, we use this model to predict what an investment would be if originally investing $1,000 and compare the it to the non-stochastic model. Lastly, we investigate how increasing Consumer Price Index, the price of a sample of commodities in a given year, affects the stock market.