Project Description

The goal of this project is to apply everything learned this semester in MA 331: Differential Equations for the Life Sciences towards a real-world application of your interest. Depending on the specific biological phenomenon that you choose to model, you will use one or more of the following techniques: finding the solution, vector fields, phase planes, determining equilibria and their stabilities, and parameter estimation.

For the full project description and grading rubric, please download the pdf

Project Topics/Datasets

Here are some examples of project ideas that you can use for your final project. If you are interested in a different project topic, please make sure to see me by November 16, so we can discuss finding/acquiring data for you to use. I highly encourage you to pursue an alternate project if there is some system you are very interested in.

Project 1: Predator-Prey
The Canadian lynx preys almost exclusively on the snowshoe hare. In the 19th century, Hudson’s Bay Company began tracking the populations of pelts obtained by trappers for both the lynx and the hare. The dataset, from 1845-1903 can be found here.

Project 2: Epidemiology
In 2014 an ebola outbreak occurred in West Africa. Ebola virus disease (EVD) is high-mortality illness that is transmitted from human-to-human contact. On average, fatalities occur in approximately 50% (range 25% to 90%) of human cases. The World Health Organization compiled a list of total cases and total deaths from EVD in Guinea, Liberia, and Sierra Leone from March 1, 2014 to February 17, 2016 [1]. Here are the datasets for Guinea, Liberia, and Sierra Leone.

Project 3: Ecology
Daphnia magna is a species of water flea used in toxicity testing because they are sensitive to environmental change. The data included here investigate the effect of food restriction on daphnid growth (as measured by the major axis length of the animal) [2]. The experiment is performed over 14 days and measurements occurred daily. The mean over approximately 30 individual daphnids are reported. Here are the datasets for control, medium, and low food levels.

Project 4: Cancer Growth and Treatment
According to the American Cancer Society, in 2017, approximately 22,440 women will be diagnosed with ovarian cancer and about 14,080 women will die from ovarian cancer [3]. The data provided come from an experiment where tumor cells were injected into mice [4] and tumor volumes were measured throughout time. When tumors start growing large, they produce angiogenic factors which induce vascularization, providing more nutrients to the tumor. Data were also collected for mice who underwent anti-angiogenic treatment (blocking the vascularization from forming). Here are the datasets for control and treatment.

 

References:

  1. ``Ebola (Ebola Virus Disease)." Centers for Disease Control and Prevention, Centers for Disease Control and Prevention, 17 Feb. 2016, www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/cumulative-cases-graphs.html.
  2. Rutter, Erica M., et al. ``Continuous Structured Population Models for Daphnia Magna." Bulletin of Mathematical Biology, 2017, doi:10.1007/s11538-017-0344-8.
  3. ``What Are the Key Statistics About Ovarian Cancer?" American Cancer Society, The American Cancer Society, www.cancer.org/cancer/ovarian-cancer/about/key-statistics.html.
  4. Mesiano, Sam, Napoleone Ferrara, and Robert B. Jaffe. ``Role of vascular endothelial growth factor in ovarian cancer: inhibition of ascites formation by immunoneutralization." The American Journal of Pathology 153.4 (1998): 1249-1256.