A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools. Students will learn to develop a differential equation model based on practical scenarios, analyze the model using mathematics as well as numerical simulation, and finally describe the results in words that are understandable by the people who are not specialists in this field. The goal of our differential equation model activity is to describe the cholera disease dynamics by a set of differential equations, find disease-free and endemic equilibrium points (if any exist), perform a stability analysis of the equilibrium points by using the Jacobian, and describe the disease dynamics by using numerical simulation. The effect of seasonality in pathogen transmission including an endemic disease as well as new outbreak cases can be added as an extension of this project for undergraduate research activities. This model is an extension of a general waterborne pathogen model.
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