Master of Science
Chris Tweddle, Ph.D.
Andrius Tamulis, Ph.D.
Dianna Galante, Ph.D.
Compartmental modeling has been used to model infectious diseases for roughly 100 years. Since 2009, several papers have modeled zombie outbreak using this method with various results. This paper will develop a unique model for the spread of the The Walking Dead zombie virus throughout the contiguous United States. Frequency dependent and density dependent transmission will be discussed, and density dependent transmission will be shown to be the appropriate choice for this model. Constant parameters, such as birth rate, bite rate, death rate, and turning rate will be determined using real-world and fictional data. After developing a basic model, modifications will be made to include the airborne pathogen and latency. A system of autonomous differential equations can then be derived, followed by a dynamical system of difference equations. The system of differential equations will be used to determine equilibria, if any exist, stability will be investigated, and numerical solutions will be calculated. Pithing, a practice usually reserved for slaughtering livestock, will be considered for human use and shown to help control the zombie population. Numerical solutions will show that pithing alone will not save the human race, but used in conjunction with zombie removal by a well-organized force, a successful zombie removal rate can be established. Finally, the model will then be modified to include zombie removal calculations and vaccination. The goal of this paper is to develop a zombie model that represents AMC's The Walking Dead outbreak and develop numerical methods by which mankind can calculate appropriate actions.
Morgan, James, "A Discrete Density-Dependent Model of the Solanum Virus" (2014). All Student Theses. 45.