Survey of Mathematical Models of Sustainability and Population Growth

Abstract

In this paper, I present a mathematical model to analyse the Mayan civilisation's collapse by focusing on water as a critical resource. Using the mathematical model developed and used in the paper ‘Mathematical Model of Easter Island Society Collapse’ by Bologna and Flores (Bologna & Flores, 2010), I interpret the resource variable as water in my case with the Maya; it is important to state that this model is a theoretical construct and is not based on empirical knowledge. I model Mayan society and its environment as an isolated system, with both the population and water resources treated as dynamic variables. This approach highlights the intricate relationship between the Mayans and their dependence on water, indicating how fluctuations in this essential resource could lead to significant societal impacts. The analysis explores the interaction between the Mayan population and water availability by applying the selected mathematical equations to illustrate the dependency and predict the civilization's eventual collapse. This model offers insights into the specific case of the Maya and aligns with existing research on other extinct civilizations, providing a robust framework for understanding how human-environment interactions can drive societal collapse. To maintain focus and clarity, the model used concentrates on water as the central variable, while other factors that contributed to the Mayan collapse, such as social, political, and economic variables, are not included in this analysis. This simplification, while necessary for the scope of this research, suggests that further studies could build on this model by integrating additional variables to offer a more comprehensive understanding of the collapse dynamics