Year: 2025
Type: book-chapter
Abstract: Population growth is a fundamental subject of study in both natural and social sciences due to its profound implications for resources, environment, and societal development. Mathematical modeling of population growth provides a quantitative framework for understanding the dynamics of population changes over time and offers predictive capabilities to support planning and policy-making. This chapter presents a comprehensive overview of the mathematical models used to analyze population growth, ranging from classical to more advanced formulations. The chapter begins by introducing the basic concepts of population modeling and the importance of mathematical representations in capturing the essential features of population dynamics. The exponential growth model, one of the earliest and simplest forms, is discussed in detail, highlighting its assumptions of unlimited resources and constant per capita growth rate. While this model serves as a foundational concept, it is often inadequate for real-world scenarios where environmental constraints play a significant role. To address these limitations, the logistic growth model is introduced, incorporating the concept of carrying capacity—the maximum population size that an environment can sustainably support. The logistic model accounts for the slowing growth rate as the population approaches the carrying capacity, thus providing a more realistic depiction of natural population trends. The analytical solutions and behavior of both models are examined, and their applicability to different biological and human populations is discussed. The chapter further explores extensions and variations of these models, such as time-dependent carrying capacities, age-structured models, and systems involving interacting populations (e.g., predator-prey dynamics or competition models). Emphasis is placed on the role of differential equations in modeling continuous population change, while discrete models are also briefly introduced for scenarios involving non-continuous reproduction cycles or data collected at fixed intervals. In addition to theoretical formulations, the chapter discusses methods for parameter estimation using empirical data, enabling the calibration of models to fit observed population trends. Case studies are presented to demonstrate the application of mathematical models to historical and contemporary population data, showing how these models can aid in predicting future trends and assessing the potential impact of policies such as birth control, immigration, and resource allocation. By the end of the chapter, readers will gain a solid understanding of the key mathematical models used to study population growth and their real-world significance. The discussion emphasizes not only the mathematical structure but also the biological and social interpretations of the models, making the content accessible to a multidisciplinary audience. Through this mathematical lens, population growth is framed not merely as a demographic concern but as a dynamic system influenced by complex and interrelated factors.
Author: Soumendu Ghosh
Institution: Brainware University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4413428256