Modeling Population Dynamics in the Indian Context: A Differential Difference Equation Approach

The study of population dynamics is of paramount importance in comprehending the evolving demographics and socioeconomic structure of a country. The task of modelling population dynamics in the Indian context poses distinct challenges and opportunities owing to the extensive and heterogeneous nature of the country's population. This research paper utilises a differential difference equation (DDE) methodology to comprehensively model population dynamics in India. The study seeks to enhance comprehension of population dynamics by considering various factors, including birth rates, death rates, migration patterns, and seasonal variations. The study employs Delay Differential Equations (DDEs) as a mathematical framework to effectively model the dynamic characteristics of population systems. These equations account for time delays, historical events, and discrete factors that play a significant role in shaping population dynamics, whether it be growth or decline. Numerical techniques, such as Euler's method and the Runge-Kutta method, are utilised in order to solve Delay Differential Equation (DDE) models and effectively simulate the dynamics of populations over a given time period. The evaluation of each method involves a comparative analysis of its accuracy, smoothness, convergence properties, and computational efficiency. The research findings presented in this study enhance our comprehension of population dynamics in India and offer significant insights that can be utilised by policymakers, urban planners, and researchers in the fields of demography, public health, and social sciences. The results have the potential to provide valuable insights for evidence-based decision-making and the development of effective policies aimed at addressing the various challenges and opportunities related to population dynamics in the Indian context.