Women Empowerment Status in India: Mathematical Modelling and Optimal Control Approach

Abstract

Women's empowerment is essential for the advancement of all women, yet the journey towards achieving it is often hindered by various challenges, such as violence, financial constraints, and cultural beliefs. In some cases, women, influenced by cultural beliefs, may unintentionally impede the progress of other women. Additionally, due to a lack of education, superstitious beliefs can lead to unethical practices within society. Among these, dowry remains a particularly significant issue for women in South Asia. Although dowry, the transfer of cash, jewellery, and other valuable assets from the bride's family to the groom's, is officially prohibited in India and Bangladesh and restricted in Pakistan, the practice continues to be prevalent across the region. In rural areas of India, the dowry system frequently discourages parents from supporting their daughters' pursuit of higher education, thereby presenting a notable barrier to women's progress and empowerment. In light of this, we propose a deterministic model to address women-related issues, dividing the population into four subclasses: common women, women facing hurdles, stressed women, and empowered women. The model identifies two equilibrium points: the hurdle-free equilibrium point and the non-trivial equilibrium point. We calculate a basic reproduction number and perform sensitivity analysis on key parameters. The local and global stability of these equilibrium points is assessed using the Routh-Hurwitz criteria and Lyapunov's function. Additionally, we extend this deterministic model to an optimal control problem, determining the optimal control profile to achieve maximum impact within a specified time frame. To validate our model, we conducted a numerical simulation using dowry-related death data from NCRB (National Crime Records Bureau of India) publications for the years 2001-2022. This data is then fitted to our model to forecast dowry-related deaths in the coming years.