Mathematical modeling of societal challenges faced by women in the society : A deterministic and stochastic approach

Abstract

In society, there are numerous hurdles hindering the advancement of women. Additionally, violence against women remains a significant issue, exacerbating their challenges. Therefore, addressing these violence-related challenges in a mature manner is crucial to creating a comfortable environment for women to thrive. In this paper, we present a nonlinear mathematical model focusing on women’s issues and empowerment as key factors. The model exhibits two equilibrium points: a violence-free equilibrium point and a violence-present equilibrium point. We analyze the stability of these equilibrium points and explore the influence of parameters within the model. Furthermore, we extend the model to incorporate stochastic effects. Subsequently, we compare the results of the stochastic model with those of the deterministic model. Our comparison reveals that the stochastic and deterministic models exhibit similar behaviors, albeit with slight oscillations in stochastic populations compared to deterministic ones.

Keywords

• Stability analysis
• Routh–Hurwitz criteria
• Stochastic differential equation
• Mathematical model
• Public health