Understanding Work/Life Balance Through Mathematical Model
Abstract
Work/life balance (WLB) remains a central yet elusive concept in social and organizational sciences, often described qualitatively without a unified quantitative framework. To address this gap, a novel compartmental mathematical model is proposed that formalizes WLB as a dynamic population-level phenomenon. The individuals are categorized into 4 compartments, namely, regularly employed, temporarily employed, imbalanced (infected), and balanced (recovered), representing balanced and imbalanced states. Role-based complaints govern the transitions between states, the conflict conversion rates of these complaints, and the recovery rate. The model, structured as a system of nonlinear ordinary differential equations, is analyzed for the existence of the equilibrium and its stability. In the analysis, the stable disease-free equilibrium is found to exist, representing complete societal balance. The other endemic equilibrium is shown to be infeasible through simulations and thus requires certain parameter constraints, which represent a specific scenario that may occur in the population. However, it is found that the endemic equilibrium always remains unstable. The model's ability to quantify how micro-level stressors spread into macro-level imbalance is demonstrated by numerical simulations, which also validate the analytical results. This work establishes a rigorous mathematical foundation for WLB, enabling future empirical and mathematical calibrations.
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BibTeX
@misc{singla2026understanding,
title = {{Understanding Work/Life Balance Through Mathematical Model}},
author = {Francy Singla and Vivek Kumar},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01091},
eprint = {2611.01091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01091},
}
RIS
TY - UNPB
TI - Understanding Work/Life Balance Through Mathematical Model
AU - Francy Singla
AU - Vivek Kumar
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01091
UR - https://arxiv.org/abs/2611.01091
AB - Work/life balance (WLB) remains a central yet elusive concept in social and organizational sciences, often described qualitatively without a unified quantitative framework. To address this gap, a novel compartmental mathematical model is proposed that formalizes WLB as a dynamic population-level phenomenon. The individuals are categorized into 4 compartments, namely, regularly employed, temporarily employed, imbalanced (infected), and balanced (recovered), representing balanced and imbalanced states. Role-based complaints govern the transitions between states, the conflict conversion rates of these complaints, and the recovery rate. The model, structured as a system of nonlinear ordinary differential equations, is analyzed for the existence of the equilibrium and its stability. In the analysis, the stable disease-free equilibrium is found to exist, representing complete societal balance. The other endemic equilibrium is shown to be infeasible through simulations and thus requires certain parameter constraints, which represent a specific scenario that may occur in the population. However, it is found that the endemic equilibrium always remains unstable. The model's ability to quantify how micro-level stressors spread into macro-level imbalance is demonstrated by numerical simulations, which also validate the analytical results. This work establishes a rigorous mathematical foundation for WLB, enabling future empirical and mathematical calibrations.
ER -