Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.01091

Understanding Work/Life Balance Through Mathematical Model

Francy Singla·Vivek Kumar
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Francy Singla, Vivek Kumar. 2026-10-31. Understanding Work/Life Balance Through Mathematical Model. https://arxiv.org/abs/2611.01091

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Hilbert's 16th problem through Morse theory

We focus on the second part of Hilbert's 16th problem and provide an upper bound on the number of limit cycles that a polynomial, differential, planar system may have, depending exclusively on the degree $n$ of the system. Such a bound turns out to be a polynomial of degree $4$ in $n$. More specifically, if $H(n)$ indicates the maximum number of limit cycles among planar, differential, polynomial systems of degree $n$, then \begin{gather} H(n)\le \dfrac52 n^4-\dfrac{23}2 n^3+ \dfrac{43}2n^2-\dfrac{37}2n+7\,\,\,\, \mbox{if $n$ is even, and} \nonumber H(n)\le \dfrac52 n^4-\dfrac{23}2 n^3+ \dfrac{41}2n^2-\dfrac{33}2n+6\,\,\,\, \mbox{if $n$ is odd}.\nonumber \end{gather} For quadratic systems, we find $H(2)=4$. Our proof is entirely variational and utilizes in a fundamental way tools and facts from Morse theory, to the point that no particular expertise in dynamical systems is necessary or required. It is particularly interesting to compare our results with the ones for the same problem recently announced and made public by OpenAI as part of the solution of hundreds of important mathematical problems.

math.DS↗
arXiv2026

On the Dynamics of Invariant Graphs for Dissipative Twist Maps

We study the persistence and internal dynamics of invariant graphs for dissipative twist maps. Explicit $C^1$ persistence and parameter estimates allow every real rotation number to be realized by varying either translation parameter, while arbitrarily small zero-mean analytic perturbations at fixed irrational horizontal parameters can yield analytic graphs with dynamics conjugate to rational rotations. With a fixed Brjuno horizontal parameter and fixed-strip analyticity, normally attracting $C^r$ graphs persist under perturbations of size $(1-λ)^γ$, for any $γ>0$ and prescribed finite $r$, as $λ\to1^-$. At the critical Lipschitz bound, the invariant graphs can carry Denjoy dynamics and have countably many nondifferentiable points, with perturbations smooth outside a null Cantor set and tending to zero in every Hölder norm of order less than one.

math.DS↗
arXiv2026

Non-stationary normal coordinates on neighborhoods of Pesin stable manifolds

We construct non-stationary normal coordinates in a neighborhood of Pesin stable manifolds \cite{Pesin}. This construction is a natural extension, via jets in the normal directions, of the non-stationary normal coordinates on stable manifolds introduced by Guysinsky and Katok. We emphasize that this extension provides a useful framework for describing the fractal geometric structures of stable and unstable foliations in smooth dynamical systems.

math.DS↗