Propagatio: A Predictive Mathematical Framework for Modelling Organisational Health and Stress Propagation

This paper introduces Propagatio, a predictive mathematical framework for modelling organisational health and stress propagation. Unlike existing diagnostic frameworks — which are predominantly static, qualitative, and retrospective — Propagatio provides a dynamic, quantitative, and forward-looking model of organisational behaviour.

The framework is built on three core innovations. First, every organisational system is characterised by three measurable variables — Capacity, Load, and Recovery — which are combined into a bounded Health Index (H) defined as H = 40 + 0.4C − 0.4L + 0.2R, yielding a 0–100 index that requires no post-hoc normalisation. Second, stress is modelled as a propagation phenomenon: stress entering one system (e.g., Commercial) transmits to others (e.g., Operations, Finance, People) with measurable coefficients, enabling prediction of systemic failure trajectories. Third, the Organisational Pulse — weekly tracking of health, change, acceleration, and 90-day forecast — provides early warning signals before stress manifests in financial or operational outcomes.

The framework is operationalised through a straightforward spreadsheet-based protocol requiring no specialised expertise. Retrospective applications to the Toyota recall crisis (2009–2010) and Nokia's smartphone collapse (2007–2010) illustrate the framework's diagnostic and predictive capabilities.

Important note: This is a working paper introducing a novel theoretical framework. It is intended to stimulate scholarly discussion and empirical testing. The retrospective case studies are illustrative demonstrations, not empirical validation. The mathematical parameters presented are theoretical priors subject to calibration using longitudinal organisational data.