Algebraic Modeling of Social Systems Evolution: Application to Sustainable Development Strategy

This paper presents ALMODES, a discrete-time modeling approach for social systems that uses matrix algebra and directed graphs. The method bridges the gap between static network analysis and continuous System Dynamics, offering a transparent framework that reduces data requirements. The method enables clear causal mapping, rapid simulation, straightforward sensitivity analysis, and natural hybridization with agent-based or discrete-event models. Two case studies illustrate its utility for sustainable-development strategy: in an urban public-health setting, modernization and sanitation policies drive sustained declines in disease despite growth, whereas reversing the population-to-modernization link triggers a morbidity rebound that can be prevented by strengthening the modernization-to-sanitation pathway; in a high-tech services Balanced Scorecard model, a baseline backlog spike depresses customer satisfaction, aggressive hiring shortens the spike but erodes income, and coordinated boosts to training and incentives (about twelve percent productivity gain) remove the backlog early, stabilize customers, and improve income, highlighting human-capital policy as a robust lever. ALMODES thus supports pragmatic policy design under limited, expert-elicited parameters. Future research will address uncertainty quantification, time-varying structures and shocks, automated calibration and empirical validation at scale, optimization and control design, richer integration with hybrid simulation, participatory interfaces for stakeholders, and standardized benchmarks across domains.