How Can We Use Math to Build More Sustainable Cities?

Have you ever thought that math could help create healthier and more sustainable cities? A new study introduces ALMODES, a method that uses algebra and graphs to simulate the evolution of social systems. This tool helps understand the causes and effects of public policies, such as modernization and sanitation, which can reduce diseases even with population growth. In a case study, ALMODES showed that improving access to modernization and sanitation can prevent the return of diseases. Another example involves high-tech service companies: hiring more staff can improve customer satisfaction but may also reduce profits. However, investing in training and incentives can eliminate backlogs, stabilize customers, and increase earnings. ALMODES is a powerful tool for designing effective policies, even with limited data. In the future, scientists want to improve this method to handle uncertainty and better integrate hybrid models.

ALMODES is a discrete-time modeling approach that uses matrix algebra and directed graphs to simulate the evolution of social systems. This method bridges static network analysis with continuous System Dynamics, offering a transparent framework that reduces data requirements. ALMODES enables clear causal mapping, rapid simulation, straightforward sensitivity analysis, and natural hybridization with agent-based or discrete-event models. The two case studies presented in the study illustrate ALMODES' utility for designing sustainable development strategies. In the first case, in an urban public health setting, modernization and sanitation policies drive sustained declines in disease despite population growth. However, reversing the population-to-modernization link can trigger a morbidity rebound that can be prevented by strengthening the modernization-to-sanitation pathway. In the second case, in a high-tech services Balanced Scorecard model, a baseline backlog spike depresses customer satisfaction. Aggressive hiring shortens the spike but erodes income. However, coordinated boosts to training and incentives (with a 12% productivity gain) eliminate 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.