Mathematical Modeling and Simulation for Health, Energy, and Climate Systems

Accelerating climate variability, rising energy transitions, and increasing public health pressures have intensified the need for unified analytical frameworks capable of capturing cross-sectoral dynamics. Mathematical modeling and simulation provide a rigorous foundation for analyzing nonlinear interactions, feedback mechanisms, and cascading risks across interconnected health, energy, and climate systems. This chapter develops an integrated system-of-systems modeling architecture that combines deterministic and stochastic differential equations, optimization theory, uncertainty quantification, and hybrid artificial intelligence–physics approaches within a coherent computational framework. Stability analysis, bifurcation theory, and sensitivity assessment are embedded to identify tipping thresholds and resilience margins under compound stress scenarios such as extreme weather events, infrastructure disruption, and epidemiological surges. Climate-constrained energy optimization and predictive health infrastructure modeling are linked through probabilistic uncertainty propagation, enabling robust scenario evaluation and risk-informed decision support. The proposed framework further incorporates digital twin architectures and explainable artificial intelligence to enhance transparency, interpretability, and policy relevance of multi-domain simulations. By bridging traditionally isolated modeling paradigms, this contribution advances methodological foundations for sustainable planning, adaptive governance, and resilience engineering within complex socio-environmental systems.