Thermo-Environmental Modeling of Cholera Dynamics: Integrating Temperature-Dependent Transmission and Exergy Analysis for System Stability

As global climate anomalies alter aquatic ecosystems, traditional epidemiological models frequently overlook the fundamental thermodynamic laws governing environmental pathogen reservoirs. This study bridges that critical gap by introducing a novel thermo-environmental modeling framework that couples the transmission dynamics of water-borne cholera with macroscopic ecosystem energetics. Utilizing a system of nonlinear differential equations embedded with temperature-dependent biological parameters, we examine the dual impact of thermal warming and metabolic entropy on epidemic intensity. Our numerical and sensitivity analyses reveal that ambient temperature acts as a critical control lever, where elevated thermal baselines concurrently compress the time-to-peak outbreak window and escalate maximum infection prevalence. Crucially, we identify striking temporal synchronization between peak human infection and maximum environmental exergy destruction E˙d within the aquatic reservoir. This energetic signature proves that explosive bacterial proliferation and host-induced pathogen shedding fundamentally destabilize the thermodynamic stability of the ecosystem. From a public health perspective, these findings establish environmental exergy profiles as a viable, nontraditional ecological diagnostic tool to forecast high-risk outbreak windows before clinical spikes occur. Ultimately, our structural sensitivity analysis demonstrates that while clinical scaling is essential for patient recovery, long-term epidemic containment rests heavily on targeted environmental sanitation and water-treatment infrastructure designed to shatter this thermo-biological feedback loop.