<p>Efficient and sustainable medical resource coordination is critical during public health emergencies, when sudden demand surges simultaneously pressure healthcare delivery, logistics operations, and hazardous medical-waste disposal. This study develops a differential game model to investigate how artificial intelligence (AI) reshapes the strategic interaction between logistics organizations and medical institutions across the emergency-response chain, including medical-resource transportation, clinical treatment, and medical-waste removal. We compare a conventional coordination setting with an AI-enabled setting in which a shared AI service reduces, but does not eliminate, information, demand-identification, and routing inefficiencies. The analytical results show that AI may strengthen medical-resource transportation incentives and the interior treatment-effort candidate when the unit cost of AI services remains below the relevant critical thresholds; beyond these thresholds, the added service burden can outweigh the coordination gains. By contrast, hazardous medical-waste transportation decisions are influenced more directly by waste-control valuation, AI-enabled monitoring benefits, and disposal-efficiency gains than by AI service costs alone. The analysis further shows that joint AI adoption is viable only when fixed implementation costs remain within the adoption thresholds of both parties, implying that payoff-increasing digital upgrading may not arise spontaneously. These findings offer a modeling basis for considering differentiated adoption support, cost-sharing arrangements, and sustainability-oriented emergency-governance priorities related to environmental risk control and system resilience during public health crises.</p>