Large-scale crises, including wars and pandemics, have repeatedly shaped human history, and their simultaneous occurrence presents profound challenges to societies. Understanding the dynamics of epidemic spread during warfare is essential for developing effective containment strategies in complex conflict zones. While research has explored epidemic models in various settings, the impact of warfare on epidemic dynamics remains underexplored. In this study, we proposed a novel mathematical model that integrates the epidemiological SIR (susceptible-infected-recovered) model with the war dynamics Lanchester model to explore the dual influence of war and pandemic on a population's mortality. Moreover, we consider a dual-use military and civil healthcare system that aims to reduce the overall mortality rate which can use different administration policies. Using an agent-based simulation to generate in silico data, we trained a deep reinforcement learning model for healthcare administration policy and conducted an intensive investigation on its performance. Our results show that a pandemic during war conduces chaotic dynamics where the healthcare system should either prioritize war-injured soldiers or pandemic-infected civilians based on the immediate amount of mortality from each option, ignoring long-term objectives. Our findings highlight the importance of integrating conflict-related factors into epidemic modeling to enhance preparedness and response strategies in conflict-affected areas.

翻译：大规模危机（包括战争和疫情）在人类历史上反复出现，其同时发生对社会构成深刻挑战。理解战争期间疫情传播的动态特性，对于在复杂冲突区域制定有效防控策略至关重要。尽管现有研究已探讨了多种情境下的传染病模型，但战争对疫情动态的影响仍未得到充分探索。本研究提出了一种新颖的数学模型，将流行病学SIR（易感-感染-康复）模型与战争动态兰彻斯特模型相结合，以探究战争与疫情对人口死亡率的双重影响。此外，我们考虑了一个旨在降低总体死亡率的军民两用医疗系统，该系统可采用不同的管理策略。通过基于智能体的仿真生成数据，我们训练了用于医疗管理策略的深度强化学习模型，并对其性能进行了深入研究。结果表明，战争期间的疫情会导致混沌动态，此时医疗系统应根据各选项即时产生的死亡率，优先救治战争伤员或疫情感染民众，而忽略长期目标。我们的研究结果突显了将冲突相关因素纳入传染病建模的重要性，以提升冲突影响区域的应急准备与响应策略。