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.