To guarantee the smooth implementation of targeted testing and treatment measures and infectious disease prevention and control, and to also formulate a scientific and reasonable distribution strategy for emergency medical supplies, a multi-center, multi-material vehicle path optimization model was constructed. Its primary objective was to maximize satisfaction and the earliest delivery service end time. First, the demand for medical supplies was predicted based on the SQEIR model for spreading infectious diseases. Second, two functions were designed to evaluate the satisfaction of different classes of material distribution for diverse emergency medical material use scenarios. Finally, the improved salp swarm algorithm was designed to solve the model, and the results were compared and analyzed with those of the traditional NSGA-II algorithm. The simulation results demonstrate that the proposed model and the improved algorithm can efficiently solve the emergency medical material distribution problem under public health emergencies, and the improved algorithm presents superior characteristics in terms of global search performance.