In order to predict the demand for emergency medical supplies at the initial stage of the sudden epidemic and allocate emergency medical supplies. Combined with the characteristics of infectious diseases and the impact of government quarantine measures on the spread of infectious diseases, an improved susceptible-exposed- infected-recovered(SEIR) model is established, and the parameters in the model are periodically updated based on the data-driven idea, so as to characterize the trajectory of epidemic diffusion. The demand is constructed as a function of infection scale to predict the demand for emergency medical supplies. On this basis, a location-allocation mold is established with the goal of minimizing weighted transport distance and constraints such as allocation fairness. And an adaptive hybrid algorithm is designed to solve it, which combines the genetic algorithm and tabu search. The results show that the data driven parameter updating method can guarantee the prediction accuracy of the improved SEIR model with a mean relative error of 3.8%. The proposed location-allocation model can optimize delivery timeliness while also taking into account fairness. The results of different scale examples show that compared with the standard genetic algorithm, the proposed algorithm converges faster and has higher solution quality.