During the attack of public health emergencies，the surge in material demand in isolated communities leads to a series of problems，i.e.，serious shortfalls in supply，fairness of distribution and special distributional needs. To address this issue，a multi-period，multi-type，cross-regional emergency material dynamic allocation problem was studied based on a hierarchical distribution network of "material supply point-distribution center-isolated community". Especially，the demand time windows were applied to characterize the realistic requirements of isolated communities for the delivery time，and the special needs of some vulnerable groups，e.g.，aging populations，were considered. Thus，a multi-objective non-linear dynamic program was developed by integrating the three dimensions of considerations：economy，material distribution satisfaction rate and distribution equity. In view of the multi-objective structure，the Epsilon constraint algorithm was used to solve the proposed model，and the material allocation during the attack of public health emergencies in Shanghai was taken as a case study to analyze the Pareto front of the optimal solutions and conduct the sensitivity analysis on some key parameters in the model. The results show that，under the constraint of limited emergency material supply，the material allocation strategy considering the aging populations helps to prioritize the material supply of vulnerable groups. However，it also contributes to an increase in the unfairness rate of the isolated communities as a whole. For the material allocation strategy considering the delivery time windows of isolated communities，the total operation cost of the cross-regional distribution network and the unmet rate of the material demand in the isolated communities are high，but the overall distribution of supplies in the system is relatively fair，and it could better meet the needs of isolated communities in terms of delivery of supplies，which provides a useful reference for the decision makers to balance the individual demand and the overall interests.