Current societies must make the necessary plans for effective responses and to reduce the destructive effects of disasters. For this reason, this research has developed a mathematical programming model under uncertainty for earthquake relief and response during COVID-19. In the presented model, the possibility of facility failure is considered according to the intensity of the earthquake and COVID-19 to increase reliability. The simultaneous occurrence of these disasters presents unique challenges in ensuring the timely delivery of essential supplies to affected regions. Distribution centers (DCs) are considered to be of two types: the first type is local DCs, which use public centers and are close to accident points. These types of centers are prone to failure because they use public facilities. Another type is the reliable DCs built outside the disrupted area, which have a very low probability of loss due to spending more money to build them. In addition, to consider the reliability capabilities, the new model has tried to provide a complete model for transportation planning by considering the multi-trip mode of vehicles. Moreover, this model considers distance restriction at the demand point for the first time because of COVID-19 during the earthquake. The proposed network design aims to offer effective solutions in promptly delivering essential items to affected areas, thereby enhancing disaster management strategies and minimizing the impact of these crises on vulnerable populations. Uncertainty is presented using the probability approach based on the modeling scenario and a case study from the city of Istanbul to illustrate the performance of the suggested model. Finally, the suggested mode is solved with an Lp-metric and goal programming (GP) approach. The results show that in this case, the proposed model shows that effective and efficient aid delivery is possible in terms of time and cost. Therefore, it can help crisis managers respond by providing the required budget and appropriate logistics planning.