The COVID-19 pandemic, which was declared by the World Health Organization on March 11, 2020, negatively impacted virtually all economic and social activities across the globe. As of March 7, 2022, more than 6 million deaths have been associated with COVID-19 disease. This health disaster, unlike many other disasters, is not limited to time or location. It has resulted in intense global competition for many essential products, from Personal Protective Equipment (PPE) to ventilators and vaccines and food products. In this dissertation, I construct, analyze, and quantitatively solve a spectrum of supply chain economic network models inspired by realities in the COVID-19 pandemic in four essays. In this dissertation, I first develop a game theory network model for integrating financial and logistical challenges that humanitarian organizations involved in disaster management are faced with. This part of the dissertation illustrates how game theory can be utilized in the modeling and analysis of the behavior of multiple decision-makers that interact with each other in disaster supply chain economic networks under different constraints. I, subsequently, construct the first Generalized Nash Equilibrium (GNE) model with stochastic demands to model competition among organizations at demand points for medical supplies inspired by the COVID-19 pandemic. The theoretical constructs are provided, and a Variational Equilibrium is utilized to enable alternative variational inequality formulations. Then, I delve more deeply into an important characteristic of disasters, that of uncertainty, by developing a two-stage stochastic game theory network model. Specifically, the first multistage stochastic GNE model is constructed for the study of competition among multiple countries for limited supplies of medical items in the disaster preparedness and response phases in the COVID-19 pandemic. Illustrative examples and algorithmically solved numerical examples, inspired by the need for N95 masks and ventilators, are presented. Finally, I turn to a key aspect of pandemic disaster management, which is the evaluation of trade instruments that governments have been applying during the pandemic to protect their citizens. Specifically, a unified variational inequality framework in the context of spatial price network equilibrium problems is constructed that focuses on a plethora of essential products, that are in high demand in the pandemic, but short in supply globally. The model allows one to seamlessly introduce various trade measures, including tariffs, quotas, as well as price floors and ceilings.