A Difference-Equation Framework for Modeling Organ Transplantation Dynamics

Abstract

Organ transplantation is a life-saving process in which patients with failing or damaged vital organs receive donor grafts to improve their condition. However, in the United States, the demand for organs consistently exceeds the available supply, leading to long waiting times and limited access to transplantation. To better understand these dynamics, this project develops a difference equation model to examine the waitlist and donor populations, median waiting time, and 3-year survival rates. Data from the Organ Procurement and Transplantation Network (OPTN) on living, donors, total donors, and transplant procedures was used to estimate key model parameters, while additional parameters were determined through biologically and clinically motivated assumptions. Parameter estimation yielded a living donor transplant efficiency of beta-live = 0.00632 (R² = 0.324) and a strong relationship between total donors and transplants with beta-all = 2.020519 (R² = 0.986). The results demonstrate how differences between donor availability and transplant demand influence waitlist growth, while changes in median waiting time and survival rates illustrate additional factors affecting transplant system dynamics. Equilibrium analysis identified conditions required for system stability, while donor-scarcity analysis characterized waitlist behavior when donor supply acts as the primary limiting constraint. Overall, this model provides a mathematical framework for understanding the intricacies of the transplantation system, aligning with the UN Sustainable Development Goal 3: Good Health and Well-Being.