Mathematical аnalysis of kidney transplant demand and availability

Abstract

Aim. To analyse the dynamics of the need and availability of donor kidneys for transplantation. To construct the predictions for the number of waiting lists. To analyse the annual number of kidney transplants and the availability ofdonor kidney.Materials and methods. Data base of Eurotransplant International Foundation 1969–2015 has been analyzed. We built a forecast of the kidney waiting list, kidney transplants quantity and availability of kidney grafts up to 2030.Results. Random process analysis of kidney transplant recipients number has shown an increasing linear trend. Growing linear trend is due to the inability to fully meet the increasing need for a kidney transplant. Presence of a regular stochastic component is revealed that provides random fl uctuations in the number of patients waiting for kidney transplantation with a period of 35–40 years. Random process of the number of kidney transplants showed an exponential asymptotic trend growing to a certain saturation value. Estimation of its autocorrelation function showed the absence of regular stochastic components in it. Preservation of 1969–2015 dynamics for the period 2015–2030 allows to suggest a signifi cant increase in the number of people waiting for transplant and a decrease in the availability of donor kidneys.Conclusion. The number of donor kidney transplantations tends to saturation limit, and limit is already lower than the current need for donor kidneys. The increase in the number of kidney transplantation programs and the improvement of organ donation system may lead to a limited increase in annual number of transplants and, possibly, the saturation limit, but not to a qualitative change in the dynamics of reduced availability of donor kidneys. A qualitative change in this dynamics towards increasing accessibility, is possible perhaps through activities that affect factors causing a constant increase in the number of people who need a transplant.