A phenomenological-based semi-physical model of the kidneys and its role in glucose metabolism

•Construction of a mathematical model of the kidneys role in glucose metabolism using the laws of nature and the conservation principle.•The kidneys have physiological aspects in the glucose regulatory system considered in the constructed mathematical model.•Estimation of the endogenous glucose production in the kidneys during post-prandial and post-absorptive states.•Estimation of the endogenous glucose production in the kidneys via four non-carbohydrates precursors.•The kidneys model can be implemented as a submodel of a whole model for the glucose homeostasis in humans.