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Immune escape is a critical gateway to malignancy; it is recently discovered that Indoleamine 2, 3 Dioxygenase (IDO) is involved in suppressing T-cell immunity in pathological settings including cancer. The modeling of the biological regulatory networks (BRNs) using kinetic logics of René Thomas, a well-known and powerful approach for modeling formalism, helps in understanding their dynamical behaviors. This paper presents the dynamic behaviors of the IDO related BRN. The sustained production after tumor invasion is detrimental which is shown as a stable steady state in the results. The homeostasis of IDO and T cell mediated immune regulation in the body, which is responsible for suppressing the tumor by controlling IDO activation, is shown by a qualitative cycle.