Stability Analysis and its Impact on the Parameters Estimation for a Logistic Growth Model

This paper presents a stability analysis of a system of differential equations describing the evolution of T-cells populations. The analyzed system corresponds to a well-known four-compartmental model of the thymus which involves a logistic growth term. Unlike existing results on stability for this model which focus either only on the global population or on the two dominant double-positive and double-negative populations, the results presented in this paper provide sufficient conditions for asymptotic stability of all four populations, taken separately. The derived conditions involve parameters related to cells proliferation, death and transfer rates and are used as constraints in the least-square optimization procedure which provides estimates for all parameters of the model. The usage of the constraints derived from the stability analysis ensures that the estimated parameters lead to a mathematical model with an asymptotically stable fixed point.