In this paper we have investigated a stability of the equilibrium states between CN (Cyclical Neutropenia) and G-CSF (granulocyte-colony stimulating factor) with infective growth rate progression. Mathematical models and FFT (fast fourier transform) simulations can be used as experimental tools for testing the control-measures and determining sensitivities of changes in parameter values. The paper deals with an investigation on a four parameters estimates consisting of cure rate (c), infective

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... ate (I), absolute neutrophil count (A N) and total carrying capacity (K) only. All six equilibrium points for this model are identified and their stability criteria are analyzed. Mathematical modelling of epidemics can lead to and motivate new results in mathematics. Keywords: Cure rate in infective, infective rate in neutropenia population, absolute neutrophil count, total carrying capacity.