The purpose of this paper is to study the G-CSF (Granulocyte-Colony Stimulating Factor) treatment of a simulations and data fit mathematical modeling of CN (Cyclical Neutropenia) with neutrophil count. This model is useful to account for the features of untreated G-CSF. It is also useful for treatment of dogs with CN. Therefore this model is considered as an accomplished one. There is fitting parameters for 3 days and not for 4 dogs for estimation or evaluation. It is also essential and necessary to model the more samples for increase in Neutrophil amplification. The proposed interventions are practical. It may reduce the amount of G-CSF. It required potential maintenance. Sometimes, it may even improve the treatment effects too. This model gives us good result in treatment. The changes would be practical and reduce the risk side as well as the cost of treatment in G-CSF. By using a four GC’s (grey collies) and ANC (Absolute Neutrophil Count), we establish some new sufficient parameters which ensure that every solution of this mathematical modeling for disease level decreases to maximum.