6th International Young Scientist Congress (IYSC-2020) will be Postponed to 8th and 9th May 2021 Due to COVID-19. 10th International Science Congress (ISC-2020).  International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Stability of the Six Equilibrium States between CN and G-CSF with Infectives Growth Rate Progression: A FFT Study

Author Affiliations

  • 1Department of Mathematics, Sri Ramanujar Engineering College, Chennai-48, INDIA
  • 2Department of Mathematics, B.S. Abdur Rahman University, Chennai-48, INDIA

Int. Res. J. Biological Sci., Volume 1, Issue (2), Pages 55-60, June,10 (2012)


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 rate (I), absolute neutrophil count (A) 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.


  1. Balamuralitharan S. and Rajasekaran S., A Mathematical Age-structured Model on Aiha Using Delay Partial Differential Equations, Australian Journal of Basic and Applied Sciences, 5(4), 9-15 (2011)
  2. Balamuralitharan S. and Rajasekaran S., A Parameter Estimation Model of G-CSF: Mathematical Model of Cyclical Neutropenia, American Journal of Computational Mathematics, 2, 12-20 (2012)
  3. Balamuralitharan S. and Rajasekaran S., Analysis of G-CSF Treatment of CN Using Fast Fourier Transform, Research, Journal of Recent Sciences, 1(4), 14-21 (2012)
  4. Bernard S., Be´lair J. and Mackey M., Oscillations in cyclical neutropenia: New evidence based on mathematical modeling, J Theor Biol., 223, 283–298 (2003)
  5. Colijn C. and Mackey M., A Mathematical Model of Hematopoiesis: II. Cyclical Neutropenia, Journal of Theoretical Biology, 237(2), 133-146 (2005)
  6. Foley C., Bernard S. and Mackey M., Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses, J. Theor. Biol., 238, 754–763(2006)
  7. Hearn T., Haurie C. and Mackey M.C., Cyclical neutropenia and the peripherial control of white blood cell production, J. theor. Biol, 192, 167–181 (1998)
  8. Foley C. and Mackey M., Dynamic hematological disease: A review, J. Math. Biol., In press, (2008)
  9. Layton J.E. and Hall N.E., The interaction of G-CSF with its receptor, Frontiers in Biosci., 11, 3181–3189 (2006)
  10. Roeder I., Quantitative stem cell biology: Computational studies in the hematopoieticsystem, Curr Opin Hematol, 13, 222–228 (2006)
  11. Shochat E., Rom-Kedar V. and Segel L.A., G-csf control of neutrophils dynamics in the blood, Bull. Math. Biol., 69,2299–2338 (2007)