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Fractional Approach for the Inhibition of Excessive Keratinocyte Growth in Psoriasis using Drugs Cyclosporin and FK506

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Mathematical Models for Therapeutic Approaches to Control Psoriasis

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Abstract

In order to demonstrate the impact of memory on the cell-biological system, a mathematical model of Psoriasis involving CD4\(^{+}\) T-Cells, Dendritic Cells, CD8\(^{+}\) T-Cells, and Keratinocyte cell population has been developed in this chapter, using fractional-order differential equations with the effect of cytokines release, which is the extended work of Chap. 7. We have tried to explore the suppressed memory associated with the cell-biological system by incorporating fractional calculus and also to locate the position of Keratinocyte cell population considering the fact that fractional derivative possesses nonlocal property.

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References

  1. C. Li, F. Zeng, Numerical Methods for Fractional Calculus (CRC Press, Taylor and Francis Group, 2015)

    Book  Google Scholar 

  2. S. Rana, S. Bhattacharya, J. Pal, G.M. N’Guérékata, J. Chattopadhyay, Paradox of enrichment: a fractional differential approach with memory. Phys. A 392, 3610–3621 (2013)

    Article  MathSciNet  Google Scholar 

  3. E. Ahmed, A.S. Elgazzar, On fractional order differential equations model for non-local epidemics. Phys. A 379, 607–614 (2007)

    Article  MathSciNet  Google Scholar 

  4. W. Lin, Global existence theory and chaos control of fractional differential equations. J. Math. Anal. Appl. 332, 709–726 (2007)

    Article  MathSciNet  Google Scholar 

  5. F.A. Rihan, D. Baleanu, S. Lakshmanan, R. Rakkiyappan, On Fractional SIRC Model with Salmonella Bacterial Infection, Abstract and Applied Analysis, Article ID 136263, 9 p (2014)

    Google Scholar 

  6. E. Ahmed, A.M.A. El-Sayed, H.A.A. El-Saka, On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, R\(\ddot{\text{ o }}\)ssler. Chua and Chen Syst. Phys. Lett. A 358(1), 1–4 (2006)

    MATH  Google Scholar 

  7. W.H. Fleming, R.W. Rishel, Deterministic and Stochastic Optimal Control (Springer, Berlin 1975)

    Book  Google Scholar 

  8. O.P. Agrawal, A formulation and numerical scheme for fractional optimal control problems. J. Vib. Control 14(9), 1291–1299 (2008)

    Article  MathSciNet  Google Scholar 

  9. N.J. Savill, R. Weller, J.A. Sherratt, Mathematical modelling of nitric oxide regulation of rete peg formation in psoriasis. J. Theor. Biol. 214, 1–16 (2002)

    Article  Google Scholar 

  10. J.A. Sherratt, R. Weller, N.J. Savill, Modelling blood flow regulation by nitric oxide in psoriatic plaques. Bull. Math. Biol. 64, 623–641 (2002)

    Article  Google Scholar 

  11. P.K. Roy, A. Datta, Negative feedback control may regulate cytokines effect during growth of keratinocytes in the chronic plaque of psoriasis: a mathematical study. Int. J. Appl. Math. 25(2), 233–254 (2012)

    MathSciNet  MATH  Google Scholar 

  12. T. Sardar, S. Rana, J. Chattopadhyay, A mathematical model of dengue transmission with memory. Commun. Nonlinear Sci. Numer. Simul. 22(1), 511–525 (2015)

    Article  MathSciNet  Google Scholar 

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Correspondence to Priti Kumar Roy .

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Roy, P.K., Datta, A. (2019). Fractional Approach for the Inhibition of Excessive Keratinocyte Growth in Psoriasis using Drugs Cyclosporin and FK506. In: Mathematical Models for Therapeutic Approaches to Control Psoriasis. SpringerBriefs in Applied Sciences and Technology(). Springer, Singapore. https://doi.org/10.1007/978-981-13-9020-3_10

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