International Journal of Nonlinear Analysis and Applications

Stability analysis of a stochastic model of absorption of the drugs problem

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Education for Girls , University of Al-Kufa, Najaf, Iraq

2 Department of Mathematics, College of Science , University of Al-Qadisiyah, Diwania, Iraq

Abstract

The main objective of this work is to study the stability of the stochastic prototypical issue of drug absorption in the cells of the human body.  In addition, we studied the statistical analysis to solve the given model in this paper.

Keywords

[1] L. Arnold and H. Crauel, Random dynamical systems, Lyapunov Exponents: Proc. Conf. held in Oberwolfach, May 28–June 2, 1990, Springer, 2006, pp. 1–22.
[2] I. Chueshov, Monotone Random Systems Theory and Applications, Springer-verlag Berlin Heidelberg New York, 2002.
[3] J.I. Freijer, T.M. Post, B.A. Ploeger, J. DeJongh, and M. Danhof, Application of the convection–dispersion equation to modelling oral drug absorption, Bull. Mathe. Bio. 69 (2007), no. 1, 181–195.
[4] I.I. Gikhman and A.V. Skorokhod, Stochastic differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, 1972.
[5] M. Grassi, G. Lamberti, S. Cascone, and G. Grassi, Mathematical modeling of simultaneous drug release and in vivo absorption, Int. J. Pharmac. 418 (2011), no. 1, 130–141.
[6] I. Khadim and S. Abd-AL Hussein, Stochastic model of the absorption of drugs problem in the cells and organs, Al-Qadisiyah J. Pure Scie. 26 (2021), no. 1, 134–142.
[7] P.E. Kloeden and E. Platen, Stochastic Differential Equations, Springer, 1992.
[8] J.E. Mann, On stochastic models of light absorption, Bull. Math. Bio. 45 (1983), no. 2, 229–237.
[9] X. Mao, Stochastic Differential Equations and Applications, 2 ed., Woodhead Publishing Limited, 2007.
[10] Bernt Øksendal and Bernt Øksendal, Stochastic differential equations, Springer, 2003.
[11] S. S¨arkk¨a and A. Solin, Applied Stochastic Differential Equations, vol. 10, Cambridge University Press, 2019.
[12] M.R. Spiegel, Applied Differential Equations, 3 ed., vol. 10, Prentice Hall Inc. Englewood Cliff, New Jersey, 1981.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 5
May 2023
Pages 159-167
  • Receive Date: 09 January 2023
  • Revise Date: 14 March 2023
  • Accept Date: 23 March 2023