Back
 IJMNTA  Vol.5 No.4 , December 2016
Modelling the Dynamical State of the Projected Primary and Secondary Intra-Solution-Particle Movement System of Efavirenz In-Vivo
Tafireyi Nemaura1,2*
Show more
Abstract: This work seeks to describe intra-solution particle movement system. It makes use of data obtained from simulations of patients on efavirenz. A system of ordinary differential equations is used to model movement state at some particular concentration. The movement states’ description is found for the primary and secondary level. The primary system is found to be predominantly an unstable system while the secondary system is stable. This is derived from the state of dynamic eigenvalues associated with the system. The saturated solution-particle is projected to be stable both for the primary potential and secondary state. A volume conserving linear system has been suggested to describe the dynamical state of movement of a solution particle.
Keywords: Ordinary Differential Equations, Stability, Nonautonomous Linear System, Concentration-Varying Eigenvalues, Solution Particle
Cite this paper: Nemaura, T. (2016) Modelling the Dynamical State of the Projected Primary and Secondary Intra-Solution-Particle Movement System of Efavirenz In-Vivo. International Journal of Modern Nonlinear Theory and Application, 5, 235-247. doi: 10.4236/ijmnta.2016.54021.
References

[1]   Ette, E.I. and Williams, P.J. (2007) Pharmacometrics. The Science of Quantitative Pharmacology. Hoboken, Wiley.

[2]   van der Kloet, P. and Neerhoff, F.L. (2002) Dynamic Eigenvalues for Scalar Linear Time-Varying Systems. Proceedings of 15th International Symposium on Mathematical Theory of Net. and Sys. MTNS, Notre Dame.

[3]   Murray, J.D. (2001) Mathematical Biology. 3rd Edition, Springer, Berlin.

[4]   Kreyszig, E. (2006) Advanced Engineering Mathematics. 9th Edition, Wiley.

[5]   Sideris, T.C. (2013) Ordinary Differential Equations and Dynamical Systems. Springer, Atlantis Press.
https://doi.org/10.2991/978-94-6239-021-8

[6]   Hirsch, M.W., Smale, S. and Devaney, R.L. (2012) Differential Equations, Dynamical Systems, and an Introduction to Chaos. Academic Press.

[7]   Slavík, A. (2013) Mixing Problems with Many Tanks. American Mathematical Monthly, 120, 806-821.
https://doi.org/10.4169/amer.math.monthly.120.09.806

[8]   Edwards, C.H. and Penney, D.E. (2006) Elementary Differential Equations. 6th Edition, Pearson, Upper Saddle River.

[9]   Nemaura, T. (2015) Modeling Transportation of Efavirenz: Inference on Possibility of Mixed Modes of Transportation and Kinetic Solubility. Frontiers in Pharmacology.
https://doi.org/10.3389/fphar.2015.00121

[10]   Kirillov Jr., A. (2008) An Introduction to Lie Groups and Lie Algebras. Cambridge Studies in Advanced Mathematics, Vol. 113, Cambridge University Press, Cambridge.
https://doi.org/10.1017/cbo9780511755156

[11]   van den Ban, E.P. (2010) Lie Groups. Lecture Notes, Spring.

 
 
Top