A Numerical Comparison for a Discrete HIV Infection of CD4+ T-Cell Model Derived from Nonstandard Numerical Scheme

A nonstandard numerical scheme has been constructed and analyzed for a mathematical model that describes HIV infection of CD4

[1]  Juan Carlos Cortés,et al.  Non-standard numerical method for a mathematical model of RSV epidemiological transmission , 2008, Comput. Math. Appl..

[2]  Ronald E. Mickens,et al.  Difference Equations: Theory and Applications , 1990 .

[3]  Ronald E. Mickens,et al.  Exact solutions to a finite‐difference model of a nonlinear reaction‐advection equation: Implications for numerical analysis , 1989 .

[4]  Agraj Tripathi,et al.  Modelling the effect of tuberculosis on the spread of HIV infection in a population with density-dependent birth and death rate , 2009, Math. Comput. Model..

[5]  Ronald E. Mickens,et al.  Advances in the Applications of Nonstandard Finite Difference Schemes , 2005 .

[6]  Xiaohua Ding,et al.  Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs , 2012, J. Appl. Math..

[7]  Patrick W Nelson,et al.  Mathematical analysis of delay differential equation models of HIV-1 infection. , 2002, Mathematical biosciences.

[8]  Ronald E. Mickens,et al.  Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition , 2007 .

[9]  M A Nowak,et al.  Mathematical biology of HIV infections: antigenic variation and diversity threshold. , 1991, Mathematical biosciences.

[10]  A. Perelson,et al.  A model of HIV-1 pathogenesis that includes an intracellular delay. , 2000, Mathematical biosciences.

[11]  R. Mickens.  Applications of nonstandard finite difference schemes , 2000 .

[12]  Murray E. Alexander,et al.  A Positivity-preserving Mickens-type Discretization of an Epidemic Model , 2003 .

[13]  Rafael J. Villanueva,et al.  Nonstandard numerical methods for a mathematical model for influenza disease , 2008, Math. Comput. Simul..

[14]  J. Lambert.  Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , 1991 .

[15]  Pei Yu,et al.  Numerical modelling of the perturbation of HIV-1 during combination anti-retroviral therapy , 2001, Comput. Biol. Medicine.

[16]  A. Perelson,et al.  Dynamics of HIV infection of CD4+ T cells. , 1993, Mathematical biosciences.

[17]  On the convergence domains of the p -cyclic SOR , 1996 .

[18]  Ronald E. Mickens,et al.  A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion , 2003 .

[19]  Dynamically consistent discrete Lotka-Volterra competition models derived from nonstandard finite-difference schemes , 2007 .

[20]  Ronald E. Mickens,et al.  Discretizations of nonlinear differential equations using explicit nonstandard methods , 1999 .

[21]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[22]  Ronald E. Mickens,et al.  Finite-difference schemes having the correct linear stability properties for all finite step-sizes III , 1994 .

[23]  S. Elaydi.  An introduction to difference equations , 1995 .

[24]  Michael Y. Li,et al.  Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells. , 2006, Mathematical biosciences.

[25]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[26]  K. Patidar.  On the use of nonstandard finite difference methods† , 2005 .

[27]  Saber Elaydi,et al.  Difference equations from discretization of a continuous epidemic model with immigration of infectives , 2003 .

[28]  R. Mickens.  Nonstandard Finite Difference Models of Differential Equations , 1993 .

[29]  S. Ruan,et al.  A delay-differential equation model of HIV infection of CD4(+) T-cells. , 2000, Mathematical biosciences.

[30]  Murray E. Alexander,et al.  A non-standard numerical scheme for a generalized Gause-type predator–prey model , 2004 .

[31]  Lih-Ing W. Roeger,et al.  Local Stability of Euler's and Kahan's Methods , 2004 .

[32]  Yanni Xiao,et al.  Threshold dynamics for an HIV model in periodic environments , 2010 .