1 |
A. M. Elaiw, T. O. Alade, S. M. Alsulami, Analysis of within-host CHIKV dynamics models with general incidence rate. International Journal of Biomathematics 11(5) (2018) Article Number: 1850062.
|
2 |
A. Korobeinikov, Global properties of basic virus dynamics models, Bulletin of Mathematical Biology, 66(4). (2004), 879-883.
DOI
|
3 |
R. E. Mickens, Nonstandard Finite Difference Models of Differential equations, World Scientific, Singapore, 1994.
|
4 |
R. E. Mickens, Dynamics consistency: a fundamental principle for constructing nonstandard finite difference scheme for differential equation. Journal of Difference Equations and Applications. 9 (2003), 1037-1051.
DOI
|
5 |
D. Ding and X. Ding, Dynamic consistent non-standard numerical scheme for a dengue disease transmission model, Journal of Difference Equations and Applications, 20 (2014), 492-505.
DOI
|
6 |
D. Ding, W. Qin, and X. Ding, Lyapunov functions and global stability for a discretized multi-group SIR epidemic model, Discrete and Continuous Dynamical Systems - Series B, 20 (2015), 1971-1981.
DOI
|
7 |
Y. Enatsu, Y. Nakata, Y. Muroya, G. Izzo, and A. Vecchio, Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, Journal of Difference Equations and Applications, 18 (2012), 1163-1181.
DOI
|
8 |
J. Liu, B. Peng, and T. Zhang, Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence, Applied Mathematics Letters, 39 (2015), 60-66.
DOI
|
9 |
Z. Teng, L. Wang, and L. Nie, Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence, Mathematical Methods in the Applied Sciences, 38 (2015), 4741-4759.
DOI
|
10 |
K. Hattaf and N. Yousfi, Global properties of a discrete viral infection model with general incidence rate. Mathematical Methods in the Applied Sciences, 39 (2016), 998-1004.
DOI
|
11 |
P. Shi and L. Dong, Dynamical behaviors of a discrete HIV-1 virus model with bilinear infective rate, Mathematical Methods in the Applied Sciences, 37 (2014), 2271-2280.
DOI
|
12 |
Y. Yang, J. Zhou, X. Ma and T. Zhang, Nonstandard finite difference scheme for a diffusive within-host virus dynamics model both virus-to-cell and cell-to-cell transmissions, Computers and Mathematical with Applications, 72 (2016), 1013-1020.
DOI
|
13 |
J. Xu, Y. Geng and J. Hou, A nonstandard finite difference scheme for a delayed and diffusive viral infection model with general nonlinear incidence rate, Computers and Mathematical with Applications, 74 (2017), 1782-1798.
DOI
|
14 |
A. Korpusik, A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection, Common Nonlinear Sci Numer Simulat, 43 (2017), 369-384.
DOI
|
15 |
Yu. Yang, Ma. Xinsheng and Li. Yahui, Global stability of a discrete virus dynamics model with Holling type-II infection function, Mathematical Methods in the Applied Sciences, 39 (2016), 2078-2082.
DOI
|
16 |
J. Wang, Z. Teng and H. Miao, Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response, Advanced in Difference Equations, 143 (2016), DOI 10.1186/s13662-016-0862-y.
DOI
|
17 |
Y. Geng, J. Xu, J. Hou, Discretization and dynamic consistency of a delayed and diffusive viral infection model, Applied Mathematics and Computation 316 (2018) 282-295.
DOI
|
18 |
Y. Yang and J. Zhou, Global stability of a discrete virus dynamics model with diffusion and general infection function, International Journal of Computer Mathematics, DOI: 10.1080/00207160.2018.1527028.
DOI
|
19 |
W. Qin , L. Wang , X. Ding , A non-standard finite difference method for a hepatitis b virus infection model with spatial diffusion, Journal of Difference Equations and Applications, 20 (2014) 1641-1651.
DOI
|
20 |
K. Manna and S.P. Chakrabarty, Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids, Journal of Difference Equations and Applications, 21(10) (2015), 918-933.
DOI
|
21 |
J. Zhou and Y. Yang, Global dynamics of a discrete viral infection model with time delay, virus-to-cell and cell-to-cell transmissions, Journal of Difference Equations and Applications, 23(11) (2017).
|
22 |
J. Xu, J. Hou, Y. Geng and S. Zhang, Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence, Advances in Difference Equations (2018) 2018:108.
DOI
|
23 |
S. Elaydi, An introduction to Difference Equations 3rd ed, Springer, New York, (2005).
|
24 |
J. N., Blankson, D. Persaud, and R. F. Siliciano, The challenge of viral reservoirs in HIV-1 infection. Annual Review of Medicine, 53 (2002), 557-593.
DOI
|
25 |
J. N., Blankson, D. Persaud, and R. F. Siliciano, The challenge of viral reservoirs in HIV-1 infection. Annual Review of Medicine, 53 (2002), 557-593.
DOI
|
26 |
A. R.M. Carvalho and C. M. A. Pinto, Contributions of the latent reservoir and of the pool of long -lived chronically infected T cells in HIV dynamics: a fractional approach, Proceedings of the ENOC2017, June
|
27 |
A. M. Elaiw, Global threshold dynamics in humoral immunity viral infection models including an eclipse stage of infected cells, J. Korean Soc. Ind. Appl. Math., 19:2 (2015), 137-170.
DOI
|
28 |
M. A. Nowak and C.R.M. Bangham. Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
DOI
|
29 |
D.S. Callaway, and A.S. Perelson, HIV-1 infection and low steady state viral loads, Bulletin of Mathematical Biology, 64 (2002), 29-64.
DOI
|
30 |
A. M. Elaiw and N. H. AlShamrani, Global analysis for a delay-distributed viral infection model with antibodies and general nonlinear incidence rate, J. Korean Soc. Ind. Appl. Math., 18(4) (2014), 317-335.
DOI
|
31 |
H. Shu, L. Wang and J. Watmough, Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL imune responses, SIAM Journal of Applied Mathematics, 73(3) (2013), 1280-1302.
DOI
|
32 |
P. Georgescu and Y.H. Hsieh, Global stability for a virus dynamics model with nonlinear incidence of infection and removal, SIAM Journal of Applied Mathematics, 67 (2006), 337-353.
|
33 |
A. M. Elaiw, E. Kh. Elnahary and A. A. Raezah, Effect of cellular reservoirs and delays on the global dynamics of HIV, Advances in Difference Equations, (2018) 2018:85.
DOI
|
34 |
L. Gibelli, A. Elaiw, M.A. Alghamdi and A.M. Althiabi, Heterogeneous population dynamics of active particles: Progression, mutations, and selection dynamics, Mathematical Models and Methods in Applied Sciences, 27, (2017), 617-640.
DOI
|
35 |
A. M. Elaiw, A. A. Raezah and B. S. Alofi, Dynamics of delayed pathogen infection models with pathogenic and cellular infections and immune impairment, AIP Advances, 8 (2018) Article ID 025323.
|
36 |
A. M. Elaiw, A. A. Raezah and S. A. Azoz, Stability of delayed HIV dynamics models with two latent reservoirs and immune impairment, Advances in Difference Equations, (2018) 2018:414.
DOI
|
37 |
K. Hattaf, N. Yousfi and A. Tridane, Mathematical analysis of a virus dynamics model with general incidence rate and cure rate, Nonlinear Analysis: Real World Applications, 13(4) (2012), 1866-1872.
DOI
|
38 |
M. Y. Li and L. Wang, Backward bifurcation in a mathematical model for HIV infection in vivo with antiretroviral treatment, Nonlinear Analysis: Real World Applications, 17 (2014), 147-160.
DOI
|
39 |
F. Zhang, J. Li, C. Zheng, L. Wang, Dynamics of an HBV/HCV infection model with intracellular delay and cell proliferation , Communications in Nonlinear Science and Numerical Simulation, 42 (2017), 464-476.
DOI
|
40 |
K.Wang, A. Fan, and A. Torres, Global properties of an improved hepatitis B virus model, Nonlinear Analysis: Real World Applications, 11 (2010), 3131-3138.
DOI
|
41 |
X. Song and A. Neumann, Global stability and periodic solution of the viral dynamics, Journal of Mathematical Analysis and Applications, 329 (2007), 281-297.
DOI
|
42 |
X. Shi, X. Zhou and X. Song, Dynamical behavior of a delay virus dynamics model with CTL immune response, Nonlinear Analysis: Real World Applications, 11 (2010), 1795-1809.
DOI
|
43 |
A. M. Elaiw and N. H. AlShamrani, Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Analysis: Real World Applications, 26, (2015), 161-190.
DOI
|
44 |
A.M. Elaiw, Global properties of a class of HIV models, Nonlinear Analysis: Real World Applications, 11 (2010), 2253-2263.
DOI
|
45 |
A.M. Elaiw, Global properties of a class of virus infection models with multitarget cells, Nonlinear Dynamics, 69(1-2) (2012), 423-435
DOI
|
46 |
A. M. Elaiw and N. A. Almuallem, Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells, Mathematical Methods in the Applied Sciences, 39 (2016), 4-31.
DOI
|
47 |
A. M. Elaiw and N. H. AlShamrani, Stability of a general delay-distributed virus dynamics model with multistaged infected progression and immune response, Mathematical Methods in the Applied Sciences, 40(3) (2017), 699-719.
DOI
|
48 |
A.M. Elaiw and S.A. Azoz, Global properties of a class of HIV infection models with Beddington-DeAngelis functional response, Mathematical Methods in the Applied Sciences, 36 (2013), 383-394.
DOI
|
49 |
A. M. Elaiw, Global dynamics of an HIV infection model with two classes of target cells and distributed delays, Discrete Dynamics in Nature and Society, 2012 (2012) Article ID 253703.
|
50 |
A. M. Elaiw, I. A. Hassanien, S. A. Azoz, Global stability of HIV infection models with intracellular delays, Journal of the Korean Mathematical Society, 49(4) (2012), 779-794.
DOI
|
51 |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM Journal of Applied Mathematics, 70(7) (2010), 2693-2708.
DOI
|
52 |
A.S. Perelson, D.E. Kirschner and R.D. Boer, Dynamics of HIV infection of CD4+ T cells, Mathematical Biosciences, 114(1). (1993), 81-125.
DOI
|
53 |
B. Buonomo and C. Vargas-De-Leon, Global stability for an HIV-1 infection model including an eclipse stage of infected cells, Journal of Mathematical Analysis and Applications, 385 (2012), 709-720.
DOI
|
54 |
A. M. Elaiw, A. A. Almatrafi, and A. D. Hobiny, Effect of antibodies on pathogen dynamics with delays and two routes of infection, AIP Advances 8 (2018), Article ID 065104.
|
55 |
A. M. Elaiw and N. H. AlShamrani, Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays, Mathematical Methods in the Applied Science, 36 (2018), 125-142.
|
56 |
A. M. Elaiw, T. O. Alade, S. M. Alsulami, Analysis of latent CHIKV dynamics models with general incidence rate and time delays. Journal of Biological Dynamics, 12(1) (2018), 700-730.
DOI
|