REFERENCES
- [1] Nowak, M. A., and C. R. M. Bangham (1996) Population dynamics of immune responses to persistent viruses, Science 272, 7479.
- [2] Shu, H., L. Wang, and J. Watmough (2013) Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL imune responses, SIAM Journal of Applied Mathematics 73(3), 12801302.
- [3] Gibelli, L., A. Elaiw, M. A. Alghamdi, and A. M. Althiabi (2017) Heterogeneous population dynamics of active particles: progression, mutations, and selection dynamics, Mathematical Models and Methods in Applied Sciences 27, 617640.
- [4] Huang, G., Y. Takeuchi, and W. Ma (2010) Lyapunov functionals for delay differential equations model of viral infections, SIAM Journal of Applied Mathematics 70(7), 26932708.
- [5] Callaway, D. S., and A. S. Perelson (2002) HIV-1 infection and low steady state viral loads, Bulletin of Mathematical Biology 64, 2964.
- [6] Elaiw, A. M., A. A. Raezah, and S. A. Azoz (2018) Stabilityof delayed HIV dynamics models with two latent reservoirs and immune impairment, Advances in Difference Equations 2018, 414.
- [7] Georgescu, P., and Y. H. Hsieh (2006) Global stability for a virus dynamics model with nonlinear incidence of infection and removal, SIAM Journal of Applied Mathematics 67, 337353.
- [8] Hattaf, K., N. Yousfi, and A. Tridane (2012) Mathematical analysis of a virus dynamics model with general incidence rate and cure rate, Nonlinear Analysis: Real World Applications 13(4), 18661872.
- [9] Elaiw, A. M., and A. D. AlAgha (2020) Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immuneresponse, Applied Mathematics and Computation 367, Article 124758.
- [10] Li, B., Y. Chen, X. Lu, and S. Liu (2016) A delayed HIV-1 model with virus waning term, Mathematical Biosciences and Engineering 13,135157.
- [11] Elaiw, A. M., E. Kh. Elnahary, and A. A. Raezah (2018) Effect of cellular reservoirs and delays on the global dynamics of HIV, Advances in Difference Equations 2018, 85.
- [12] Zhang, F., J. Li, C. Zheng, and L. Wang (2017) Dynamics of an HBV/HCV infection model with intracellular delay and cell proliferation, Communications in Nonlinear Science and Numerical Simulation 42, 464476.
- [13] Zhang, S., and X. Xu (2017) Dynamic analysis and optimal control for a model of hepatitis C with treatment, Communications in Nonlinear Science and Numerical Simulation 46, 1425.
- [14] Elaiwand, A. M., and E. Kh. Elnahary (2019) Analysis of general humoral immunity HIV dynamics model with HAART and distributed delays, Mathematics 7(2), Article Number: 157.
- [15] Li, M. Y., and H. Shu (2012) Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response, Nonlinear Analysis: Real World Applications 13,10801092.
- [16] Shi, X., X. Zhou, and X. Song (2010) Dynamical behavior of a delay virus dynamics model with CTL immune response, Nonlinear Analysis: Real World Applications 11, 17951809.
- [17] Elaiw, A. M., and N. H. AlShamrani (2015) Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Analysis: Real World Applications 26, 161190.
- [18] Elaiw, A. M. (2010) Global properties of a class of HIVmodels, Nonlinear Analysis: Real World Applications 11, 22532263.
- [19] Elaiw. A. M. (2012) Global properties of a class of virus infection models with multitarget cells, Nonlinear Dynamics 69(12), 423435.
- [20] Elaiw, A. M., and N. A. Almuallem (2015) Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells, AppliedMathematicsand Computation 265, 10671089.
- [21] Elaiw, A. M., and N. A. Almuallem (2016) Global dynamicsof delay-distributed HIVinfection modelswith differential drug efficacy in cocirculating target cells, Mathematical Methods in the Applied Sciences 39, 431.
- [22] Elaiw, A. M., and N. H. AlShamrani (2017) Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response, Mathematical Methods in the Applied Sciences 40(3), 699719.
- [23] Elaiw, A. M., I. A. Hassanien, and S. A. Azoz (2012) Global stability of HIV infection models with intracellular delays, Journal of the Korean Mathematical Society 49(4), 779794.
- [24] Elaiw, A. M., and S. A. Azoz (2013) Global properties of a class of HIV infection models with BeddingtonDeAngelis functional response, Mathematical Methods in the Applied Sciences 36, 383394.
- [25] Elaiw, A. M., and N. H. AlShamrani (2018) Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays, Mathematical Methods in the Applied Science 36, 125142.
- [26] Elaiw, A. M., S. F. Alshehaiween, and A. D. Hobiny (2019) Global properties of delay-distributed HIV dynamics model including impairment of B-cell functions, Mathematics 7, Article Number: 837.
- [27] Elaiw, A. M., and N. H. AlShamrani (2019) Stability of a general adaptive immunity virus dynamics model with multi-stagesof infected cellsand two routes of infection, Mathematical Methods in the Applied Sciences. doi: 10.1002/mma.5923
- [28] Korobeinikov, A. (2004) Global properties of basic virus dynamics models, Bulletin of Mathematical Biology 66(4), 879883.
- [29] Culshaw, R. V., S. Ruan, and G. Webb (2003) Amathematical model of cell-to-cell spread of HIV-1 that includes a time delay, Journal of Mathematical Biology, 46,425444.
- [30] Cheng, W., W. Ma, and S. Guo (2016) Aclass of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells and its stability analysis, Communications on Pure and Applied Analysis 15(3), 795806.
- [31] Lai, X., and X. Zou (2014) Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-tocell transmission, SIAM Journal of Applied Mathematics 74, 898917.
- [32] Pourbashash, H., S. S. Pilyugin, P. De Leenheer, and C. McCluskey (2014) Global analysis of within host virus models with cell-to-cell viral transmission, Discrete & Continuous Dynamical Systems-Series B 10, 33413357.
- [33] Chen, S.-S., C.-Y. Cheng, and Y. Takeuchi (2016) Stability analysis in delayed within-host viral dynamics with both viral and cellular infections, Journal of Mathematical Analysis and Applications 442, 642672.
- [34] Wang, J., M. Guo, X. Liu, and Z. Zhao (2016) Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Applied Mathematics and Computation 291, 149161.
- [35] Yang, Y., L. Zou, and S. Ruan (2015) Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions, Mathematical Biosciences 270, 183191.
- [36] Hobiny, A. D., A. M. Elaiw, and A. Almatrafi (2018) Stability of delayed pathogen dynamics models with latency and two routes of infection, Advances in Difference Equations 2018, 276.
- [37] Elaiw, A. M., A. Almatrafi, A. D. Hobiny, and K. Hattaf (2019) Global properties of a general latent pathogen dynamics model with delayed pathogenic and cellular infections, Discrete Dynamics in Nature and Society 2019, Article ID 9585497.
- [38] Elaiw, A. M., and A. A. Raezah (2017) Stability of general virus dynamics models with both cellular and viral infections and delays, Mathematical Methods in the Applied Sciences 40(16), 58635880.
- [39] Enatsu, Y., Y. Nakata, Y. Muroya, G. Izzo, and A. Vecchio (2012) Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, Journal of Difference Equations and Applications 18, 11631181.
- [40] Mickens, R. E. (1994) Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore.
- [41] Korpusik, A. (2017) A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection, Communications in Nonlinear Science and Numerical Simulation 43, 369384.
- [42] Anguelov, R., Y. Dumont, J. M.-S. Lubuma, and M. Shillo (2014) Dynamically consistent nonstandard finite difference schemes for epidemiological models, Journal of Computational and Applied Mathematics 255, 161182.
- [43] Wood, D. T., D. T. Dimitrov, and H. V. Kojouharov (2015) A nonstandard finite difference method for ndimensional productive-destructive systems, Journal of Difference Equations and Applications 21(3), 240 254.
- [44] Ding, D., and X. Ding (2014) Dynamic consistent non-standard numerical scheme for a dengue disease transmission model, Journal of Difference Equations and Applications 20, 492505.
- [45] Ding, D., W. Qin, and X. Ding (2015) Lyapunov functions and global stability for a discretized multi-group SIR epidemic model, Discrete and Continuous Dynamical Systems - Series B, 20, 19711981.
- [46] Teng, Z., L. Wang, and L. Nie (2015) Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence, Mathematical Methods in the Applied Sciences 38,47414759.
- [47] Yang, Y., J. Zhou, X. Ma, and T. Zhang (2016) 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, 10131020.
- [48] Xu, J., Y. Geng, and J. Hou (2017) A nonstandard finite difference scheme for a delayed and diffusive viral infection model with general nonlinear incidence rate, Computers and Mathematical with Applications 74, 17821798.
- [49] Yang, Y., X. S.Ma,and Y.H. Li(2016) Globalstability of a discrete virus dynamics model with Holling typeII infection function, Mathematical Methods intheApplied Sciences 39, 20782082.
- [50] Wang, J., Z. Teng, and H. Miao (2016) Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response, Advanced in Difference Equations 143. doi: 10.1186/ s13662-016-0862-y
- [51] Geng, Y., J. Xu, and J. Hou (2018) Discretization and dynamic consistency of a delayed and diffusive viral infection model, Applied Mathematics and Computation 316, 282295.
- [52] Qin, W., L. Wang, and X. Ding (2014) Anon-standard finite difference method for a hepatitis b virus infection model with spatial diffusion, Journal of Difference Equations and Applications 20, 16411651.
- [53] Elaiw, A. M., and M. A. Alshaikh (2019) Stability analysis of a general discrete-time pathogen infection model with humoral immunity, Journal of Difference Equations and Applications. doi: 10.1080/10236198. 2019.1662411
- [54] Elaiw, A. M., and M. A. Alshaikh (2019) Stability of discrete-time HIV dynamics models with three categories of infected CD4+ T-cells, Advances in Difference Equations 2019, 407.
- [55] Xu, J., J. Hou, Y. Geng, and S. Zhang (2018) Dynamic consistent NSFD scheme for a viral infection model with cellular infection and general nonlinear incidence, Advances in Difference Equations 2018, 108.
- [56] Mickens, R. E. (2000) Application of Nonstandard Finite Difference Scheme, World Scientific, Singapore.
- [57] Mickens, R. E. (2007) Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition, Numerical Methods for Partial Differential Equations 23, 672691.
- [58] Shi, P., and L. Dong (2014) Dynamical behaviors of a discrete HIV-1 virus modelwith bilinear infective rate, Mathematical Methods in the Applied Sciences 37, 22712280.
- [59] Hattaf, K., and N. Yousfi (2016) Global properties of a discrete viral infection model with general incidence rate, Mathematical Methods in the Applied Sciences 39, 9981004.