[Alexander, M.E., Summers, A.R. and Moghadas, S.M. (2006). Neimark-Sacker bifurcations in a non-standard numerical scheme for a class of positivity-preserving ODEs, Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences 462(2074): 3167-3184.10.1098/rspa.2006.1724]Search in Google Scholar
[Anderson, R. and May, R. (1991). Infectious Diseases of Hu- mans: Dynamics and Control, Oxford University Press, Oxford/New York, NY.]Search in Google Scholar
[Anguelo, V.R. and Lubuma, J. (2003). Nonstandard finite difference method by nonlocal approximation, Mathematics and Computers in Simulation 61(3): 465-475.10.1016/S0378-4754(02)00106-4]Search in Google Scholar
[Arenas, A., Morao, J. and Cort´es, J. (2008). Non-standard numerical method for a mathematical model of RSV epidemiological transmission, Computers and Mathematics with Applications 56(3): 670-678.10.1016/j.camwa.2008.01.010]Search in Google Scholar
[Bruggeman, J., Burchard, H., Kooi, B.W. and Sommeijer, B. (2007). A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems, Applied Numerical Mathematics 57(1): 36-58.10.1016/j.apnum.2005.12.001]Search in Google Scholar
[Chen, M. and Clemence, D. (2006). Stability properties of a nonstandard finite difference scheme for a hantavirus epidemic model, Journal of Difference Equations and Applications 12(12): 1243-1256.10.1080/10236190600986537]Search in Google Scholar
[Chinviriyasit, S. and Chinviriyasit, W. (2010). Numerical modelling of an SIR epidemic model with diffusion, Applied Mathematics and Computation 216(2): 395-409. Dimitrov, D.T. and Kojouharov, H. (2005). Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems, Applied Mathematics Letters 18(7): 769-774.]Search in Google Scholar
[Dimitrov, D. and Kojouharov, H. (2007). Stability-preserving finite-difference methods for general multi-dimensional autonomous dynamical systems, International Journal of Numerical Analysis and Modeling 4(2): 280-290.]Search in Google Scholar
[Dimitrov, D. and Kojouharov, H. (2008). Nonstandard finite difference methods for predator-prey models with general functional response, Mathematics and Computers in Simulation 78(1): 1-11.10.1016/j.matcom.2007.05.001]Search in Google Scholar
[Ding, D., Ma, Q. and Ding, X. (2013). A non-standard finite difference scheme for an epidemic model with vaccination, Journal of Difference Equations and Applications 19(2): 179-190.10.1080/10236198.2011.614606]Search in Google Scholar
[Dumont, Y. and Lubuma, J.M.-S. (2005). Non-standard finite-difference methods for vibro-impact problems, Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences 461(2058): 1927-1950. Enatsu, Y., Nakata, Y. and Muroya, Y. (2010). Global stability for a class of discrete SIR epidemic models, Mathematical Biosciences and Engineering 7: 347-361.]Search in Google Scholar
[Enszer, J.A. and Stadtherr, M.A. (2009). Verified solution method for population epidemiology models with uncertainty, International Journal of Applied Mathematics and Computer Science 19(3): 501-512, DOI: 10.2478/v10006-009-0040-4.10.2478/v10006-009-0040-4]Search in Google Scholar
[Gumel, A. (2002). A competitive numerical method for a chemotherapy model of two HIV subtypes, Applied Mathematics and Computation 131(2): 329-337.10.1016/S0096-3003(01)00150-3]Search in Google Scholar
[Hildebrand, F. (1968). Finite Difference Equations and Simulations, Prentice-Hall, Englewood Cliffs, NJ.]Search in Google Scholar
[Jódar, L., Villanueva, R., Arenas, A. and Gonz´alez, G. (2008). Nonstandard numerical methods for a mathematical model for influenza disease, Mathematics and Computers in Simulation 79(3): 622-633.10.1016/j.matcom.2008.04.008]Search in Google Scholar
[Jang, S. (2007). On a discrete west Nile epidemic model, Computational and Applied Mathematics 26(3): 397-414.10.1590/S0101-82052007000300005]Search in Google Scholar
[Jang, S. and Elaydi, S. (2003). Difference equations from discretization of a continuous epidemic model with immigration of infectives, Canadian Applied Mathematics Quarterly 11(1): 93-105. Jansen, H. and Twizell, E. (2002). An unconditionally convergent discretization of the SEIR model, Mathematics and Computers in Simulation 58(2): 147-158.]Search in Google Scholar
[Kouche, M. and Ainseba, B. (2010). A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation, International Journal of Applied Mathematics and Computer Science 20(3): 601-612, DOI: 10.2478/v10006-010-0045-z.10.2478/v10006-010-0045-z]Search in Google Scholar
[Lambert, J. (1973). Computational Methods in Ordinary Differential Equations, Wiley, New York, NY.]Search in Google Scholar
[Ma, Z., Zhou, Y., Wang, W. and Jing, Z. (2004). The Mathematical Modeling and Study of the Dynamics of Infectious Diseases, Science Press, Beijing.]Search in Google Scholar
[Mickens, R. (1994). Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore.10.1142/2081]Search in Google Scholar
[Mickens, R. (2000). Advances in the Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore. Mickens, R. (2002). Nonstandard finite difference schemes for differential equations, Journal of Difference Equations and Applications 8(9): 823-847.10.1142/4272]Search in Google Scholar
[Mickens, R. (2005). Dynamic consistency: A fundamental principle for constructing nonstandard finite difference schemes for differential equations, Journal of Difference Equations and Applications 11(7): 645-653.10.1080/10236190412331334527]Search in Google Scholar
[Moghadas, S., Alexander, M. and Corbett, B.D.and Gumel, A. (2003). A positivity preserving Mickens-type discretization of an epidemic model, Journal of Difference Equations and Applications 9(11): 1037-1051.10.1080/1023619031000146913]Search in Google Scholar
[Moghadas, S. and Gumel, A. (2003). A mathematical study of a model for childhood diseases with non-permanent immunity, Journal of Computational and Applied Mathematics 157(2): 347-363.10.1016/S0377-0427(03)00416-3]Search in Google Scholar
[Muroya, Y., Nakata, Y., Izzo, G. and Vecchio, A. (2011). Permanence and global stability of a class of discrete epidemic models, Nonlinear Analysis: Real World Applications 12(4): 2105-2117. Obaid, H., Ouifki, R. and Patidar, K.C. (2013). An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection, International Journal of Applied Mathematics and Computer Science 23(2): 357-372, DOI: 10.2478/amcs-2013-0027.10.2478/amcs-2013-0027]Search in Google Scholar
[Oran, E. and Boris, J. (1987). Numerical Simulation of Reactive Flow, Elsevier, New York, NY.]Search in Google Scholar
[Parra, G.G., Arenas, A. and Charpentier, B.C. (2010). Combination of nonstandard schemes and Richardson’s extrapolation to improve the numerical solution of population models, Mathematical and Computer Modelling 52(7): 1030-1036.10.1016/j.mcm.2010.03.015]Search in Google Scholar
[Potter, D. (1973). Computational Physics, Wiley-Interscience, New York, NY.]Search in Google Scholar
[Sekiguchi, M. (2009). Permanence of some discrete epidemic models, International Journal of Biomathematics 2(4): 443-461. Sekiguchi, M. (2010). Permanence of a discrete SIRS epidemic model with time delays, Applied Mathematics Letters 23(10): 1280-1285.]Search in Google Scholar
[Sekiguchi, M. and Ishiwata, E. (2010). Global dynamics of a discretized SIRS epidemic model with time delay, Journal of Mathematical Analysis and Applications 371(1): 195-202.10.1016/j.jmaa.2010.05.007]Search in Google Scholar
[Stuart, A. and Humphries, A. (1996). Dynamic System and Numerical Analysis, Cambridge University Press, Cambridge.]Search in Google Scholar
[Sundarapandian, V. (2003). An invariance principle for discrete-time nonlinear systems, Applied Mathematics Letters 16(1): 85-91. 10.1016/S0893-9659(02)00148-9]Search in Google Scholar