[1] Kribs-Zaleta C M, Velasco-Hernández J X. A simple vaccination model with multiple endemic states. Mathematical Biosciences, 2000, 164(2):183-201
[2] Arino J, McCluskey C C, van den Driess P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM Journal on Applied Mathematics, 2003, 64(1):260-276
[3] Li J, Ma Z, Zhou Y. Global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria. Acta Mathematica Scientia, 2006, 26B(1):83-93
[4] Liu X, Takeuchi Y, Iwami S. SVIR epidemic models with vaccination strategies. Journal of Theoretical Biology, 2008, 253(1):1-11
[5] Li J, Yang Y. SIR-SVS epidemic models with continuous and impulsive vaccination strategies. Journal of Theoretical Biology, 2011, 280(1):108-116
[6] Zhu Q, Hao Y, Ma J, Yu S, Wang Y. Surveillance of hand, foot, and mouth disease in mainland china (2008-2009). Biomedical and Environmental Sciences, 2011, 24(4):349-356
[7] Martcheva M. Avian flu:modeling and implications for control. Journal of Biological Systems, 2014, 22(1):151-175
[8] Wang W, Ruan S. Simulating the SARS outbreak in beijing with limited data. Journal of Theoretical Biology, 2004, 227(3):369-379
[9] Liljeros F, Edling C R, Amaral L A N. Sexual networks:implications for the transmission of sexually transmitted infections. Microbes and Infection, 2003, 5(2):189-196
[10] Liu W M, Levin S A, Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological model. Journal of Mathematical Biology, 1986, 23(2):187-204. 18
[11] Capasso V, Serio G. A generalization of the Kermack-McKendrick deterministic epidemic model. Mathematical Biosciences, 1978, 42(1/2):43-61
[12] Hattaf K, Lashari A A, Louartassi Y, Yousfi N. A delayed SIR epidemic model with general incidence rate. Electronic Journal of Qualitative Theory of Differential Equations, 2013(3):1-9
[13] Wang L, Liu Z, Zhang X. Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence. Applied Mathematics and Computation, 2016, 284:47-65
[14] Hattaf K. Global stability and Hopf bifurcation of a generalized viral infection model with multi-delays and humoral immunity. Physica A:Statal Mechanics and its Applications, 2020, 545:123689
[15] Wang J, Huang G, Takeuchi Y, Liu S. SVEIR epidemiological model with varying infectivity and distributed delays. Mathematical Biosciences and Engineering, 2011, 8(3):875-888
[16] Xu R. Global stability of a delayed epidemic model with latent period and vaccination strategy. Applied Mathematical Modelling, 2012, 36(11):5293-5300
[17] Duan X, Yuan S, Li X. Global stability of an SVIR model with age of vaccination. Applied Mathematics and Computation, 2014, 226:528-540
[18] Meng X, Chen L, Wu B. A delay SIR epidemic model with pulse vaccination and incubation times. Nonlinear Analysis:Real World Applications, 2010, 11(1):88-98
[19] Gao S, Chen L, Nieto J J, Torres A. Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine, 2006, 24(35/36):6037-6045
[20] Zhang T, Zhang T Q, Meng X. Stability analysis of a chemostat model with maintenance energy. Applied Mathematics Letters, 2017, 68:1-7
[21] Zhang T, Liu X, Meng X, Zhang T Q. Spatio-temporal dynamics near the steady state of a planktonic system. Computers and Mathematics with Applications, 2018, 75(12):4490-4504
[22] Hattaf K, Yousfi N. Global stability for reaction-diffusion equations in biology. Computers Mathematics with Applications, 2013, 66(8):1488-1497
[23] Webby R J, Webster R G. Are we ready for pandemic influenza? Science, 2003, 302:1519-1522
[24] Xu Z, Ai C. Traveling waves in a diffusive influenza epidemic model with vaccination. Applied Mathematical Modelling, 2016, 40(15/16):7265-7280
[25] Abdelmalek S, Bendoukha S. Global asymptotic stability of a diffusive SVIR epidemic model with immigration of individuals. Electronic Journal of Differential Equations, 2016, 2016(129/324):1-14
[26] Xu Z, Xu Y, Huang Y. Stability and traveling waves of a vaccination model with nonlinear incidence. Computers and Mathematics with Applications, 2018, 75(2):561-581
[27] Mickens R E. Nonstandard Finite Difference Models of Differential Equations. World Scientific, December 1993
[28] Arenas A J, Morano J A, Cortés J C. Non-standard numerical method for a mathematical model of RSV epidemiological transmission. Computers and Mathematics with Applications, 2008, 56(3):670-678
[29] Hattaf K, Yousfi N. Global properties of a discrete viral infection model with general incidence rate. Mathematical Methods in the Applied Sciences, 2016, 39(5):998-1004
[30] Hattaf K, Yousfi N. A numerical method for delayed partial differential equations describing infectious diseases. Computers and Mathematics with Applications, 2016, 72(11):2741-2750
[31] Liu J, Peng B, Zhang T. Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence. Applied Mathematics Letters, 2015, 39:60-66
[32] Muroya Y, Bellen A, Enatsu Y, Nakata Y. Global stability for a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population. Nonlinear Analysis:Real World Applications, 2013, 13(1):258-274
[33] Qin W, Wang L, Ding X. A non-standard finite difference method for a hepatitis B virus infection model with spatial diffusion. Journal of Difference Equations and Applications, 2014, 20(12):1641-1651
[34] Geng Y, Xu J. Stability preserving NSFD scheme for a multi-group SVIR epidemic model. Mathematical Methods in the Applied Sciences, 2017, 40(13):4917-4927
[35] Ding D, Ma Q, Ding X. A non-standard finite difference scheme for an epidemic model with vaccination. Journal of Difference Equations and Applications, 2013, 19(2):179-190
[36] Yang Y, Zhou J, Ma X, Zhang T. Nonstandard finite difference scheme for a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions. Computers and Mathematics with Applications, 2016, 72(4):1013-1020
[37] Zhou J, Yang Y, Zhang T. Global dynamics of a reaction-diffusion waterborne pathogen model with general incidence rate. Journal of Mathematical Analysis and Applications, 2018, 466(1):835-859
[38] Martin R H, Smith H L. Abstract functional differential equations and reaction-diffusion systems. Transactions of the American Mathematical Society, 1990, 321(1):1-44
[39] Fujimoto T, Ranade R R. Two characterizations of inverse-positive matrices:the Hawkins-Simon condition and the Le Chatelier-Braun principle. The Electronic Journal of Linear Algebra, 2004, 11:59-65
