References
[1] Bai, Y.& Mu, X. (2018). Global asymptotic stability of a generalized SIRS epidemic model with transfer from infectious to susceptible, J. of Applied Analysis and Computation, 8, 402-412. doi: 10.11948/2018.402 [2] Brauer, F., van den Driessche, P., Wu, J. . (2008) Mathematical Epidemiology, Lecture Notes in Mathematics. Mathematical Biosciences Subseries, Vol. 1945, Springer, Berlin, Heidelberg. [3] Brauer, F., Castillo-Chavez, C., & Feng, Z. (2019). Mathematical models in epidemiology. Springer. [4] Buonomo B. and Lacitignola D. (2011) On the backward bifurcation of a vaccination model With nonlinear incidence, Nonlinear Analysis: Modelling and control, Vol. 16, No. 1, pp. 30-46. [5] Diekmann, O., Heesterbeek, J. A. P. & Roberts, M. G. (2010). The construction of next- generation matrices for compartmental epidemic models, J. R. Soc., Interface, 7, 873- 885. doi: 10.1098/rsif.2009.0386 [6] Diekmann, O., Heesterbeek, J. A. P., & Britton, T. (2013). Mathematical tools for understanding infectious disease dynamics. Princeton University Press. [7] Dubey, B., Dubey, P. and Dubey, U. S. (2016) Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate. Applications and Applied Mathematics: An International Journal, Vol. 11, iss. 1, pp. 97 – 116. [8] Elaiw, A. M. and Azoz, S. A. (2013) Global properties of a class of HIV Infection Models with Beddington-DeAngelis Functional Response. Mathematical Methods in the Applied Science, 36, 383 – 394. [9] Feng, X., Teng, Z., Wang, K. and Zhang, F. (2014) Backward Bifurcation and Global Stability in an Epidemic Model with Treatment and Vaccination. Discrete and Continuous Dynamical Systems Series B, Vol. 19, No. 4, pp. 999 – 1025. [10] Funk, S., Salathé, M., & Jansen, V. A. A. (2010). Modelling the influence of human behaviour on the spread of infectious diseases: A review. Journal of the Royal Society Interface, 7(50), 1247–1256. [11] Gao Y., Zhang W., Liu ., and Xiao Y. (2017) Bifurcation Analysis of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function. Journal of Applied Analysis and Computation, Vol. 7( 3), pp.1070 – 1094. [12] Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4), 599– 653. [13] Hu, Z. X., Ma, W. B. & Ruan, S. (2012). Analysis of SIR epidemic models with nonlinear incidence rate and treatment, Math. Biosci., 238 (2012), 12- 20. doi: 10.1016/j.mbs.2012.03.010 [14] Hu, Z., Ma, W. B. & Ruan, S. (2011). Bifurcations of an SIRS epidemic model with nonlinear incidence rate, Discrete Contin. Dynam. Syst. Ser. B, 15 , 93- 112. doi: 10.3934/dcdsb.2011.15.93. [15] Huang, G., Ma, W. and Takeuchi, Y. (2011) Global Analysis for Delay Virus Dynamics Model with Beddington-DeAngelis Functional Response. Applied Mathematics Letters, Vol. 24, 1199 – 1203. [16] Kaddar, A. (2010) Stability Analysis in a delayed SIR epidemic Model with a Saturated Incidence Rate”. Nonlinear Analysis Modelling and Control, Vol. 15, pp. 299 – 306. IJCSMT [17] Keeling, M. J., & Grenfell, B. T. (2002). Understanding the persistence of measles: Modelling the interplay of epidemiology and demography. Proceedings of the Royal Society B, 269(1489), 335–343. [18] LaSalle, J., Lefschez, S. (1976) The Stability of Dynamic Systems. SIAM, Philadelphia. [19] Li, G-H., Zhang, Y-X. (2017). Dynamic behaviours of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates. PLoS ONE 12(4): 30175789. [20] Li, G.H. & Zhang, Y. X. (2017). Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates, Plos One, 2017, 1- 28. doi: 10.1371/journal.pone.0175789. [21] Lloyd, A. L., & May, R. M. (2001). How viruses spread among hosts. Science Journal, 292(5519), 1316–1317. [22] Lin, Y. G., Jiang, D. Q. & M. L. Jin, (2015). Stationary distribution of a stochastic SIR model with saturated incidence and its asymptotic stability, Acta Mathematica Scientia, 35 , 619- 629. doi: 10.1016/S0252-9602(15)30008-4 [23] Liu, Q., Jiang, D., Hayat, T. & Ahmad, B. (2018). Analysis of a delayed vaccinated SIR epidemic model with temporary immunity and Levy jumps, Nonlinear Analysis: Hybrid Systems, 27 , 29-43. doi: 10.1016/j.nahs.2017.08.002. [24] Lu, M., Huang,J., Ruan, S. & Yu, P. (2019). Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate, J. Diff. Eqs., 267, 1859-1898. doi: 10.1016/j.jde.2019.03.005. [25] Mehta, R. & Deshmukh, A. (2025). Advanced Mathematical Epidemiology and Dynamic Modeling Approaches for Infectious Disease Spread: Insights, Challenges, and Future Prospects. Journal of Engineering Mathematics & Statistics, 9(2), 73 -83. [26] Naji, R. K. and Abdulatee B. H. (2017). The Dynamics of SIIR Model with Nonlinear Incidence Rate and Saturated Treatment Function. Sci.Int. , 29(6), 1223 – 1236. [27] Okuonghae, D. (2018) Backward Bifurcation of an Epidemiological Model with Saturated Incidence, Isolation and Treatment Functions: Qualitative Theory of Dynamical Systems, doi:10.1007/s12346-018-0293-0 [28] Pastor-Satorras, R., & Vespignani, A. (2001). Epidemic spreading in scale-free networks. Physical Review Letters, 86(14), 3200–3203. [29] Riley, S. (2007). Large-scale spatial -transmission models of infectious disease. Science Journal, 316(5829), 1298–1301. [30] Ryu, S., Chun, J. Y., Lee, S., Yoo, D., Kim, Y., Ali, S. T., & Chun, B. C. (2022). Epidemiology and Transmission Dynamics of Infectious Diseases and Control Measures. Viruses, 14(11), 2510. https://doi.org/10.3390/v14112510 [31] Safi, M. A., Garba, S. M. (2012) Global stability analysis of SEIR model with Holling type II incidence function. Comput.,Math. Methods Med. [32] Udoo, I. J. M. (2019). A qualitative analysis of an SIIR epidemic model with saturated incidence, awareness and treatment functions. Journal of Nigerian Society for Mathematical Biology. 2(1), 145-172 [33] Zhou, L. H. and Fan, M. (2012) Dynamics of an SIR epidemic model with limited medical resources revisited, Nonlinear Anal.: Real World Appl., Vol. 13, pp. 312 – 324