Open Access
Issue
Math. Model. Nat. Phenom.
Volume 16, 2021
Article Number 13
Number of page(s) 26
DOI https://doi.org/10.1051/mmnp/2021004
Published online 22 March 2021
  1. F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology. Springer, New York (2011). [Google Scholar]
  2. V. Capasso and G. Serio, A generalization of the Kermack-Mckendric deterministic epidemic model. Math. Biosci. 42 (1978) 43–61. [Google Scholar]
  3. S.A. Carvalho, S.O. da Silva and I.C. da Cunha, Mathematical modeling of dengue epidemic: control methods and vaccination strategies. Preprint arXiv:1508.00961 (2015). [Google Scholar]
  4. O. Diekman and J.A.P. Heesterbeek: Mathematical Epidemiology of Infectious Disease. Wiley, New York (2000). [Google Scholar]
  5. O. Diekmann, J.A.P. Heesterbeek and M.G. Roberts, The construction of next-generation matrices for compartmental epidemic models. J. R. Soc. Interface 7 (2010) 873–885. [CrossRef] [PubMed] [Google Scholar]
  6. J.K. Ghosh, U. Ghosh, M.H.A. Biswas and S. Sarkar, Qualitative analysis and optimal control strategy of an SIR model with saturated incidence and treatment. To appear in: Differ. Equ. Dyn. Syst. (2019), https://doi.org/10.1007/s12591-019-00486-8.. [Google Scholar]
  7. S. Jana, S.K. Nandi and T.K. Kar, Complex dynamics of an SIR epidemic model with saturated incidence rate and treatment. Acta Biotheor. 64 (2016) 65–84. [PubMed] [Google Scholar]
  8. Y.A. Kuznetsov: Elements of Applied Bifurcation Theory. Springer, New York (1998). [Google Scholar]
  9. A.A. Lashari, Optimal control of an SIR epidemic model with a saturated treatment. Appl. Math. Inf. Sci. 10 (2016) 185–191. [Google Scholar]
  10. S. Lenhart and J.T. Workman, Optimal control applied to biological model. Mathematical and computational biology series. Chapman and Hall/CRC, Boca Raton (2007). [Google Scholar]
  11. J. Li, Z. Teng, G. Wang, L. Zhang and C. Hu, Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment. Chaos. Solit. Fract. 99 (2017) 63–71. [Google Scholar]
  12. M. Lu, J. Huang, S. Ruan et al., Global dynamics of a susceptible-infectious-recovered epidemic model with a generalized nonmonotone incidence rate. To appear in: J. Dyn. Differ. Equ. (2020) https://doi.org/10.1007/s10884-020-09862-3.. [Google Scholar]
  13. M. Lu, J. Huang, S. Ruan and P. Yu, Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate. J. Differ. Equ. 267 (2019) 1859–1898. [PubMed] [Google Scholar]
  14. M. Martcheva, An Introduction to Mathematical Epidemiology. Springer, New York (2015). [Google Scholar]
  15. J.D. Murray, Mathematical Biology. Springer, New York (1993). [Google Scholar]
  16. S.K. Nandi, S. Jana, M. Mandal and T.K. Kar, Complex dynamics and optimal treatment of an epidemic model with two infectious diseases. Int. J. Appl. Comput. Math. 5 (2019) 29. [Google Scholar]
  17. L. Perko, Differential Equations and Dynamical Systems, in Vol. 7. Springer, New York (2000). [Google Scholar]
  18. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes. Wiley, New Jersey (1962). [Google Scholar]
  19. O. Sharomi and T. Malik, Optimal control in epidemiology. Ann. Oper. Res. 251 (2017) 55–71. [Google Scholar]
  20. R.K. Upadhyay, A.K. Pal, S. Kumari and P. Roy, Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates. Nonlinear Dyn. 96 (2019) 2351–2368. [Google Scholar]
  21. P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease trans-mission. Math Biosci. 180 (2002) 29–48. [Google Scholar]
  22. W. Wang, Backward bifurcation of an epidemic model with treatment. Math. Biosci. 201 (2006) 58–71. [Google Scholar]
  23. W. Wang and S. Ruan, Bifurcation in an epidemic model with constant removal rate of the infectives. J. Math. Anal. Appl. 291 (2004) 775–793. [Google Scholar]
  24. J. Wang, S. Liu, B. Zheng and Y. Takeuchi, Qualitative and bifurcation analysis using an SIR model with a saturated treatment function. Math. Comput. Model. 55 (2012) 710–722. [Google Scholar]
  25. D. Xiao and S. Ruan, Global analysis of an epidemic model with a nonlinear incidence rate. Math. Biosci. 208 (2007) 419–429. [Google Scholar]
  26. R. Xu, Z. Ma and Z. Wang, Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity. Comput. Math. Appl. 59 (2010) 3211–3221. [Google Scholar]
  27. X. Zhang and X.N. Liu, Backward bifurcation of an epidemic model with saturated treatment function. J. Math. Anal. Appl. 348 (2008) 433–443. [Google Scholar]
  28. J. Zhang, J. Ren and X. Zhang, Dynamics of an SLIR model with nonmonotone incidence rate and stochastic perturbation. Math. Biosci. Eng. 16 (2019) 5504–5530. [PubMed] [Google Scholar]
  29. Z. Zhonghua and S. Yaohong, Qualitative analysis of a SIR epidemic model with saturated treatment rate. J. Appl. Math. Comput. 34 (2010) 177–194. [Google Scholar]

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