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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 12
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Research Article

Global asymptotic stability for a distributed delay differential–difference system of a Kermack–McKendrick SIR model

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Pages 3463-3475 | Received 29 Sep 2021, Accepted 02 May 2022, Published online: 14 May 2022

References

  • Adimy M, Chekroun A, Ferreira CP. Global dynamics of a differential–difference system: a case of Kermack–McKendrick SIR model with age-structured protection phase. Math Biosci Eng. 2020;17(2):1329–1354. doi:10.3934/mbe.2020067
  • Adimy M, Chekroun A, Kuniya T. Traveling waves of a differential–difference diffusive Kermack–McKendrick epidemic model with age-structured protection phase. J Math Anal Appl. 2022;505(1):125464.
  • Adimy M, Chekroun A, Touaoula TM. Age-structured and delay differential–difference model of hematopoietic stem cell dynamics. Discrete Contin Dyn Syst B. 2015;20(9):2765–2791.
  • Adimy M, Chekroun A, Touaoula TM. Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics. Appl Anal. 2017;96:429–440. doi:10.1080/00036811.2016.1139698
  • Beretta E, Takeuchi Y. Global stability of an SIR epidemic model with time delays. J Math Biol. 1995;33:250–260.
  • Beretta E, Hara T, Ma W, et al. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal. 2001;47:4107–4115.
  • Takeuchi Y, Ma W, Beretta E. Global asymptotic properties of a delay SIR epidemic model with finite incubation times. Nonlinear Anal. 2000;42:931–947.
  • McCluskey CC. Complete global stability for an SIR epidemic model with delay – distributed or discrete. Nonlinear Anal: Real World Appl. 2010;11:55–59.
  • McCluskey CC. Global stability of an SIR epidemic model with delay and general nonlinear incidence. Math Biosci Eng. 2010;7:837–850.
  • Li MY, Shuai Z, Wang C. Global stability of multi-group epidemic models with distributed delays. J Math Anal Appl. 2010;361:38–47.
  • Enatsu Y, Nakata Y, Muroya Y. Lyapunov functional techniques for the global stability analysis of a delayed SIRs epidemic model. Nonlinear Anal: Real World Appl. 2012;13:2120–2133.
  • Chekroun A, Kuniya T. An infection age-space structured SIR epidemic model with Neumann boundary condition. Appl Anal. 2020;99(11):1972–1985.
  • Bai Z, Zhang S. Traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates and distributed delay. Commun Nonlinear Sci Numer Simul. 2015;22:1370–1381.
  • Hale JK, Cruz MA. Existence, uniqueness and continuous dependence for hereditary systems. Ann Mat Pura Appl. 1970;85(1):63–81.
  • Hale JK, Verduyn Lunel SM. Introduction to functional differential equations. New York: Springer; 1993.
  • Cruz MA, Hale JK. Stability of functional differential equations of neutral type. J Differ Equ. 1970;7(2):334–355.
  • Gu K, Liu Y. Lyapunov–Krasovskii functional for uniform stability of coupled differential-functional equations. Automatica. 2009;45(3):798–804.
  • Diekmann O, Getto P, Nakata Y. On the characteristic equation λ=α1+(α2+α3λ)e−λ and its use in the context of a cell population model. J Math Biol. 2015;72:877–908.
  • Li MY. An introduction to mathematical modeling of infectious diseases. Springer Cham: Springer International Publishing; 2018. (Mathematics of planet earth collection). Available from: https://www.springer.com/gp/book/9783319721217.
  • Hou M, Duan G, Guo M. New versions of Barbalat's lemma with applications. J Control Theory Appl. 2010;8(4):545–547.

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