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Journal of Applied Mathematics and Computing

Erschienen in:

16.08.2018 | Original Research

Stability and Hopf bifurcation analysis for an HIV infection model with Beddington–DeAngelis incidence and two delays

verfasst von: Hui Miao, Chengjun Kang

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2019

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Abstract

In this paper, we investigate the dynamical properties for a model of delayed differential equations which describes a virus–immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. The model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria for the CTL immune response model has been studied.

Vorheriger Artikel M-polynomial revisited: Bethe cacti and an extension of Gutman’s approach

Nächster Artikel Oscillation of Emden–Fowler type nonlinear neutral delay dynamic equation on time scales

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Culshaw, R., Ruan, S.: A delay-differential equation model of HIV infection of CD4+T-cell. Math. Biosi. 165, 27–39 (2000)CrossRefMATH

Ebert, D., Rohringer, C.D.Z., Carius, H.J.: Dose effects and density-dependent regulation of two microparasites of Daphnia magna. Oecologia 122, 200–209 (2000)CrossRef

Regoes, R.R., Ebert, D., Bonhoeffer, S.: Dose-dependent infection rates of parasites produce the Allee effect in epidemiology. Proc. R. Soc. Lond. Ser. B. 269, 271–279 (2002)CrossRef

Miao, H., Teng, Z., Abdurahman, X.: Stability and Hopf bifurcation for a five dimensional virus infection model with Beddington–DeAngelis incidence and three delays. J. Biol. Dyn. 12, 146–170 (2017)MathSciNetCrossRef

Zhu, H., Zou, X.: Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discret. Contin. Dyn. Syst. Ser. B. 12, 511–524 (2009)MathSciNetCrossRefMATH

Miao, H., Teng, Z., Kang, C., Muhammadhajia, A.: Stability analysis of a virus infection model with humoral immunity response and two time delays. Math. Methods Appl. Sci. 39, 3434–3449 (2016)MathSciNetCrossRefMATH

Li, M.Y., Shu, H.: Global dynamics of an in-host viral model with intracellular delay. Bull. Math. Biol. 72, 1492–1505 (2010)MathSciNetCrossRefMATH

Ji, Y.: Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Math. Biosci. Eng. 12, 525–536 (2015)MathSciNetCrossRefMATH

Wang, K., Wang, W., Pang, H., Liu, X.: Complex dynamic behavior in a viral model with delayed immune response. Physica D 226, 197–208 (2007)MathSciNetCrossRefMATH

10.

Wang, X., Elaiw, A., Song, X.: Global properties of a delayed HIV infection model with CTL immune response. Appl. Math. 218, 9405–9414 (2012)MathSciNetMATH

11.

Zhu, H., Luo, Y., Chen, M.: Stability and Hopf bifurcation of a HIV infection model with CTL-response delay. Appl. Math. 62, 3091–3102 (2011)MathSciNetMATH

12.

Pawelek, K.A., Liu, S., Pahlevani, F., Rong, L.: A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data. Math. Biosci. 235, 98–109 (2012)MathSciNetCrossRefMATH

13.

Li, D., Ma, W.: Asymptotic properties of an HIV-1 infection model with time delay. J. Math. Anal. Appl. 335, 683–691 (2007)MathSciNetCrossRefMATH

14.

Song, X., Neumann, A.: Global stability and periodic solution of the viral dynamics. J. Math. Anal. Appl. 329, 281–297 (2007)MathSciNetCrossRefMATH

15.

Wang, T., Hu, Z., Liao, F.: Stability and Hopf bifurcation for a virus infection model with delayed humoral immunity response. J. Math. Anal. Appl. 411, 63–74 (2014)MathSciNetCrossRefMATH

16.

Miao, H., Abdurahman, X., Teng, Z., Kang, C.: Global dynamics of a fractional order HIV model with both virus-to-cell and cell-to-cell transmissions and therapy effect. IAENG Int. J. Appl. Math. 47, 1–11 (2017)MathSciNet

17.

Lv, C., Huang, L., Yuan, Z.: Global stability for an HIV-1 infection model with Beddington–DeAngelis incidence rate and CTL immune response. Commun. Nonlinear Sci. Numer. Simul. 19, 121–127 (2014)MathSciNetCrossRefMATH

18.

Beddington, J.R.: Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44, 331–340 (1975)CrossRef

19.

DeAngelis, D.L., Goldstein, R.A., O’Neill, R.V.: A model for trophic interaction. Ecology 56, 881–892 (1975)CrossRef

20.

Hale, J.K., Lunel, S.: Introduction to Functional Differential Equations. Springer, New York (1993)CrossRefMATH

21.

Huang, G., Ma, W., Takeuchi, Y.: Global properties for virus dynamics model with Beddington–DeAngelis function response. Appl. Math. Lett. 22, 1690–1693 (2009)MathSciNetCrossRefMATH

22.

Huang, G., Ma, W., Takeuchi, Y.: Global analysis for delay virus dynamics model with Beddington–DeAngelis function response. Appl. Math. Lett. 24, 1199–1203 (2011)MathSciNetCrossRefMATH

23.

Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, San Diego (1993)MATH

24.

Li, X., Wang, J.: On the zero of a fourth degree exponential polynomial with applications to a neural network model with delays. Chaos Solit. Frac. 26, 519–526 (2005)MathSciNetCrossRef

25.

Yan, X., Li, W.: Stability and bifurcation in a simplified four-neural BAM network with multiple delays. Discret. Dyn. Nat. Soc. 2006, 1–29 (2006)MATH

26.

Korobeinikov, A.: Global asymptotic properties of virus dynamics models with dose-dependent parasite reproduction and virulence, and nonlinear incidence rate. Math. Med. Biol. 26, 225–239 (2009)CrossRefMATH

27.

Huang, G., Takeuchi, Y., Ma, W.: Lyapunov functionals for delay differential equations model of viral infection. SIAM J. Appl. Math. 70, 2693–2708 (2010)MathSciNetCrossRefMATH

Titel: Stability and Hopf bifurcation analysis for an HIV infection model with Beddington–DeAngelis incidence and two delays
verfasst von: Hui Miao
Chengjun Kang
Publikationsdatum: 16.08.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2019
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-018-1213-9

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