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Huang, Gang; Ma, Wanbiao; Takeuchi, Yasuhiro

Global properties for virus dynamics model with Beddington-DeAngelis functional response. (English) Zbl 1178.37125

Appl. Math. Lett. 22, No. 11, 1690-1693 (2009).
The paper investigates the global stability of a three dimensional virus dynamics model with Beddington-DeAngelis infection rate. By constructing a Lyapunov functional for the system of equations, it is shown that the uninfected steady state is globally asymptotically stable if the reproductive ratio of the virus less than or equal to one, and the infected steady state is globally asymptotically stable for a reproductive ratio larger than one.
Reviewer: Iulian Stoleriu (Iaşi)

Cited in 99 Documents

MSC:

37N25 Dynamical systems in biology
92D30 Epidemiology

Keywords:

virus dynamics; global stability; Lyapunov function
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\textit{G. Huang} et al., Appl. Math. Lett. 22, No. 11, 1690--1693 (2009; Zbl 1178.37125)
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References:

[1] Anderson, R.M.; May, R.M., The population dynamics of microparasites and their invertebrate hosts, Phil. trans. roy. soc. B, 291, 451-524, (1981)
[2] Nowak, M.A.; Bangham, C.R.M., Population dynamics of immune responses to persistent virus, Science, 272, 74-79, (1996)
[3] Beddington, J.R., Mutual interference between parasites or predators and its effect on searching efficiency, J. animal ecol., 44, 331-340, (1975)
[4] DeAngelis, D.L.; Goldstein, R.A.; O’Neill, R.V., A model for trophic interaction, Ecology, 56, 881-892, (1975)
[5] Li, D.; Ma, W., Asymptotic properties of an HIV-1 infection model with time delay, J. math. anal. appl., 335, 683-691, (2007) · Zbl 1130.34052
[6] Song, X.; Neumann, A., Global stability and periodic solution of the viral dynamics, J. math. anal. appl., 329, 281-297, (2007) · Zbl 1105.92011
[7] B. Hou, W. Ma, Stability analysis of an HIV-1 infection model with Beddington-DeAngelis functional response, Math. Practice Theory (in press)
[8] Korobeinikov, A., Global properties of basic virus dynamics models, Bull. math. biol., 66, 879-883, (2004) · Zbl 1334.92409
[9] Korobeinikov, A., Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. math. biol., 68, 615-626, (2006) · Zbl 1334.92410
[10] Korobeinikov, A., Global properties of infectious disease models with nonlinear incidence, Bull. math. biol., 69, 1871-1886, (2007) · Zbl 1298.92101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.