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Global dynamics of a cell mediated immunity in viral infection models with distributed delays. (English) Zbl 1221.34225
The author extends the work of M. A. Nowak and C. R. M. Bangham [Science 272, No. 5258, 74–79 (1996), doi:10.1126/science.272.5258.74] taking into account two distributed time delays expressing the infection-time of a cell and the replication-time of the virus. They formulate the viral-immune interaction in vivo, and perform a linear stability analysis of the uninfected equilibrium and the infected equilibrium. Then, motivated by [C. C. McCluskey, Nonlinear Anal., Real World Appl. 11, No. 1, 55–59 (2010; Zbl 1185.37209)], several Lyapunov functionals are constructed to prove the global stability of the equilibria with or without the immune response. Furthermore, they improve the stability results of H. Zhu and X. Zou [Discrete Contin. Dyn. Syst., Ser. B 12, No. 2, 511–524 (2009; Zbl 1169.92033)].
MSC:
34K60Qualitative investigation and simulation of models
92D30Epidemiology
92C60Medical epidemiology
34K20Stability theory of functional-differential equations
References:
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