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Zbl 1221.34225
Nakata, Yukihiko
Global dynamics of a cell mediated immunity in viral infection models with distributed delays. (English)
[J] J. Math. Anal. Appl. 375, No. 1, 14-27 (2011). ISSN 0022-247X

The author extends the work of {\it M. A. Nowak} and {\it 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 [{\it 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 {\it H. Zhu} and {\it X. Zou} [Discrete Contin. Dyn. Syst., Ser. B 12, No.~2, 511--524 (2009; Zbl 1169.92033)].
[Zhonghua Zhang (Xi'an)]

MSC 2000:: *34K60 Applications of functional-differential equations
92D30 Epidemiology
92C60 Medical epidemiology
34K20 Stability theory of functional-differential equations

Keywords: viral infection; global asymptotic stability; Lyapunov functional; immune response

Citations: Zbl 1185.37209; Zbl 1169.92033

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