Global dynamics of a cell mediated immunity in viral infection models with distributed delays (Q616687)

The author extends the work of \textit{M. A. Nowak} and \textit{C. R. M. Bangham} [Science 272, No.~5258, 74--79 (1996), \url{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 [\textit{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 \textit{H. Zhu} and \textit{X. Zou} [Discrete Contin. Dyn. Syst., Ser. B 12, No.~2, 511--524 (2009; Zbl 1169.92033)].