In this paper, the dynamical behaviors for a five-dimensional virus infection model with diffusion and two delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and a general incidence function are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization methods, the threshold conditions on the global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and antibody and CTL responses, respectively, are established if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion, intracellular delay and production delay are obtained by the numerical simulations.
Virus infection model Delay Adaptive immune response Diffusion General incidence function Global stability
Mathematics Subject Classification
34D40 35Q92 92B05
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This work was supported by the Natural Science Foundation of Shanxi University of Finance and Economics (Starting Fund for the Shanxi University of Finance and Economics doctoral graduates research, Grant No. Z18116), the National Natural Science Foundation of China (Grant nos. 11771373 and 11661076), the Natural Science Foundation of Xinjiang (Grant no. 2016D03022) and the Doctorial Subjects Foundation of the Ministry of Education of China (Grant no. 2013651110001).
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