The stability analysis of a general viral infection model with distributed delays and multi-staged infected progression

• We investigate general delayed virus dynamical model with multi-staged infection.
• We establish the global threshold dynamics based on the basic reproductive number.
• Dynamics of many types of viruses are described.

We investigate an in-host model with general incidence and removal rate, as well as distributed delays in virus infections and in productions. By employing Lyapunov functionals and LaSalle’s invariance principle, we define and prove the basic reproductive number R0R0 as a threshold quantity for stability of equilibria. It is shown that if R0>1R0>1, then the infected equilibrium is globally asymptotically stable, while if R0⩽1R0⩽1, then the infection free equilibrium is globally asymptotically stable under some reasonable assumptions. Moreover, n+1n+1 distributed delays describe (i) the time between viral entry and the transcription of viral RNA, (ii) the n-1n-1-stage time needed for activated infected cells between viral RNA transcription and viral release, and (iii) the time necessary for the newly produced viruses to be infectious (maturation), respectively. The model can describe the viral infection dynamics of many viruses such as HIV-1, HCV and HBV.