ACTA UNIVERSITATIS APULENSIS Special Issue GLOBAL PROPERTIES FOR A VIRUS PROPAGATION MODEL WITH STAGED PROGRESSION

We consider the global dynamics of a virus propagation model in which infective cells pass through several successive stages, assuming that the incidence of infection and the removal rate of the virus are nonlinear functions given in an abstract, unspecified form. Suitable Lyapunov functionals are constructed to establish the existence of a threshold parameter, the basic reproduction number R0 of the system. It is shown that if R0 > 1, then the disease-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable (the disease remains endemic, that is), while if R0 ≤ 1 then there is no endemic equilibrium and the disease-free equilibrium is globally asymptotically stable (the disease dies out, that is). 2000 Mathematics Subject Classification: 92D30, 34D20.