Complex dynamic behavior in a viral model with delayed immune response

The rich dynamics of a viral infection model is studied under the assumption that the immune response is retarded. It is shown that if the basic reproductive ratio of the virus is less than one, the infection-free equilibrium is globally asymptotically stable. Analytical and numerical results show that if the basic reproductive ratio of the virus is greater than one, the combined effect of the strength of the lytic component, the time delay of the immune response and the birth rate of susceptible host cells is to create a rich dynamics, which includes the occurrence of stable periodic solutions and chaotic dynamical behavior. The route from periodic oscillations to chaos is investigated. These results can be used to explain irregular real time series data on the immune state of patients.