Stability study of virus replication model

An HIV infection model with time delay in which uninfected cells become infected cells is analysed. We studied conditions under which steady states will be asymptotically stable. We also examined that for endemically infected equilibrium a critical value of time delay may occur. The steady state will be asymptotically stable when delay is less than a critical value. Else the uninfected cells, infected cells, free virus, and CTLs may undergo cyclic oscillations. We estimate the delay length to maintain stability. Numerical simulations are done to aid mathematical findings.