Lyapunov functionals for virus-immune models with infinite delay

We present a systematic method to construct Lyapunov functionals of delay differential equation models of infectious diseases in vivo. For generality we construct Lyapunov functionals of models with infinitely distributed delay. We begin with simpler models without delay and construct Lyapunov functionals for the complex models progressively. We construct those functionals using our result obtained previously instead of constructing each functional independently. Additionally we discuss some problems that arise from the mathematical requirements caused by the infinitely distributed delay.