A piecewise model of virus-immune system with effector cell-guided therapy

To assess the effectiveness of structured treatment interruptions (STIs) for treating HIV patients, recent clinical studies have investigated the plasma HIV RNA and CD4 T cell-guided therapies. Here, we consider a piecewise model with a particular focus on the effector cell-guided therapy. We prove that there always exist two sliding segments, and under certain conditions two pseudo-equilibria can occur simultaneously. We also examine the global dynamics of the model by using the theory of sliding dynamics. Compared with our previous work on the system with HIV RNA-guided therapy, we show that the model for effector cell-guided therapy captures much more complex dynamics, including the coexistence of multiple attractors and infinitely many possible topological structures of the attractors. Our analysis show that with appropriate use of the effector cell-guided therapy, we can enlarge the controllable region substantially in a variety of ways for different attractors. We also note that the virus load may grow to infinity for certain initial conditions (which are patient dependent). Therefore, an optimal control strategy for the effector cell-guided therapy should be personalized, by taken into account individual patient data.