Sliding Dynamics and Bifurcations of a Filippov System with Nonlinear Threshold Control

Considering the effectiveness of introducing the change rate of viral loads into the threshold setting policy for triggering interventions, we propose an immune-virus Filippov system with a nonlinear threshold. By developing new analytical and numerical methods, we systematically studied the rich dynamical behaviors and bifurcations of the proposed system, including the existence of three sliding segments and three pseudo-equilibria, boundary-center bifurcation, boundary-saddle bifurcation, pseudo-saddle-node bifurcation and tangency bifurcation. We further showed that the proposed system can exhibit virous structures in the coexistence of multiple steady states. Phenomena include bistability of two pseudo-equilibria, tristability and multiplestability of two pseudo-equilibria with regular equilibria or touching cycles. The modeling methods, as well as the analytical and numerical methods, can be widely applied to many other fields.