Dynamical modeling and analysis of delayed paradoxical feedback loops in immune responses

Paradoxical feedback is prevalent in immune cell circuits, where the same factors can simultaneously activate and suppress immune responses. This study develops a mathematical model to investigate bistability and oscillations regulated by delayed paradoxical feedback in antiviral immune responses. Our analysis identifies five distinct infection outcomes-uninfected, low infection, moderate infection, severe infection, and recurrent infection-each with specific stability criteria. We demonstrate a state transition between low and severe infection states, driven by two mechanisms: initial infection dose and viral incubation period. Furthermore, we show that prolonged viral incubation induces Hopf bifurcation in the low-infection steady state, leading to periodic oscillations. These oscillations can be mitigated by enhancing NK cell-mediated antiviral responses. Our findings provide a theoretical framework for understanding the nonlinear dynamics in immune-viral interactions and suggest that targeted modulation of NK cell function may offer therapeutic strategies for infection control.