Qualitative Analysis of a Piecewise Immunosuppressive Infection Model With Nonlinear Threshold Policy Control

ABSTRACT This paper examines a class of Filippov immunosuppressive infection models with nonlinear threshold functions to describe control strategies that are activated when viral suppression leads to the number of newly inactivated immune cells surpassing a specific threshold. It also discusses how sliding mode control and multi‐stability can be utilized to modulate the therapeutic effect. The existence conditions for sliding segments, sliding dynamics, and several types of equilibria are derived, and theoretical and numerical analyses are performed on local bifurcations such as boundary‐node bifurcation, boundary‐focus bifurcation, boundary‐saddle bifurcation, and boundary‐saddle‐node bifurcation. Findings suggest that the introduced model could exhibit multiple sliding segments, a situation linked to the nonlinear threshold function. Numerical global behavior analysis indicates that if the threshold for new inactivated immune cells is set excessively high or low, the threshold control strategy loses its effectiveness, potentially leading to an unbounded increase in viral load. Consequently, it is crucial to select an appropriate threshold level so that the number of newly inactivated immune cells is minimized or the fluctuation range is reduced, approaching the ideal attractor. Our exploration will provide evidence for treatments for AIDS and other diseases.