This paper proposed a Filippov blood glucose insulin model with threshold control strategy and studied its dynamic properties. Using Filippov's convex method, we proved the global stability of its two subsystems, the existence and conditions of the sliding region of the system were also given, and different types of equilibrium states of the system were also addressed. The existence and stability of pseudo equilibrium points were thoroughly discussed. Through numerical simulations, we have demonstrated that it is possible to effectively control blood sugar concentrations to achieve more cost-effective treatment levels by selecting an appropriate threshold range for insulin injection.
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