Robust static output-feedback vaccination policy design for an uncertain SIR epidemic model with disturbances: Positive Takagi–Sugeno model approach

Abstract

An analytic vaccination policy is established for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances by using only the inaccurate information of the infected through the positive Takagi–Sugeno (T–S) fuzzy approach. The SIR model is exactly represented as the fuzzy model in the T–S form. Two conditions for fuzzy static output-feedback controllers are formulated using the symmetric and diagonal Lyapunov matrices. These controllers exhibit L∞–L∞ disturbance attenuation performance, are robust against norm-bounded parametric uncertainties, and preserve closed-loop positivity. The case study for the positive stabilization of the uncertain nonlinear SIR model demonstrates the effectiveness of the proposed methodology.