Robust Vaccination Strategy based on Dynamic Game for Uncertain SIR Time-Delay Model

Abstract

In this paper, a robust Pareto suboptimal strategy for an uncertain susceptible-infected-recovered (SIR) model with state delay is investigated, based on the static output feedback (SOF). After linearizing the original nonlinear SIR model, a sufficient condition for the existence of a proposed strategy set is derived in terms of high-order cross-coupled matrix equations (HCMEs). Using the guaranteed cost control technique, both robust stability and existence of the cost bound are attained. To avoid high complexity of directly solving the HCMEs, a recursive algorithm based on the linear matrix inequality (LMI) is presented. Finally, a practical SIR time-delay model is used to demonstrate the effectiveness and reliability of the proposed strategy.