T-S fuzzy modeling and control for a class of epidemic system with nonlinear incidence rates

An epidemic model with nonlinear incidence rate has complicated dynamic phenomena with time evolution. In this paper, a control strategy based on T-S fuzzy model is proposed. Firstly, the dynamic behavior of the system is analyzed by using method of numerical simulation. The bifurcation and chaos in the epidemic system are verified. Furthermore, in order to control the infectious disease effectively, the T-S fuzzy model of an epidemic system with nonlinear incidence rate is established. The control problem of nonlinear system can be converted to a control problem of the linear system. Then a H_∞, controller of the T-S fuzzy model is designed by using linear matrix inequalities (LMIs). The proposed controller approaches successfully eliminate the chaos appeared in the system. The effectiveness is verified by some numerical simulation results.