Modeling and control for a descriptor epidemic system with nonlinear incidence rates

This paper is concerned the bifurcation and chaos robust control of a descriptor epidemic system with nonlinear incidence rate based on T-S fuzzy model. To do this, the dynamic behavior of the epidemic system is analyzed by numerical simulation, the parameter variations leading to the bifurcation behavior and chaos of the epidemic system is verified by Lyapunov exponent. In order ameliorate the exiting results, a T-S fuzzy model is adopted to describe the infectious disease, under this way the solution to control problem of nonlinear system is changed into solution to the control problem of the linear system. Then a controller for this T-S fuzzy system 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.