Dissipative control for an epidemic system with exponential incidence rate

In this paper, the bifurcation and chaos dissipative control for a class of epidemic system with exponential incidence rate. Firstly, the dynamic behavior analysis of epidemic system is provided in detail. The bifurcation and chaos characters of the system with parameter variations is verified through numerical simulations. Furthermore, a effective T-S fuzzy model for infectious disease is adopted, and the control problem of nonlinearity system is transformed into the control problem of the linear system. Linear matrix inequalities (LMIs) technique is used to design the dissipation controller to simplify the solve process. The proposed dissipative controller approaches successfully eliminate the bifurcation and chaos appeared in the system. The effectiveness is verified by some numerical simulation results.