Optimal and adaptive control of an epidemic model of influenza with unknown parameters

This paper deals with the nonlinear dynamics‎, ‎chaos‎, ‎optimal and adaptive control of an epidemic model for H1N1 influenza with unknown parameters‎. ‎Two different control strategies are explored‎. ‎First‎, ‎we use the optimal control theory to reduce the infected individuals and the cost of vaccination‎. ‎Then‎, ‎we study the problem of optimal control of unstable steady-states of H1N1 influenza system using a nonlinear‎ ‎control approach‎. ‎Finally‎, ‎we propose the Lyapunov stability to control of the chaotic epidemic model of influenza with unknown parameters by a feedback control approach‎. ‎Matlab bvp4c and ode45 have been used for solving the autonomous chaotic systems and the extreme conditions obtained from the Pontryagin's maximum principle (PMP)‎. ‎Furthermore‎, ‎numerical simulations are included to demonstrate the effectiveness of the proposed control strategies.