Nonlinear robust adaptive sliding mode control of influenza epidemic in the presence of uncertainty

Abstract

In this paper, a nonlinear robust adaptive sliding mode control strategy is presented for the influenza epidemics in the presence of model uncertainties. The nonlinear epidemiological model of influenza with five state variables (the numbers of susceptible, exposed, infected, asymptomatic and recovered individuals) and two control inputs (vaccination and antiviral treatment) is considered. The objective of the proposed controller is decreasing the number of susceptible and infected humans to zero by tracking the desired scenarios. As a result of this decreasing, the number of exposed and asymptomatic individuals is also decreased and converged to the zero. Accordingly, it is shown that the number of recovered humans is increased to its maximum steady state value. The stability and tracking convergence of the control system are proved via the Lyapunov stability theorem. For the first time, a robust controller is designed and investigated for the uncertain process of influenza treatment in a population. Through a comprehensive evaluation, the effects of treatment period and the uncertainty amount on the performance of the controlled system are studied. According to the results, the nonlinear sliding mode controller guarantees the robust performance against a wide range of parametric uncertainties. Moreover, it is shown that much less rates of vaccination and antiviral treatment are required as the treatment interval is increased.