Adaptive Sliding Mode Control for Cholera Epidemic Model

Cholera is an acute diarrhoeal infection caused by bacteria Vibrio cholerae. The SIQRB (Susceptible-Infected-Quarantined-Recovered-Bacteria) epidemic model with a control function is studied to analyze the dynamics of cholera. The control function represents the fraction of infected individuals that are submitted to treatment in quarantine until complete recovery. One of the drawbacks of mathematical modeling is the presence of parametric uncertainties Designing a control strategy used in accommodating these uncertainty factors drives the development of robust control. In this case, the sliding mode control is applied to handle parametric uncertainties The sliding mode control objective is reducing the number of infected individuals to zero through the desired tracking scheme of a reference function. The Lyapunov stability theorem and Barbalat's lemma are used to examine the success of the tracking scheme. Lack of apriori knowledge related to the boundedness of the parametric uncertainties is settled using an adaptive method by updating the switching gain of sliding mode control so that the strategy is called the adaptive sliding mode control. Chattering problem that often appears in the application of sliding mode control can be reduced. Numerical simulations show that the adaptive sliding mode control satisfies the controller objectives and able to handle parametric uncertainties Copyright (C) 2020 The Authors.