Observer-based adaptive PI sliding mode control of developed uncertain SEIAR influenza epidemic model considering dynamic population

• Published in: Journal of theoretical biology 2019-12, Vol.482, p.109984-109984, Article 109984
• Main Authors: Mehra, Amir Hossein Amiri, Zamani, Iman, Abbasi, Zohreh, Ibeas, Asier
• Format: Article
• Language: English
• Subjects: Adaptive PI sliding mode; Dynamic population; Lyapunov stability; Observer-based control; SEIAR model
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2019.08.015

•Giving a new model of influenza epidemic outbreak.•Analysis of the basic reproduction number and the equilibrium points.•Parallel control design consisting of vaccination and antiviral treatment strategy.•Nonlinear adaptive PI sliding mode controller design.•Design an observer-based adaptive controller in the presence of the uncertainties. This paper presents a new Susceptible, Exposed, Infected, Asymptomatic, and Recovered individuals (SEIAR) model for influenza considering a dynamic population. In the given model, the possibility of transmission of asymptomatic individuals (infectious with no visible symptoms) to infected individuals (infectious exhibiting symptoms) is considered. The basic reproduction number and the equilibrium points of the new model are given while the stability of the equilibrium points is analyzed by using the Jacobian matrix. Then a multi-controller scheme consisting of a parallel controller defined by two control inputs (vaccination and antiviral treatment) is given where both of them are based on Proportional-Integral (PI) and sliding mode controllers, which are parameterized adaptively to guarantee the convergence of trajectories to the sliding surface with minimum amount of chattering. The proposed control scheme is able to asymptotically stabilize the SEIAR model in the sense of eradication of the infected and susceptible individuals. Moreover, a (reduced-order) observer is designed to estimate the actual state variables that are used in the implementation of the control signals. By using MATLAB® software, a comprehensive simulation and evaluation of treatment and performance are carried out to support the presented theoretical results.