Nonlinear Robust Adaptive Sliding Mode Control Strategy for Innate Immune Response to Influenza Virus

Abstract

This paper aims to design a nonlinear robust adaptive sliding mode control strategy for a mathematical model describing the innate immune response to influenza virus infection. This model possesses seven state variables (respiratory tract epithelial cells in four possible states, namely: healthy, partially infected, infected, and resistant-to-infection, and interferon (IFN) molecules, natural killers, and viruses). This model is based on resistance-to-infection derived from IFN molecules and the removal of infected cells by natural killers. Two control strategies (vaccination and antiviral treatment) are introduced to eradicate the infection. First, a vaccination strategy is applied to convert healthy cells into resistant-to-infection ones inside the body of the susceptible individual. Second, the infected individual undergoes an antiviral treatment strategy that fights against the spread of the concentration of viruses and converts the healthy cells into resistant-to-infection ones simultaneously. The Lyapunov stability theorem is employed to analyse the stability of the desired strategies. Finally, the simulation results show that the goal is fulfilled satisfactorily.

KEYWORDS:

• Adaptive sliding mode control
• Influenza virus
• Innate immune response
• Stability analysis
• Vaccination
• Antiviral treatment

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

A. Ibeas is partially supported by the Spanish Ministry of Economy and Competitiveness (MINECO) through grant DPI2016-77271-R and by the University of the Basque Country (UPV/EHU) through grant PPG17/33.

Notes on contributors

Z. Abbasi

Zohreh Abbasi is currently a PhD student in control and dynamical systems at the University of Waterloo, Waterloo, Canada. Her research interests include epidemiological modelling, control theory, applied mathematics, multi-agent systems, and hybrid dynamical systems. Email: [email protected]

I. Zamani

Iman Zamani received PhD degree in control engineering from the Amirkabir University of Technology, Iran, in 2013. Currently, he is an assistant professor of electrical engineering at Shahed University, Iran. His research interests include hybrid systems, biological systems, nonlinear system, and fuzzy systems.

S. H. Nosrati

Shahram Nosrati received BSc degree in electrical engineering from KNT University of Technology, Tehran, Iran, in 2000, and his MSc and PhD degrees in control engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran, in 2003 and 2010, respectively. He is currently an assistant professor in the Department of Electrical and Computer Engineering at the Qom University of Technology, Qom, Iran. His research interests include robotics and automation, distributed control, cooperative control and optimisation of networked multi-agent systems, and synthesis of collective behaviours. Email: [email protected]

A. H. Amiri Mehra

Amir Hossein Amiri Mehra received the BSc degree in electrical control engineering from Qom University of Technology, Qom, Iran, in 2015, his MSc degree in control engineering from Shahed University, Tehran, Iran, in 2018, and PhD degree in control engineering from University of Kashan, Kashan, Iran, in 2022. His research interests include epidemiological modelling, control theory, multi-agent systems, and hybrid systems. Email: [email protected]

M. Shafieirad

Mohsen Shafieirad received a BSc degree in control engineering from Isfahan University of Technology, Iran in 2005. Also, He received MSc and PhD degrees in control engineering from Amirkabir University of Technology, Iran in 2007 and 2013, respectively. He is currently an assistant professor of control engineering at the University of Kashan, Iran. M.Shafieirad overall research output has culminated in more than 40 publications. His research interest includes multi-agent systems, biological systems, system identification, ad-hoc/sensor networks, and multi-dimensional systems. Email: [email protected]

A. Ibeas

Asier Ibeas was born in Bilbao, Spain, in 1977. He received his MSc in applied physics and his PhD in automatic control from the University of the Basque Country, Spain, in 2000 and 2006, respectively. He is currently an associate professor of control engineering at the Autonomous University of Barcelona, Spain. His research interests include time-delayed systems, robust adaptive control, biological systems, and applications of artificial intelligence to control systems design. Email: [email protected]