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

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.