Integral manifolds for impulsive HCV conformable neural network models

Abstract

ABSTRACTIn this paper, we offer a new modelling approach for hepatitis C virus (HCV) infection models with cytotoxic T lymphocytes (CTL) immune responses. The standard neural network models with reaction-diffusion terms are generalized to the discontinuous case considering impulsive controllers. Also, the conformable approach is proposed as a more adjustable modelling apparatus which overcomes existing difficulties in the application of the fractional-order modelling technique. In addition, the existence of integral manifolds for the proposed model is investigated and efficient criteria are established. Since stability and control of a neural network model are essential for its proper application, stability results for the constructed integral manifold are presented. These results extend and generalize the stability results for steady states of proposed HCV models with CTL immune responses and contribute to the development of new innovative modelling approaches in biology. The qualitative analysis is performed via the conformable Lyapunov function method. The established results are demonstrated through an example.

Keywords

• Neural network models in biology
• HCV
• CTL immune responses
• conformable derivatives
• impulses
• integral manifolds