Numerical simulation of a nonlinear hepatitis B virus mathematical model using the Dickson collocation technique

Abstract

Abstract This work introduces an innovative nonlinear model of hepatitis B virus (HBV) dynamics, emphasizing the utilization of the Dickson collocation method for numerical simulation. Our method, in contrast to conventional techniques, adeptly tackles the complex interactions between the virus and the host’s immune response using a system of ordinary differential equations (ODEs). We present a transformation of the ordinary differential equations into a nonlinear system of algebraic equations, facilitating the determination of unknown coefficients in a truncated Dickson polynomial series. The novel implementation of the Newton algorithm for addressing this nonlinear system improves computing efficiency and convergence rate. Our findings indicate that the Dickson collocation method provides highly precise approximations and surpasses traditional artificial neural network models regarding convergence rate and computational efficiency. This study highlights the Dickson collocation approach as an effective instrument for simulating intricate biological systems, offering valuable insights into HBV dynamics and laying the groundwork for future research.