A study on fractional tumor immune interaction model by the semi-analytic and numerical approach

Abstract

This work investigates a fractional-order tumor–immune interaction model formulated using the Caputo fractional derivative. Due to the presence of memory and hereditary effects in biological systems, the fractional framework provides a more realistic description of tumor–immune dynamics. The semi-analytical method namely the fractional multi-step differential transform method (FMs-DTM) and the Newton polynomial interpolation based numerical method (NPM) are employed to obtain approximate solutions of the proposed model. A comparative study is carried out to validate the accuracy and reliability of both methods for different fractional orders. Furthermore, the influence of key biological parameters, vaccination strategy, and fractional order on tumor and immune cell populations is analyzed to gain deeper biological insight. Numerical simulations demonstrate close agreement between the proposed methods and existing numerical schemes.