A mathematical exploration of HBV infection using fractional derivatives and the homotopy decomposition method

This study employs the homotopy decomposition method (HDM), a novel and an efficient approach for solving fractional order differential equations, to analyze the hepatitis B virus (HBV) infection model. Unlike traditional methods, HDM avoids the need for linearization or discretization, thus reducing computational complexity while maintaining accuracy. This makes it particularly suitable for studying complex biological systems that exhibit time dependent or delayed responses, such as the immune response to HBV. The clinical implications of this research are significant: early treatment predictions derived from the fractional order model demonstrate the potential to mitigate the peak of viral spread and preserve cellular integrity. This insight underscores the model’s utility in optimizing treatment timing, ultimately contributing to reduced disease burden and improved patient outcomes in managing acute and chronic HBV infections. Despite without an explicit memory kernel, the Gohar derivative’s logarithmic scaling effectively reflects biological dynamics that are slow and non instantaneous.