Localized training structures in a hepatitis model with both diffusive and therapeutic effects

We investigated delocalized nonlinear excitations and formations in the hepatitis model. We focused our study on the formation, propagation of localized diffusive patterns as well as the treatment of hepatitis. For this, the Novak model was extended by taking into account both treatment and spatial diffusion. Using the multiple scale expansion method, we show that, the extended Nowak model can be reduced to a two dimensional modified complex Ginzburg–Landau equation (mCGLE). Through the linear analysis, one can predict the birth of multi-localized formation structures. One remark is that the decrease in excitation modes with the increase in treatment parameters, which justifies the fact that the treatment used here aims to suppress or reduce the domains where viral cells are localized. Studying the effect of this parameter on the governing equation allowed us to reduce the areas of turbulence or instabilities and therefore identify areas of hepatitis prevalence. The analytical solution is plotted and we observed the transition of viral hepatitis states with an increase in the treatment parameter \(k_u\) $k_u$ . The analytical results proved to be consistent with the numerical results. Finally, we demonstrated that the associated diffusion and treatment effects could also lead to the development of new preventive and therapeutic strategies, either to reduce or eradicate the proliferation of hepatic cells in the human body.