The basic reaction–diffusion model is extended to study liver metastasis disease with applied drug therapy by the term which describes the interaction between the tumor and normal cells. The drug therapy is taken as a function of tumor shape as well as time duration. The model is solved using an analytical eigenvalue approach. The results obtained from the model are presented graphically for different case studies to show the response of tumor decay and growth respectively in the presence and absence of the drug therapy. Finally, the model outcome and their simulations are compared with the known clinical results to prove the feasibility and efficacy of the proposed model.