On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth - Urszula Ledzewicz; Omeiza Olumoye; Heinz Schättler (Mathematical Biosciences and Engineering)
In this paper, a mathematical model for chemotherapy that takestumor immune-system interactions into account is considered for astrongly targeted agent. We use a classical model originallyformulated by Stepanova, but replace exponential tumor growth with ageneralised logistic growth model function depending on a parameter$ν$. This growth function interpolates between a Gompertzian model(in the limit $ν→0$) and an exponential model (in thelimit $ν→∞$). The dynamics is multi-stable andequilibria and their stability will be investigated depending on theparameter $ν$. Except for small values of $ν$, the system hasboth an asymptotically stable microscopic (benign) equilibrium pointand an asymptotically stable macroscopic (malignant) equilibriumpoint. The corresponding regions of attraction are separated by thestable manifold of a saddle. The optimal control problem of movingan initial condition that lies in the malignant region into thebenign region is formulated and the structure of optimal singularcontrols is determined.