Slow-fast model and therapy optimization for oncolytic treatment of tumors

Pierre Cordelier (1) , Manon Costa (2) , Jérôme Fehrenbach (2)

1 CRCT - Centre de Recherches en Cancérologie de Toulouse
2 IMT - Institut de Mathématiques de Toulouse UMR5219

The present work studies models of oncolytic virotherapy without space variable in which virus replication occurs at a faster time scale than tumor growth. We derive the asymptotic of a three-species slow-fast model and obtain a two-species dynamical system, where the variables are tumor cells and infected tumor cells. We fully characterize the behavior of this system depending on the various biological parameters. In a second part we address the modelling of virus injection and its expression in the two-species system, where the amount of virus is not explicitly a variable. We prove that the injection can be described by an instantaneous jump in the phase plane, where a certain amount of tumors cells is transformed instantly into infected tumor cells. This description allows to discuss qualitatively the timing of different injections in the frame of successive treatment strategies. This work is illustrated by numerical simulations. The timing and amount of injected virus may have counterintuitive optimal values, nevertheless the understanding is clear from the phase space analysis.

Mots clés: oncolytic therapy; slow-fast system; boundary layer; asymptotic system

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Pierre Cordelier, Manon Costa, Jérôme Fehrenbach. Slow-fast model and therapy optimization for oncolytic treatment of tumors. 2021. ⟨hal-03364097⟩