Competing species system as a qualitative model of radiation therapy

• Four species prey–predator lattice model was examined. The model is a qualitative model of radiation therapy.
• Both Monte Carlo simulations and mean field approximation were used.
• Radiotherapy shifts the tumor’s limit of starvation making it easier to extinguish by slowing the rate of metabolism.

To examine complex features of tumor dynamics we analyze a competing-species lattice model that takes into account the competition for nutrients or space as well as interaction with therapeutic factors such as drugs or radiation. Our model might be interpreted as a certain prey–predator system having three trophic layers: (i) the basal species that might be interpreted as nutrients; (ii) normal and tumor cells that consume nutrients, and (iii) therapeutic factors that might kill either nutrient, normal or tumor cells. Using a wide spectrum of parameters we examined survival of our species and tried to identify the corresponding dynamical regimes. It was found that the radiotherapy influences mainly the limit of starvation i.e. the value of an update probability where the tumor cells go extinct as a result of insufficient nutrient supply and competition with normal cells. The other limiting value of this probability, corresponding to the coexistence of the normal and tumor cells in abundance of nutrients, is almost not affected by radiotherapy. We have also found the coexistence of all species on the phase diagrams.