Tumour–host dynamics under radiotherapy

Tumour–host interaction is modelled by the Lotka–Volterra equations. Qualitative analysis and simulations show that this model reproduces all known states of development for tumours. Radiotherapy effect is introduced into the model by means of the linear-quadratic model and the periodic Dirac delta function. The evolution of the system under the action of radiotherapy is simulated and parameter space is obtained, from which certain threshold of effectiveness values for the frequency and applied doses are derived. A two-dimensional logistic map is derived from the modified Lotka–Volterra model and used to simulate the effectiveness of radiotherapy in different regimens of tumour development. The results show the possibility of achieving a successful treatment in each individual case by employing the correct therapeutic strategy.

Highlight
► Tumour–host interaction is modelled by Lotka–Volterra equations.
► A brief review of the motion integral and analysis of linear stability is presented.
► Radiotherapy is introduced into the model, using a periodic Dirac delta function.
► A two-dimensional logistic map is derived from the modified Lotka–Volterra model.
► It is shown that tumour can be controlled by a correct selection of therapy strategy.