Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment

We investigate a new mathematical model that describes lung cancer regression in patients treated by chemotherapy and radiotherapy. The model is composed of nonlinear integro-differential equations derived from the so-called kinetic theory for active particles and a new sink function is investigated according to clinical data from carcinoma planoepitheliale. The model equations are solved numerically and the data are utilized in order to find their unknown parameters. The results of the numerical experiments show a good correlation between the predicted and clinical data and illustrate that the mathematical model has potential to describe lung cancer regression.

► We investigate cases of patients who developed lung cancer and underwent cancer treatment.
► We apply a mathematical model derived from the so-called kinetic theory for active particles.
► Clinical data from carcinoma planoepitheliale are utilized to find unknown parameters of the model.
► Numerical results show a good correlation between the clinical and predicted data.
► The results illustrate that the mathematical model has a potential to describe lung cancer growth.