Modeling cancer growth and its treatment by means of statistical mechanics entropy

In this paper, we have modeled cancer growth and its treatment based on nonextensive entropies. To this end, five nonextensive entropies are employed to model the cancer growth. The used entropies are Tsallis, Renyi, Landsberg-Vedral, Abe and Escort. First, we have proposed the growth of cancer tumor as a function of time for all the entropies with different nonextensive parameter q. When the time passes, the entropies show a bounded growth for cancer tumor size. The speed of tumor size growth is different for all the entropies. The Tsallis and Escort ones have highest and lowest speed, respectively. For q > 1, the Escort entropy cannot predict a bounded growth for cancer tumor size. Then, we have investigated the cancer tumor treatment by adding a cell-kill function to the evolution equation. For q < 1, a constant cell-kill function is unable to reduce the cancer tumor size to zero for all the entropies. But, for q > 1, a cell-kill term is a suitable case. According to the results, it is found that the nonextensive parameter q, type of entropy, and cell-kill function are important factors for modeling the cancer growth and its treatment.