Stochastic dynamics of a targeted chemotherapy-cancer model

Abstract

This study aims to provide a stochastic mathematical model of the growth of cancerous tumors with targeted chemotherapy, where the cells were divided into three types of normal cells, cancer cells and responsive cells. The stability and long-terms behavior of the given system was studied. It has been shown, under certain conditions, that the tumor-free equilibrium state is almost globally stable. Accordingly, we conclude that the prescribed therapy can terminate cancer cells and thus the value of the tumor growth rate is obtained. What was also concluded during the study is that if the tumor is small, targeted chemotherapy drugs can be used in a smaller amount to eliminate the tumor from the body with less damage to other healthy cells. And vice versa. Finally, in order to verify our results, we conducted a numerical simulation.