Mathematical Modeling of Tumors Growth: Competition based on Gompertz model in Two Dimensions

Abstract

This article studies the competition between cancer cells within the human body depending on Gompertz’s growth. This model depends on two types of cancer cells, which grow to a certain extent, termed the carrying capacity. The carrying capacity is taken into account and defined as the number of cancer cells in which a certain density of cells eventually reaches stability. When this happens, the growth rate fluctuates, either it goes a little above or a little below the carrying capacity. This paper will cover the mathematical modeling aspects of Gompertz growth and a means to determine how competition creates growth and whether it leads to stability or instability. The paper includes growth equations that show two competing species which lead to extinction, coexistence or the emergence of one species superior to the other.