Received: November 08, 2018; Published: November 15, 2018
*Corresponding author: E Ahmed, Department of Mathematics, Faculty of Science, Egypt
Recently new type of cancer cells has been observed. It is called Hybrid cells. A simple mathematical model is proposed to describe them. It implies that they will be near the tumor surface or circulating. Some comments about the possibility of their reaching brain are given.
Recently [1,2,3,4] hybrid tumor cells have been discovered. They have the following properties:
a) They circulate more than ordinary tumor cells.
b) They have greater ability to migrate and invade other tumors.
c) They have greater ability to form metastases.
Motivated by this the following simple model is presented:
Let N1, N2 be the ordinary and hybrid tumor cells respectively. Let N=N1+N2 hence the tumor growth can be represented by
The equilibrium solution for the coexistence of both types is:
It is unstable.
The single species solution is
And it is stable if r1>2/3.
Hence the following conclusion is reached: If r2 > r1 > 2 / 3 then most tumors consist of ordinary (non-hybrid) cells. Hybrid cells exist near tumor surface OR circulate.
Since hybrid cells have a greater ability to invade other cells, it is expected that they will invade brain cells. Hence brain diseases can be a good source for identifying them. Moreover, trying to attract them to less important sites can be a feasible strategy to deal with them. It will be difficult to test this idea experimentally, because the hybrid state will not be stable.
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