Hybrid cancer cells have been recently discovered. They have greater ability to form metastasis. Here a simple mathematical
model is given for this phenomenon. Some comments about the possibility of their reaching brain are given.
Metastasis comprises a sequence of linked steps leading to the
dissemination of cancer cells from a primary tumor to other distant
tissues the overwhelming majority of cancer-related deaths still
result from the progressive growth of metastasis that are resistant
to conventional therapies [1,2].
Motivated by this the following model is presented for the
metastasis of hybrid cancer cells:
Let T1, H1 be the ordinary and hybrid tumor cells respectively
of the first tumor. Let N=T1+H1. The second tumor is assumed
to contain ordinary tumor cells T2. Hence the model can be
where a1,b1,b2,c2 are positive constants. The metastasis term
The reason for the power 2/3 is that ordinary tumor cells grow
due to surface cells [3,4].
The equilibrium solution for the coexistence of both tumors is:
T1eq= [b1(a1-1-c2)/(a1-c2)]^3 (2)
It is locally asymptotically stable if:
Since hybrid cells have a greater ability to invade other cells, it
is expected that they will invade brain cells. Hence brain tumors 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 may be difficult to test this idea experimentally, because the
hybrid state, in general, is unstable .