CELL DIVISION DYNAMICS WITH APPLICATIONS TO TUMOR GROWTH
Maria Curie-Skłodowska University
Nowadays, it is well established that the initiation and progression of tumor
is related to cell division mechanisms. In particular, the initiation of tumor is
related to (driver) mutations, that may occur in the course of division.
In the model which we consider, a finite (random) collection of entities
(cells) undergoes a continuum time Markov evolution which amounts to two
events: fission and death. The state of an entity is characterized by two
variables, x and y, where positive x is time to fission
whereas y describes
a collection of relevant traits. The evolution is the drift in x towards zero
that may be interrupted by a death occurring at random with intensity m(x).
If the entity manages to stay alive until x reaches zero, it fisses to produce
two new entities with random x and y, the distribution of which depends on the
value of y of the mother entity. A detailed analysis of this evolution will be
done, and some of its therapeutic-relevant conclusions will be discussed.