CELL DIVISION DYNAMICS WITH APPLICATIONS TO TUMOR GROWTH

Yuri Kozitsky

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.