Abdelazeem Abdelkreem Seneen Abo2017-11-012017-11-012017http://hdl.handle.net/123456789/7014Thesis Presented as a Partial Fulfillment for MASTER OF SCIENCE IN MATHEMATICS in the Department of Mathematics & Applied Mathematics ALNEELAIN UNIVERSITYAbstract In this thesis we presented a quasispecies mathematical model for two com- peting cell populations. We toke into account the dynamics of heterogeneous tumor cell populations competing with healthy cells. We analyze a mathemat- ical model of unstable tumor progression using the quasispecies framework to define a minimal model incorporating the dynamics of competition between healthy cells and a heterogeneous population of cancer cell phenotypes involv- ing changes in replication-related genes.MATHEMATICS